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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 trac.;0hjp; xd kt c4h)xaveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheelhk)acx0x. ;dj ;cpt4hs?
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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 d1 fo93jywq: dangular velocity. Does a point on the rim have radial and/or tangential acceleration? Iy3odwj1d9 :qf f the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component 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 be +36qj(ttzr4ojwfj6 ndescribed 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 larger forrqoszt, (*wx2 ce? 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 do a sit-up with your hands bgppfsf-viq-9r ebml ,kr*73t1 j 7lxltf-.v 6ehind your head than when your arms are stretched out in front of you? A 79-frbkj,g.t v flp1-e-fis7m rx tp6ll vq3*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 rea 0+f w qxmh1gp/q -e3wsz6bcj*r wheel and three at the pedal cranks. In which gear is it harder to pedal, a smallqe+/-g *hz mc1wb6 sjq pwfx30 rear sprocket or a large rear sprocket? Why? In which gear is it harder 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 lower legs wu9+. j,b .rgdqfmj: )cco vzo)ith flesh and muscle concentrated high, close to the c9. qujzg))+ rm,jfvo .d:bco body (Fig. 8–34). On the basis of rotational dynamics, explain why 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. 8–35) carryit 9qucy.6x0f4rgf- l 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,o084x hfq/swwa 2 onf is zero, is the net torque also zero? If the net torque on a sys,hf /o 0wof4x2qawn s8tem is zero, is 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 same height but hm-s4 lhv.4kp gl8cr3 make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Ehclp3m r.k8l-g 4sh4 vxplain.
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12#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Two solid spheres simultaneously sta)11wx9eju san rt rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? jnw19 )xes1auWhich 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 havey d+h/o 4s(zte the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? + zy h4do(/steWhich 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 momenl2x3p0rk*elu :l. vrktum are conserved. Yet most moving or rotating objects eventually slow down andlr :rxpk 3ell v*20u.k 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 migration of people toward the Earth’s equae1ku fwde74gl, 4;mqv *hfm8 ftor, how would this affect 4m,elfufhd; 4v8q*mf1k7g we 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. 8–29 do a somersault w)2c jd eisk8d+ithout having any initial rotation when she leaves the board? 8k+dd cs2ie)j
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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 3n0/pkejtytp(b-by47jc ;n wa rotating solid disk about an axis through its center of mass itcb b(n-jw; /pny 0tk7jy34pes $\frac{1}{2}WR^2$ (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-kg mass in each outstrer bcl*gqrab(az64 3) vtched hand. If you sudde6cabgzr *v4ra)3l qb (nly drop the masses, will your 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 havea9kpp ).syiv p; ev8z* the same mass. However, one is hollow and the other is solid. Describe an experimeavipe8;*z9.svppky ) nt 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 velocity of a9urrsco7(qzwj- ;5p c93fyash:e2j g 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 th9: 7jjsrosupyqec w(h;a5f-z3rc 2 9ge tangential linear acceleration of this point at the top of the wheel. Is the 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 o7xdi3c90 jyp959 yxfnly8fa dn the edge of a large freely rotating turntable. What happens if you walk to37ly9xn8cf9yaxd p9 fj0iy5 dward 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 the air to catch a ball and throw it quscmpx4 u-gx (69so,mu ickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). xpus,x -m( m6g9souc4Explain.
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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 conseru+zgh. g2/z1 u.u4-qnis f x5y i ehdwzrd315dvation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the i zeuy/. dz2 4. zgsd1ihn 15uf5h-3wguxdqr+ 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 n79vsj 1*tn/ aq 10mrcr/k9apzfys e/radians: (a) 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 coincidence. Calculate,-se 468ilvgk4pel c:hx p(4qv,zl h6 v using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as svqxgl h(44is68vlvp,ee4 hk6c :zp-leen on Earth.
