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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 the w6k 5fagk j4a6tyn4)xct no/q(heel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch whee(q a4cy/t 5 6ktnoajgxkf)46nls?
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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 angular velocity. Does a point on the rimyg4i79uo2ps2z5qdxyl2 i: x w6o/(kc 2lza hw have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point h2 9 yxzg2ixdl/usykpz:cw2w745o6l h (2o aqiave 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 described by a single vrmluhv8hq:s:c.mk22q 9 q 8vwalue 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 force? Expla +lx y/ktdc6*zin.
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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 behind yourxsuoh e0 3:cop:/v p4-pkm p/r head than when your arms are stretche /4pu-kchm :3 eov: xprpps0/od out in 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 seve.898h/ ibczigk au2 pen sprockets at the rear wheel and 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 geazi.ac e /9 b82iph8gkur 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 flt bea;2hotfx: kx- 9,ast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamiclaf2,:t -xket ; ohb9xs, 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) c l)vuds+5).(fepon*plru 9 sz*q; wraarry 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 theb6 ;pdhg 9z/qqtl2 be/ net torque also zero? If the net torque on a system t6/blebq2z; g d/phq9is 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 make different angles with the horizontal.rj-es/uti7q4jfqfe -6+8 l py The same steel balll fuip6- 4 j/78-+jqy rqesfte is rolled down each incline. On which incline 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 si6l9 mo zsjg (cg9m*ofp96l h:nmultaneously 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 the incline first? Which has the greater speed there? Which has the greater 99z6ghms:9f o cjl6p mlo(gn* 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 stwxd.n5 nfi+ 3pcu*21i-0 p)kkf bpj xtart from rest at the top of an incline. Which reaches the botx-k p t0kwuf f3*p1 5+cijni)bxpn d2.tom first? Which has the greater 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 momen5/xpu-0*4h wxx ph 0iofzqe;u- pdrq0tum are conserved. Yet most moving or rotating objects eventually sxqeqop0 w4 d/u ;pf z*i-0pxh05xruh-low 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 grea0ng /vehawo c 8,lr2m,t migration of people toward the Earth’s equator, how would this ag/ v0rce82a, ,nolmwhffect 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 welt2j b2px+b6 ithout having any initial rotation when she leaves the board+e6xpbj2bl 2 t?
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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 axisar3 k/g- ,5pb( jpqx vqml+1:.:c1qrxlxw cps through its center of maswc.1(rsp1a:mlr xc+j 3k,qxx-5g:qqpv l/bps is $\frac{1}{2}WR^2$ (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 e4 mz-:mp9y3my5me xk yach outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, orm9mm: y5kxm4p -3 eyyz 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 have the sanl*wagsvg x3()kvg3;n 2 ysv8me mass. However, one is hollow and the other is solid. Describe an experiment to determine which is g3avgw)s*y(vl;vnnkx8 s g3 2 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 a wheel rotating oxy o 0b8/n:bylkwny r036u74uax14q)canyvb n a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If bwu)b 0n x6l34k7 :vyq4 oyarbun/0a8c xyy n1the angular acceleration points east, describe the 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 on thsm:,i,8.nb xud8 t ;nyiv40cz ps y/cie edge of a large freely rotating turntable. What happens if you walk towadiyp0,/v, 4 :mnbccny 8.z8txii; ssurd 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 cagi6z u 8fc/t- t.rgam vc)+e2ymt0d.r tch a ball and throw it quickly. 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 op+.mu6/8ti gm td0ry t-vg .r2ecca) fzposite 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 ansdmq o0:-wu dy4qtc+g- k5ed/z es/6b gular momentum, discuss why a helicopter must have more than one rotor0smz buoq+ q 5kdyeec gtw-/-d/s6 d:4 (or propeller). 