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习题练习:gc textbook chapter 8 Rotational Motion



 作者: admin   总分: 110分  得分: _____________

答题人: 匿名未登录  开始时间: 24年12月27日 14:40  切换到: 整卷模式

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1#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A bicycle odometer (which measures distance traveled) is attached near tij7g fnq ;ptedmav1rzwb637 ;6y 8g)jhe wheel hub and is designed for 27-inch wheels. What happej mpgqnda6)br ;tf 67wi81g7; v zjy3ens if you use it on a bicycle with 24-inch wheels?
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2#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Suppose a disk rotates at constant angul.*vlb7xuf t 7lar velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either *f77. btl ulxvcomponent of linear acceleration change?
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3#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Could a nonrigid body beknzzqqacy pd 48n8 ;1j)nm7ry/ 3w(id described by a single value of the angular velocity $\omega$ Explain.
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4#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Can a small force ever exert a greater torque than a laranw45 aavp+cac/w6 /fger force? Explain.
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5#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.
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6#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Why is it more difficult to docai// dd09xhak ukr58 a sit-up with your hands behind your head than when your arms are stretched out inku9 dia dxh8/k50cr/a front of you? A diagram may help you to answer this.
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7#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A 21-speed bicycle has seven sprockets at the rear wheel aiq:ofr0u .y1p5 vs)abmy6 ti* nd three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it hardbo: i6yrv)ypqm0 u5s.*f 1ta ier to pedal, a small front sprocket or a large front sprocket? Why?
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8#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Mammals that depend on being able to run fast have slender optm(c 9tx:k k/z)mm2lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain whzmx/p mo tck2( )k9mt:y this distribution of mass is advantageous.
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9#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Why do tightrope walkers (Fig v6tl:wcoz8)wao t7 lup7 h,o9. 8–35) carry a long, narrow beam?
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10#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If the net force on a system is zero, is the net torque also zk b b 5kx(spr*9.sab3zero? If the net torque on a system is zero, i.b5sbpk k3a9xsr(*z bs the net force zero?
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11#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Two inclines have the x9 4pds ej2 vk+dfl);9car7v isame height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which inclicvj;7 ) kpedrd9a4+ xilsf2v9ne will the speed of the ball at the bottom be greater? Explain.
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12#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Two solid spheres simu p.i a2ga 66ejqje l56,+bv;ti gvlol)ltaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of tltgbl. ;6vlp)a i6 +6g5jia,qv2jee ohe incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?
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13#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A sphere and a cylinder have the same radius and the same mass. They starnf4jgi xh0q(6vdw ,w9iona - 0t from rest at the top of an incline. Which reaches the bottom first? Which has the grjfxi0h0 w 9no(vd6wqgna,- 4 ieater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?
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14#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
We claim that momentum and angular momentum are conserved. Yet most m3trc65)+al6 imgjgx-cc5 fsvoving or rotatic 3sg vjx- c6)g6riflma+c5t 5ng objects eventually slow down and stop. Explain.
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15#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If there were a great migrat*kz9 ln6 gxc zzuu/c:giz(a 3(ion of people toward the Earth’s equator, how would thc9u*(gzk gnlx 3 /u (zia:c6zzis affect the length of the day?
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16#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Can the diver of Fig. 8fb njjp/j.36z–29 do a somersault without having any initial rotation when she leaveb 6f/ 3j.jzjpns the board?
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17#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
The moment of inertia of a rotating solid disk about an axis through its c.oit yrk11x(k z5p1l6a 0,f,aft puvaenter of mass is,xkputayfap61,ft arz0li5vk ( o.1 1 $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?
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18#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Suppose you are sitting on a rotating stool holding a 2-kg3 n(; zt e nqcttc:,esfsz)*t3 mass in each outstretched hand. If you suddenly drop the masses, will youre t3se, zcsz:( ttcf )*nntq3; angular velocity increase, decrease, or stay the same? Explain.
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19#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Two spheres look identical and havbars l1m5-pl xmh)17 6uk vbty,6) tace the same mass. However, one is hollow and the other is solid. tr),6tbla1h m c- )plk75x 61u bamvysDescribe an experiment to determine which is which.
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20#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
In whatdirection is the Earth’s angular velocity vector as it rotates daily about itsaxis?
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21#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
The angular velocityz bd6 /pn+i7isbr0pz)d b)o 2w of a wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is tno+6dbp /pwib2 i70)r )bz dzshe angular speed increasing or decreasing?
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22#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Suppose you are standing on the edge of a large fyb.v0hdov d 0x g;l4-sm q.i- (5wmtozreely rotating turntable. What happens ifb( 5dgh- ydx0olv-iqt .m.4owm 0;zvs you walk toward the center?
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23#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A shortstop may leap into t)npw )t .svh,li e84zche air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickl)v8)np h czi w,s.elt4y you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.
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24#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
On the basis of the law of conservation of angular momentum, dim8g1n1mf7zs-zct6kr scuss why a helicopter must have more than one rotor (or prkgsc-n7mt 1mz1 r8 6fzopeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.
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25#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Express the following angles in radians: (a) u9xr8r)j xwk5 nz2,ye 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