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 Earth. The beam dive b vm+w5lg(zw6rges at (wbg5vm6 lwz+an angle $\theta$ (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 rate of 6500 rpm. When the motoo-zy9dv u f pvf8t xn65kw55+3u,d dhzr is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accele5fhd vzd ,+ozf 9 wvpyu5u 36tdx-8nk5ration 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 levdu1 j-x4pp, r;xrs-jsel floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diar pxjxdr 1u-sps -4j;,meter?    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 diamn;jtls *sjz 6qa0/f z:r2ams.eter travels 8.0 km. How many revolutions do the wh2a6 js*.m/nqfazr t:s z0j;s leels 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 diameterdc8ijqt v/vb.nke ):l m727hx rotates at 2500 rpm. Calculate its angular velocity 2jhbi: v8nk)tmev /7qlcd . x7in $rad/s$ $\omega$ =    $rad/sec$
(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-round makes one c/t 3rg 9jdz:maomplete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a chzg t9j/am:3rd ild 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 velo2 if3 ji/pe+ e)8fk5zd aeqz9ycity of the Earth (a) 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 speed of a poy /+lg9 ilf3upes0z 3wint
(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 n8-bthen z/0- 6ktt9desudx4a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceteen stbh8n0t/9 z 4dx -udk-6leration of 100,000 $g’s$?    $rpm$

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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 rpm6xby t-*hv ck5 to 280 rpm in 4.0 s. Detey t* -b6c5vkxhrmine
(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 radius gp5 bo 7al+ g:.p d3m; jqitgfv2t*:bp$R_1$ 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 Apollo spacecraft put themsel vms1.l8)g uwsc j nk-e9i vh(j6jb(r.ves into a slow rotation to distlk)sejw.vgriun 1 (j 98.ms( 6-v hjcbribute the Sun’s energy 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 from rest to 15,000 rpm in 220 s. Through hok)u cwvhmh-l9hy5 6qjuun d/n7 u4/1gw many revowq1uuu4hg/) hdc/v nnk7 hmy-uj 9l56lutions did it turn in this time?    $rev$

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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 in 2.4rss t-pz p1u.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 oq 4m4:qe5krd-6srtzv f flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 comqv d4eq6 zm 5kr:tsr-4plete 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 diamez8hn9rtn gd d 5*as6d cf1ij44ter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How d168 s445n*ncd adrfj9gihztfar will a point on the 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/min It turns 1500 revo hkc k8972lrurlutions before it comes trh9 8r7k2kl cuo 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 65n8)6q34tchxswuk lhq zg- t2 ; revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have aq6k8 t-4uqh xgc3wt; lh)n 2zs diameter 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 revolut :m5o- )yzl hyj .t(zf)4edhekions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m. ykej 5h:)ohdy fz)e.z-( l4mt
(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 her weight on e2tc ef(q f;sc jo,*n 73cd7ot.isbjj8-jm.svach pedal when climbing a hill. The ,-.. v7jom872jf;t n3jetsbcc i*(jfcqod ss pedals rotate in a circle of 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 ii0ur 4+hxgno1s the magnitude of the torquxniog40rhu +1 e 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 ab2zm3e:7ozv 3lfq/hpd; fd.7nn 6jorbout the axle of the wheel shown in Fig. 8–39. Assume that a friction torq 7ozvdbe.3m ; 6fr/2 n3d:ohpflqnjz7ue 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 py p-;xvmm fk,ug99w/a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of fk pmuv 9,xwmgp9/-y;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 head of an engine require tightening t3xm1mfcingskmg s 6/( 7a2w, so a torque of 38 3m igms7 (knfca ,sxw6 /m2sg1$m \cdot N$ 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-kg sphere of radius 0.6wlmjvgei (822ufe1wl8:qs0 s48 m when the axis of rotation is through its center. gsi2w2v:e qj(llm0f8 s8uew1    $kg \cdot m^2$

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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 diameter. The rim zh+hdl1t 6m)dy+ pk8g and tire have a combined ma+gt8m1pldh +zhd yk6)ss of 1.25 kg. The mass of the hub can be ignored (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 thi-u ofb( z*ujw u,r(2eqn, light rod is rotated in a horizontal circle of radius 1.2 m. Calcu(o2rbq ejz(u- w uu*,flate