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 ra i;*2b sxoh+oddians: (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. Calcuyyor gpji v5l *+ d.56;/jiydglate, using the information inside the Front Cover, the angular diameters (in radians) of ther/55i.jp+yl6dod* ygiv ;y jg Sun and the Moon, as seen 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,22(7jggpw( zdpq2i du 380,000 km from Earth. The beam diverges aj pdq2g gdiu( 2z2pw7(t 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 blenbji/ g,d)5rf) qv4ylkder rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the igr,5fyk) v4j/b ld)qblades 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 flo u80pd(j na-hzor 3.5 m to another child. If the ball makes 1hz- 8j(d n0aup5.0 revolutions, what is its diameter?    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. Hir 2/w mamo6a sz*/j6now many revolutions do the wheels makezr/m2 oa* si6anmwj/6?    $rev$

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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 rotatm .yzr9gcvh9. es at 2500 rpm. Calculate its angular vely9zrvh .mg9 .cocity 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-round makes one complete revolution in 4.f mv:s(wn0/,tewu 9*t e*vxe bdhl7djp8m 1;o0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the cend eew7w 1s(nm/p xvemt0lv:d9hob tf*j,;u* 8ter?    $m/s$
(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 (a) in ibs xp9+:k f0ldts 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 spe ;oec9r a+y9k hijk2+led 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 a centrifuge rotate if a 808a vwdoer9bws 3nu: particle 7.0 cm from the axis of rotation is to experience an accelerat b8 sar83v w9eond:0uwion 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 accelerat( z4fwy1us** x x9pw:v-8ozz(re oozqes uniformly about its center from 130 rpm to 280 rpm in 4.0 s-1zze9 x(* r8ufowox:*zv(4ysz p oqw. Determine
(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 radiukyvtc8/ yp: z6s $R_1$ 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 q u tpj 3.cpu3hdp;30ithemselves into a slow rotation to distribute 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 h utdq3cp pi3p;.j 03uspacecraft 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 15leghg,0k(8s w,000 rpm in 220 s. Through how many r0glg,h sw 8(ekevolutions 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 )e9h;sjpg+jw 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 flyo1 dse);slkr n8q r52ling highspeed jets in a whirling “human centrifuge,” which taslqer2s8 5)nd1 ;rolkkes 1.0 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 diameter accelerates uniformly from 240 rpm to 360 rpm ind,mc.avk;6nkh5ng)v/ l1 nqb 6.5 s. How far will a point on the edge of the wheel have traveled inlk),cnn6m/. k hba 5gv;nq1vd 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 u*3*dgh3 iin*yqxv1 jrevolutions before it comjd xi*yqhu3 g1*n3 iv*es 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 uniformlypu2*yw/ ac x/qy:edd; from 95km/h to 45km/h The tires have a diameter of 0.8;/pcwdy* a d:y qu2e/x0 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 kz 0nyar.j9 )i.mi jj/q12yr a65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a dkjmnzqiay 9 a/.r1 jry) j2i.0iameter 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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46#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 55-kg person riding a bike put/sl0+ ui7e6cu,fsdw. d0wil,u*b x t ms all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm. cd fxu7id0*swl6b,eu m0il. sw/, +tu
(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 (t* uq1djjkf 9l89fmm9yem+z magnitude9jlut198*q 9( +yf mfmemjzd k of the 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. A 2 d2tddt9zzd:ssume that a frictionz9dtddt2 z :2d torque 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 attachf lcb- je(+v iun b7joj)xarb( l5(;g8ed to the ends of a massless rod which pivots as shown in Fig. 8–40. Irgaf +bocjjv (()ju 7;58lx n-e(iblbnitially 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 head of an engine reqys(wh4 ul4es 5,ouwnp z9ex+3uire tightening to a torque of 38u (zl,up3 4o5wee4sxsw9+nhy $m \cdot N$ 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 0.648 m when *xni vpn vk9;mrr79d;the axis of rotation is through i v; kxn97;*r vdim9prnts 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 -vr )w.40zhf giq wuj9of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass ofqrwvih-wzju 4.)gf0 9 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 thin, light rod is rotated in a h6 acqjghl3x* /orizontal circle of radius *qc ahl g3/j6x1.2 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’h ke z f4ceyzs.90k8.r wvml03s wheel rotating at constant angular speed (Fig. 8–42). The fri4.cym e83zk00esh w.krlf9 vzction force between 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 point objects shown in dq-.vzx7 o8gsn4 t g;xa pxg(,Fig. 8–43 abngzvd4gq xa7g . o(, -p;xxt8sout