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26#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Eclipses happen on Earth because of an amazing coin g .gd5r(qehp;cidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on E;q5 (ph edggr.arth.
Sun =    $rad$ Moon =    $rad$

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27#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A laser beam is directed at the Moon, 380,000 km from Eze 7pxlbkp7( .( h5wvearth. The beam diverges at an ang lx vw(57 .ezhpeb(pk7le $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m



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28#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The blades in a blender rotate at a *-pjmcziw( p4fdx3s1 rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is4*w-jp zdmspfc i 13x( the angular acceleration as the blades slow down?    $rad/s^2$

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29#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A child rolls a ball on a level floor 3.5 m to another child. If the ballb j-xo,hbild r9bg3y )0zq. (b makes 15.0 revolutions, what is its hblg drb- ob ,0xj.3)yq(bz9idiameter?    m

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30#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revotpbx.wsy l m 90-py0c;lutions do thcbt0pp;0l . 9yyw-xsme wheels make?    $rev$

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31#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcula*n (8s/szyw qqte its angulwqsyqns */( 8zar velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

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32#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A rotating merry-go-roundb ,wyx.n/lo(9dp eb q, makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a chil,d(.9nexqyb,ow bp /ld seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$    the center

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33#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the angular velocity of the Earth (t )g0qjv 1uk-ka) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

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34#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the linear speejj .qp:ul: :cdd of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

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35#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How fast (in rpm) must afk64cf8 rr-2qz9u :n6xyr j.ub is5wi centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100fxb-ru w.i5c2fi s4zq6y8 n69r: rkuj ,000 $g’s$?    $rpm$

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36#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpmm,zu,: xe.u unl,-wqbfg( s*jm/a,sq to 280 rpm in 4.0 s. D/wg(,q,xslm, j e qn*zu-sb m:a,uu. fetermine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

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37#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A turntable of radiusg 2 a1;s*jw6xhxir0u w)b:ei2ys h/ cs(unl 8w $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$
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38#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  In traveling to the Moon, astronauts aboard the Apoqq:t h+ifyi1k rs2bh ty +cse / l00305groj.wllo spacecraft put themselves into a slow rotation to distribute the Sun’s enerish:j ie0tly whqr0s3 5k1/bcgrfyo t2q.0++ gy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

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39#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A centrifuge accelerates uniformly fro -eum z4:co:bzm rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this tim4ozm c-: eu:bze?    $rev$

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40#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An automobile engine slows down from 4500 rpm to 1200 rpm il u (sl/pgf1br s69ca)g sr/i.n 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

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41#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Pilots can be tested for the stresses of flying 4j 8aijvy c 156glkvv3highspeed jets in a whirling “human centrifuge,” which takes 1.a3856ig vklj cjvy4 v10 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

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42#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A wheel 33 cm in diamfa 3ee/(q ,7ewc3m u/3bqdypheter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on 3,pae/mqeydbq c(euh /f3 7w3the edge of the wheel have traveled in this time?    m