(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 rotating at constant angular s2ng0 nimxk/ sk/*bbm32 zbfg8peed (Fig. 8–42). The friction force 80x2zs3b gfmk /mbnbg/2n*kibetween her hands and the clay is 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 inertia of the array of poimu f,ntgh.() 4dot msgh* w):ont objects shown in Fig. 8–43 aboutf4 w,ugg mo)hm)*h dns.: (tot
(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 oxygen atoms whose total b2w i0 83egqpjmass 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 cyli.09owst1 d1wz lrpp 1qndrical satellite spinning at the correct rate, engineers fire four tangential rockets 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 roc sp19rwz0ot wpd11q.lket 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 0pxv, a10rerea uniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculatea ,v0x0rep 1re
(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 bat, accelerating 6 gazpc/u,z:rgv /ckar; 8ok ;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 small hand-driven merr 0(2e4emou7gjo4 tay xy-go-round and is able to accelerate it from resta7u0 eoy24 (4ojtxge m to a frequency of 15 rpm in 10.0 s. Assume the merry-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 rotatingh,kkrt3,16 o -t jqxi3 7kaysu at 10,300 rpm is shut off and is eventually brought uniformlkh1u6 t-roxy kq 3k,aji3s t7,y 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 accelerates a 3.6-kgpv/0z1f baye+ x2ee 9;xq 9fct 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 th/z +z1n5lx 4nlzsix6b rown solely by the action of the forearm, which rotates about the elbow joint under thz+4nlx /lznixz5 1bs6e action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest 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 consprgj28a3 7sv (8acvm fidered a long thin rod, as shown in Fig. 8–46.fmjsv28a( rvca g3p87
(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 consb qxh5uh8;o0i.c3bos ists of 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 rest within four full cp, wn yrg)5p 9vk)a4 *ox hs9bx+neb)turns (revolution,5 vnpragsy4x )*bboc+ 9en9k ))phwxs) and releases it 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 mosu*98vajz :s.v5 kznx ment 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 torque or:ant 1epz(j1r .b),kh ddop;f 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 cm rolls without slr)mk9s9b u 9hs gdjc(*ipping down a lane at sr( kmcg bd9j*9u)9hs 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 energyt+4og e11 zgtp of the Earth with respect to the Sun as the sum of two termeg gt1p+1z4 tos,
(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 / 88 cextds5fxf q*v7sradius of 7.50 m. How much net work is required to accelerate it from rest to a rq7/e cv8s5f td*8xxsf otation rate of 1.00 revolution 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 rest and rolls 2e ehzbe5p94 vwithout slipping down a 30.2e bpv4ezh5e9 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 balanced vertically on its tip. It starts to fa0n/i 1 v nr kitu2t5.f;r-jejbll and its lower end does not slip. What will be the speed of the upper end of the pole just before j rr/ .0;n1v5-ti2b enuik ftjit 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 of a 8tyaa,x: 4t91zrbmdu f /p zp3kyy8d 3thin string in a circle of radius 1.10 m at an angular speed of 3 318xpzkrau8 pt,zdt9aydby m/y f4:10.4 $rad/s$?    $kg \cdot m^2$

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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 unifor0gci8p r z+s4lm cylindrical grinding wheel of radius 18 cmz0r 8gi pl4+cs 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 rotatisjk64ai d 7b87h r7wmxng at a rate of 1.3rev/s If he raises w bdrha7s xj677k 4im8his arms to a horizontal position, 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 oneidhln h t7q)9rt:h.p5 shown in 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 she makes 2.0 rotations in 1.5 s when in the tuck position, whqrtl9 :tp.d hih5 n)7hat 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 increo6,f2z* ycy6inc 6h grase her spin rotation rate from an initial rate of 1.0 rev evrygz h6ocn6yi2c f*,6ery 2.0 s to a final rate of 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 center9soqg2w9jiyz:1i/ h/ xrg s5d 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 t951wzo xy:rd2 q/g9 jgs ihi/she center of the rotating wheel. What is the frequency of the 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 momentum of a figure skater spinninb/ tk:6up5dl03j;* 0gl b9 ol hiqljlig 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 momehh+c1.4pmeq y:j+v++vb t6 bns cs)jyntum 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 x eo axo*e/j3qjga*) :onto an identical disk rotatinxe:a/jgj)oa*x* o3e q g at 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 turns at 2)b) b p5uytk t;r90x2h qcx-vw.