(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 mahxz nvs992yayq:ufk63q +:sf ss 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 cylindrical satellite spinning at the correct ratepf0+g,nbt6u8usga t0, engineers fire four tangential rockets as shown in Fig. 8–44. If t0nuu 08,ts abpfg +t6ghe 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 uniform cylinder with a radius of 8.50 cm and a mx4fis fx/y t hc9+*bjm 5wn+b/ass of 0.580 khw s/n/my5f +bt + j4ic9xx*fbg. Calculate
(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 0-aqf0j(vtf a a bat, 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 tan5(easf3puw4 j 27gpz bgentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s.w a452 sp7upe jbgf3z( 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 rotating at 10,300 rpm is shut off and is evq th1n02- *xsb*pomdvn )* o74rmryld entually brought un) - s*mm dpl17 q*on2dnvr4t ho*0rxbyiformly 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-fdbd,c0fa6o xe)6dd )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 action of the * +6ml neo c5ad9w6dppcu +d5aforearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is acceler+ cwcl+dd5e5*an p 9p6oad mu6ated 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 c *o/esr;d.5yw b3 x tx45fwth+m *yctean be considered a long thin rod, as shown in Fig. 8–4/xhoxsy.tf;w e 5**cb e3 t d+5rtmyw46.
(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 two massel 66ve/s tpvk;o*kaf0s, $m_1$ 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 turns6za;qbi -w)tz eyd5+ h (revolutions) and releases it at a speed of 28 w i 6zy5t; )dh-eq+zab$m/s$ 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 moment of ip.uz7zblg9 u9 nertia 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 of */f xb:o5(l8fwdu omtvgp9r *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 radws+jygbq 50. 0tae cr:ius 9.0 cm rolls without slipping down a lane at 3:y05jqc 0abts wreg+..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 kineticm6;:te0m v pyj energy of the Earth with respect to the Sun as the sum of two tet :mj0v ymep;6rms,
(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 7.501 vw(v jyx/f8*o wk5yc w+7fjs m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it isywoc wv*+s x8/wf(71fvjkjy5 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 reu-xqk4ue i)xee:u3v +j-j4k sst and rolls without slipping dj 4k3 jek+vsxuu-- ex4e)i: quown 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 balanced vertically on its tip. It startr.wbdnfy((rea 8m p/e:gi /r -s to fall and its lower end does not slip. What will be the speed of the upper end of the m (w(peyrb 8naf/rr -gi /:de.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. /zovy,wec.l )210-kg ball rotating on the end of a thin string in a cir,/c lev y)o.wzcle of radius 1.10 m at an 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 2.8-5ula8msg 037xs .c ym6gfh3w vkg uniform cylindrical grinding wheel of radius 18 cm when l 6s38fxa7.sw3gmv0u myc5hgrotating 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 hism h3 pulqo8 (:puoqg)y:ha 5)s side, on a platform that is rotating at a rate of 1.3reh) :(u3qp huo85p: sy qlm)agov/s If he raises his 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 one shown in Fig. 8– g9xu v;k5ctz,is1*z qk+m iv329) can reduce her moment of inertia by a factor of about 3.5 when changing from the straigh;i5czvzq +ix k *gtum,9ksv13t position to the tuck position. If she 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 her spin rotation rate from an initial rate of bnc39 wehk. 8 p)iwn1c1.0 rev every 2.0 s toihkwcpbw3)en1c.9 8 n 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 center aer1 9ixbe:4jh;5jbcft a frequency ofrxbi5e4h f 1;:jej9b c 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 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 spik y70seq 2 +(g ijinwb 1n+qy1hmc,rm/nning 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 angulafiql rxzzc85 1s)id7rxys9u -),0mh qr momentum 