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43#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A cooling fan is turned off when it is running at 850rev/m(xpp9l )8btwn;ho43-sweu yfin It turns 1500 revolutions befo3s b9 netw48p xyp(of;l)hw- ure it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

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44#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The tires of a car make 65 revolutions as the car reduces its speed unutv wtynh2f8 x7):ald/;l0 nyiformly from 95km/h to 45km/h The tires have a diamete0) ;vyt2 7 nuf/dnyl8hx:tlwar of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

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45#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The tires of a car make 65 revolutions as the car reduces its szs.w)e/+(crlh tg 5 o w6cgbkv4y5okxb8f2n2peed uniformly from 95km/h to 45km/h The tires have a diameter of 0.)n4 2wlgb8yz.g oc+ tbsf2 orx 5/ c5whekk6(v80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

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46#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 55-kg person riding a bike puts all +/2 ux;7g eewgftf q9lher weight on each pedal when climbing a hill. The pedals rotate in a circle g2e ugx/f9;q tw+7lefof radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

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47#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A person exerts a force of 55 N on the end of a door 74 cm wide. What is the ma/p 4a3 5cpn0ntwwp. fzgnitude of thpwtwc 40nzn/.pf3p5a e torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

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48#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the net torque about the axle of the wheel shown in Fig. 8–39;fxk2 z ztg*t(az0j 5c. Assume that a friction toztafjtkgz5x c ;( *z02rque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  



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49#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Two blocks, each of mass m, are attached to the ends of am),fvx5s w;xh dxb.e5 massless rod which pivots as shown in Fig. 8–40. Inh)wx 5xd.ve b;,sf5 xmitially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.
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50#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The bolts on the cylinder hebs*mb8)tv+v f ad of an engine require tightening to a torque of 38 sv8f+* v)btm b$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N


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51#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Determine the moment of inertia of a 10.8-n e.yga9krvj ut1vvle 94;n2c0zf 4j3kg sphere of radius 0.648 m when the axis of rote4y c19vzau49 rg.vekj 2ntvn ;30 lfjation is through its center.    $kg \cdot m^2$

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52#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the moment of inertia of a bicycle wheel 66.7 cm in dia -jele(p9 (znnl 6ain+meter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored 6 ei+nln-a(ezl(np 9 j(why?).    $kg \cdot m^2$

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53#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A small 650-gram ball on the end of a thin, lizrk35j+p+bi3hv yx/s ga1 ,jjght rod is rotated in a horizontal circlv5 3jxgk1 y/zaibs+ jr j+3,hpe of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

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54#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A potter is shaping a bowl on a potter’s wheel rh90* bvwu brr of/;cs6otating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay isvbh0* f;/s96 urobwcr 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

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55#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the moment of inertihx w(bo a 2xg1. wb.6lhn8m5ctqks9vl;y- b)ra of the array of point objects shown in Fig. 8–43 abbr.wo q 9swl8 (; xbx) cghn2y.mt5kl -v16habout
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?



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56#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An oxygen molecule consists of two k5ja(q5x *0gcmi97f e h-skvuv*(ark oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

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57#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  To get a flat, uniform cylindric286 jlmy vm,al..gy;wzuos7 yal satellite spinning at the correct rate, engineers fire four tangential rocyll 8 7.2,mgvyjs;muyoz.6 awkets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)


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58#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A grinding wheel is a un l7agij7k5 t./ ldwk4wiform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculate5 j7k dllag7tw. wk4/i
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

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59#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A softball player swings a batpej)(a.u p.dk,mo .hy , accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

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60#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A teenager pushes tangentially on a smal c)*eub g0/ykzl hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the me/b *eku0g zc)yrry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

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61#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually br4t+ /gq-ibw uyought uniformgwb4iy/ +u- qtly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

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62#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The forearm in Fig. 8–45 a t;pfrnusm* 2vy4o 9n*ccelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N


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63#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Assume that a 1.00-kg ball is thrown solely by the actioi k8:oia5f1o y9 q9t0 ebvp2yjn of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from res1k0a:95qvj o8y boyfeiip29 t t to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N