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 th rqt j6/r2gg .5qzzrwg /8:l5okqk yz5e center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 92yt :kqzz g2qgwg .rjor/5 65qkz8l 5r/0 $kg \cdot m^2$ 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 merry-go-round is rotating freely with angno ;6m,dnf7h angular velocity of 0.;d7nmo6, n ghf8 $rad/s$ 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 tylzto5: t*w9collapses into a white dwarf, losing about half its mass in the process, ant5*:zlwt t y9od winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular 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 exce nq)p)arh / 6vt6vcloo ;q7;goss 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 wjq, 4tvai;z j:o0h+v$ 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, initially at rest, that8 6 d8su4dvymupbp5 cp- sa 48xulp-o6 can rotate freely without friction. The moment of inertia of the person plus the pb48pdy v s5a-pdx4l cp8 - 8uus6o6pumlatform 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.;84 t2ahj vqcfy9-r jn5-m diameter merry-go-round turntable that9;-arcf2 nh4v8qyt j j is mounted on frictionless bearings and has a moment of inertia 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 wesl:xhm c-an13c1l :aith the end of the rope lying on the top edge of the spool. A person grabs the end of the rclnh1 :1asacle-3m : xope 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. 3,mef04(1jg hrfln jeDetermine the ratio 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 t0f1erf m jjg4h3enl(, he 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 acceleratesqd cxm6u 9a3z* from rest 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 shape of a uniform cylinder of radius 0.20 m acquirenml c5v,s6iwc5 v/j 0+rpqf(es a rotational rate of from rest owce6 ,5pl i jcmf+rvqv/(5sn0ver a 6.0-s interval 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 cylindrfw1 /edsk+xb-v5kh ojd+ 86 - nutfjx8ical disks, 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 lw+ 8dxfn/- 8- e6vfj5xkbos1t +uk jdhinear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from 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 th-jbr+1j,.5 htn7lh 1lq jg4 vtghv3rye angular speed of the rear wheel ($\omega_R$) 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 ofltd83c4pu; xe our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gralx3 up8t dc;4evitational 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 low-pollution automobile is ,)elq/5 (aov3zlw0mn4-xzetvt p , ( ofop.smfor it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform5 o p(./ e4e0lt,mav q,sno3p)zvlxotfw (-zm cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be 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 illustrates an;dxdy:j t vb:7bwn b4) $H_2O$ 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 surface at speed v f)ddy0;cku8e*t +h 7 d;kcvql=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 1u 7p iwhpio-m z :*pcw*f/q7mw2 llx3and length 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 the tip of the rod. Assume that the force of gravity acts atw/ *pm lop7iwicwq puxf:zm123h 7*-l 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 g1d;4 jez8ytz 5m4fmo+ov51 6j wymozR. It is standing vertically on the floor, and we want 14e;tg mwy4z8 155zj+vo mzyd6foomj 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 v=4.2m/so h+xop3 9b ks)qg(* 3rd/x ym7byrjo,)zoid9 on a flat road is making a turn with a radius The forces acting on the cyclist7goz,pdi9*/ (x mq+khyds3) )brx yooj3 br9o and 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 sling of length 1.5 m and begins whi-2nd msxjqa: 1, tpg/srling the rock in a nea/gs :qsmadtxj2 1p -n,rly 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 this 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 skaterk 9q2zc m)jyz-’s body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched armszk2j9cqm -z)y , 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 c6oi*egh 1f2gionsists of two cylindrical plates, of ifi6 g1eog2h*mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 aio7w4u0k/ lxabzn l1; nd radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must dwb xz ni;/0a 4l71ouklrop 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 ass)3svk jj 5b;a,lwn pd:ume $r\ll R$ 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 8zkp1 1jqmc53o ;- hxvb5 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. c3 -m11pxvqzkj ;o5 bh(a) What was the angular acceleration 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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