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 di4p pq7d+cx+uqyix0+kgca 7 r3sk of moment of inertia I is dropped onto an identical disk rotating at angulara7 iry++ u4pxp3 70+qgcdcqxk 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 k:j,u3w/wrh. dc 6eqgat 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 rot m:hnh)j c180jhcp0eb ating merry-go-round platform of radi)j:b m0p hc0n8he1 hcjus 3.0 m and 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 merry-go-round is rotating freely with an angular velocity of 9k10h-nc /wa+oemonfz r,4r u0+arhkzmcu-9nnoo r fw4 ,/e01 .8 $rad/s$ 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 a white dwarf, losing about hazc. pm.l0ilj 8lf its mass in the process, and winding up with a radius 1.0% o0l8.jmi lcz .pf 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 excesswp:r: fasn934 (oale)tw.knv 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 ,grxcwp lk,,jx v m 2hfn.mk.7+ 7(asi$ 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, that cad81u ba 6xahwzeyyadz-8l5. ) n rotate freely without friction. The moment of inertia of the person plus the abh1w eduzd6 a.axy-)y858l zplatform 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-uih(4n6bmo cu-wk p.5round turntable that is mounted on frictionless bearings and has 6(-ombw k4.5inp hucu 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 with the end of the rope lying on g1 6oshlk1*-kz b 2cohthe top edge of t-oz c1hhglbs126o* kkhe spool. A person grabs the 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 Ea ,xm9ntsp ,efp)v:rm9rth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentu ne 9)9mpvtmfp rx:,,sm. (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 rest at a rate of 1 foh3syl.o gswecepcg w 2 :v4,-/x4e6m/$s^2$ 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 acqbk wff g5i1d:.uires a rotational rate of from rest over a 6.0-s interval at const5f.w1 bd kf:igant 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 disks, each of mass 0.050 kg andw on,s1o ) yz1a8phl vpf0,lo9qbl 5t: diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub )zwbaf1,l8s 9loovh,t1yp l: o0 5 pqnof 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 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 the angular speed of the rear wheel f qsx h6*a f7e),/q(m+dvmqh g($\omega_R$) 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, but with mass 8.0 times as great, werca6 ,gun6 fw3we rotating at a speed of 1.0f3a 66gwnwc ,u revolution every 12 days. 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 low-pollution automobilegk 0gy9k:481 ubf frca 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 k4cy 0arfb:f 9gk 18ugand 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 illustratts3qq fnq4/n3w.px 8ch9 y rs8es 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 surface at speed v=3.yw8 5 xez0id0a6zk2 yj3 $m/s$ 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 L can pivot freelysi)ccg ll5: ha 05pfe- (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 lip0g h)fllc5i5as: c-enear acceleration of the 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 floor, anwj d,k-a 21mydd we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Figd dj,a1-wm2k y. 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/s w m/ep d0o9ou,on a flat road is making a turn with a radius The forces acting uwom0edp9 o/,on the cyclist 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 a o-ga ,d6no*gznd 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 this feat, and where does the g *,zod6-ogantorque 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 skaterhe v1ua * vx7/hqj9nk3’s body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angularvkah9 e/x*3vnh7j1u q 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 bm19d x4orfosh* j*i0xx ,yx /assembly which consists of two cylindrical plates, of mass 4xrhxi1 yxx* sfoo m*db,9/ 0j$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loopedmeowv a.5 7r7x rough track of Fig. 8–58. What is the minimum value of the vertical hm 5xrv. o7ae7weight h 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 ah0829uqw m ndt e6bbv5ssume $r\ll R$ 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 reyu;lt/tij/ fn q); 1noamo1u2volutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameteoua itu/);2nmo 1;j f/qty1lnr of 0.90 m. (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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