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64#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A helicopter rotor blade can be consiufpq*xy p02r;7bx5 codered a long thin rod, as shown in Fig. 8–46. 70f; 25qcux*xobrpyp
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$


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65#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
An Atwood’s machine consists of/() zzv mfcyus v:u-y) two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

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66#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A hammer thrower accelerates the hammer from res/kd axk4w:d j(31ks ejt within four full turns (revolutions) and releases k4 jx3sej/awd(dkk : 1it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

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67#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A centrifuge rotor has a momen, )3 q y idcu;0htf0gvr wm0l*xsba6a.t of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

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68#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An automobile engine develops a torquef3p3lww+x jm+ of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

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69#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A bowling ball of mass 7.3 kg and radius 9.0 c np5+k3 cn nb*ncu2 oph2m/rsxlu1 8(bm rolls without slipping down a lanso ncu1hb*8m b3c 5( ulpnk+nxr 22pn/e at 3.3 $m/s$ Calculate its total kinetic energy.    J

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70#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate the kinetic energ+fsh ( 1,ntgg+s:cp ; /bumx-yhln do3y of the Earth with respect to the Sun as the sum of two term sxlgn;/ fuy(ns+og c3 -,htph1bdm+:s,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

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71#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much nettvj + )bhk al0d m7+38/ehvsgk work is required to accelerate it from rest to a rotation rate of 1.00 revoluva h73)+mkh jb 0gt 8l+v/dekstion per 8.00 s? Assume it is a solid cylinder.    J

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72#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A sphere of radius 20.0 cm and mass 1.80 kg starts from res;ikp 3+fj19pqjr4 fb*cpbkfv (pka t m,7w-q;t and rolls without slippif m*kbkqpa+w j tpib,vcr- fpjk7p;149 (q;3fng down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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73#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$


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74#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 2.30-m-long pole is bal) yoepm.uc;g6 anced vertically on its tip. It starts to fall and its lower end does not slipm6)u; yepcgo. . What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

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75#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the angular momentum of a 0.210-kg ball rotating on the end oat mlnrkcv44x7c:c ;5y;ejv :f a thin string in a circle of radius 1.10 m at an 4:txe v avc n;rkyl5c4j7mc:;angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

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76#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wh n(c,oad0mb97s- klz;*qw,dixp 9i oceel 9ccn - d( 0oo7azw,mlp*,qi; sdbki9 xof radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

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77#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A person stands, hands at his side, on a platform that is rotf nhm3 pgp9lo :-lle 36lig:f6ating at a rate of 1.3rev/s If he raises his arms to a horizontal poll69-e mpl3ipn::6fo hgfg3 lsition, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

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78#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A diver (such as the one shown i g (qd:b2zmrfjj g7:,bn Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If sh2bgr : bg7m:fjzj(,dqe makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$


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79#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A figure skater can increase h;:6wn 3ll 7j6i56cq k ooevtxmer spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate jeo: 3vo k566; nm76twllicqxof 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

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80#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A potter’s wheel is rotating around a vertical axis through its ovrwdqp 2f6q e ph dow*-b-;-,3uc3gzcenter at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of thevpd;w uhzfg, b- -r q6cdpoe3q*23wo- wheel after the clay sticks to it?    $rev/s$

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81#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) What is the angular momy3)o 0 iv)rffx dc0a l4*zj38acz.jjyentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

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82#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Determine the angular moment t4ohk 6-ok4 3pv3zwlcum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

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83#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A nonrotating cylindrical disk of moment of inertia I is dropped opn7m+iu :r1utnto an identical disk rotating amuit n17r:up+ t angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?
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84#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A uniform disk turnsw r hm.mm:l2.r at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$


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85#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A person of mass 75 kg stands at the center of a rotating merry-qu 0vd5 wl0 ./oja-u(nz/l/ byql gl:ygo-round platform of radius 3.0 m unll/y0 o 0l5a /jw/d-.:zbuyqqgl (vand moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

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86#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 4.2-m-diameter merr u 74ynda1n vs dfqo2v-6rrz a*a874qvy-go-round is rotating freely with an angular velocity of 0.7*nqq 6frysao4 dr-v78 2 and avz14vu8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

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87#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose our Sun eventually collapses into a6 r:iz+kqv-au white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no an6rzu+ ia -:kvqgular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

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88#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Hurricanes can involve winds in-0axoinh7. w ol3j*m, z33xzrq, uam s excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

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89#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An asteroid of mass de -+ eej.afl j0x;+uv$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

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90#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A person stands on a platform, initialn(k*z vt3s cgjx-z6h.t*mqx/ ly at rest, that can rotate freely without friction. The moment of inertia of tg* v(-ttz z j* x6cqn.3kxsmh/he person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?
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91#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-roeggn/v*bra6c. w(e8 vfi9na7und turntable that is mounted on frictionless bearings and has a moment of w/ g. bn *7ea(af8 9egrivncv6inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

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92#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A large spool of rope rolls on the ground with the end of the rope( wy l4ggl j2dbp7gjm: ufz9 ed+l3c86 lying on the top edge of the spool. A person grabs fydm(8jgg9 472 3l dcwg+b j:lzlpeu6the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?
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93#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The Moon orbits the Earth such that the same side always faces the Earth. Def z.m j9 - h-r4twhfycj86s*rstermine the ratio 6t9f8*hh.ysr-4 c wmfj zr-js of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

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94#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A cyclist accelerates from resty+r 0royv ;i1i/l-rfo at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$


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95#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 1.4-kg grindstone in the 73mt7p1 dft n 9sx-5g x5glws v6y;hrqshape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s it-lht3 fm7xrpx 975gs vw51 6 ygdqns;nterval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

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96#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) A yo-yo is made of two solid cylindrical hco3 c97ce4 .peph m.y7a tq8,aosr mlea,/7rdisks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released frocr.oa3c7yml7ho ,p/ c8t4a9eq.m ,rs7h eeap m rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

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97#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) For a bicycle, how is the angular speed of the rear wheel s-vhcvi;khv3 4b *g3m($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   


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98#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose a star the size of our Sun, bun nn-) 9yl4rkjt with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days)94nl -nrky nj. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

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99#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  One possibility for a ey- s+.km*op blow-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be msb*p oe.-ky+ able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

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100#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Figure 8–53 illustrate e19+w93o e0gerhdslcs an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$


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101#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A hollow cylinder (hoop) is rolling on a horizontal siuw li4*9ha7:qto07 ozw m w2 pbmtt(9urface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

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102#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A uniform rod of mass M and length*4ku6fus2qh-liggge9li l19 b 4wfs ; L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of thlwsuuf *1g2lbi 4 s-ile; fh96gg94qke tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

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103#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A wheel of mass M has radius R. It is standing vertically on the floor1rscoz4lhaz4e(1 i w o/c :(ki, and we want 411icezsc:olwh az/ r(koi 4(to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

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104#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A bicyclist traveling with speed x: s b- muuu1,g/nmvc9qw-;avv=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist anvu9q,; -g-a:ws /1muuxc mbvn d cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m



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105#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose David puts a 0.50-kg rock into a 1 s yhy-zmq9*fsling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve thizm-h yy9*1qs fs feat, and where does the torque come from?    $m \cdot N$

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106#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Model a figure skater’s body as a /2fren q0f4ujie 1f;8wud ,xusolid cylinder and her arms as thin rods, making reasonable estimates for the , u ;fenfxue0f4w81q/id2 rujdimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

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107#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  You are designing a clutch assembly which consists ofz +yt56/cb 9ef;h :tjkzfbap/ two cylindrical plates, of mass :zba/6f5 zt9+efpby c/jkh;t$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$


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108#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A marble of mass m and radius r rolls along the looped rough track of Fig. 8–58.o: h8 gfm6)x5 rsoqki8 What is the minimum value of the vertical height ho8qkx o6m:)8h5rfi gs that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R



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109#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Repeat Problem 84, but do not assume c)2db3u6wqug+dt 1hj$r\ll R$ h =    (R-r)

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110#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The tires of a car make 85 re7(l5k9thtuh c0 u zh9lvolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular a(h9h5 uhzcul7tt 90k lcceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

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