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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 traveleg(q)m,t1 w:y,cps olrmjz - 9xd) is attached near the wheel hub and imqs-x:o,zpt9l),wm 1jg ry(cs designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?
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2#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Suppose a disk rotates at constant angular velocity. Does a p3hktdppg6s4cxza6 p h5 jg278oint on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does tkhs 5jgx6ctp6a 7 8pg3h2dz4phe 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 described by a single val)xst;iw60 (0qae;y)nb *tdn nm1r p.vbr3hjiue 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 lltxfjy6wa 65nl/ w va2:*2leg arger force? Explain.
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5#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.
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6#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Why is it more difficult to do a sit-up with your hands behind your90gkts- gf )9z*usqgg head than when your arms are stretched out in front of you? A diagram may help ysgs*-k gt9 g zu9f)q0gou 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 sprocketl)dxhg g9om1w ae4 y 5o2p/uf2s 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 gear is it harder to pedal, a small front sprocket or a large front spr/m9g y 2ueodgw1 x4 a)pl52fhoocket? 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 ou7v8j jghc .v,n being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageousc8 uv.jj gv7,h.
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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 (Fig9da 0zsl ra,dayr.:*(89hna)f qfcl9saws4b . 8–35) carry a long, narrow beam?
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10#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If the net force on a system is zero, is the net torque also zero? 05t4alf;pb r9a ht 1ogIf the net torque on a system is zero, ib09gta4 ap hr51;tfols 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 dip k28ai mpoig e( 0)h./jf/wamfferent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the bal.)(aj28gepmfi hkoa /mi0wp/l 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 simultaneously start rollin. hu4.*rildd yg (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 total kinetic e.4hdy*lir. u dnergy 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 start frpy.ay*tt 0 bxy5 l0 7q-c;36dnwmab nbiq e+8rom rest at the top of an incli.0 8y*6cbbtm7en3nx+;tywy raq-p 05dbq laine. Which reaches the bottom 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 mlf;7jgekvq.hz+hs-j:dlo6 )2f9 7/ utum os romentum are conserved. Yet most moving or rotating objects eventually slow down and stopfvq 7:e+.s or f/-ujs)do z6jhk7ml 29;hgltu . 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 dvy4*.rf b5vbn:b 8ffpeople toward the Earth’s equator, how would this affect the length of the f fb85 vyfv:r4bn bd.*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 x5uzz/znaba +h ,5 fc5somersault without having any initial rotation when she leaves the,a/az+fzz5 x n5h5ubc board?
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17#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
The moment of inertial p-/sgda cn nc6t ck747/e3yw of a rotating solid disk about an axis through its center of mass ec 7pgk6da4l7c-stnwny3 //cis $\frac{1}{2}WR^2$ (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 m:qj4olal 3-jst(;lrnk/g/d holding a 2-kg mass in each outstretched hand. If yonog: 3ar(s t-jdmk l;lj //q4lu suddenly 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 have theld p3 cm6dx3betv,9h* same mass. However, one is hollow and the other hm ,x6tbe3vdp9 c3l d*is solid. Describe an experiment to determine which is which.
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20#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
In whatdirection is the Earth’s angular velocity vector as it rotates daily about itsaxis?
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21#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
The angular velocity of a wheel rot7 bena1bb/9r;njs9v r1 ;8x e eea1hmfating on a horizontal axle points west. In what direction is the linear velocity o r 9en1; aneh97fj81beb/xs mrb;1avef a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is 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 the edge0b 7bz3w+abr3fxp8 5v 8s mtov of a large freely rotating turntable. What happens if you walk towards bv308zo8mta 7vx3pwf+ b5rb 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 qu:)c53gn .nq/y:defvmlx r )unickly. As he throws the ball, the uppere g).5ycnn: n /qfxv 3)du:lrm 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). 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 c )u22p1 ujow fbpu:g1of conservation 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 keew2jp:p uu b211u gcof)p the helicopter stable.
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25#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Express the following angles in radians: (a) ,g1vda q wwg99f(gpx udl066 e30 $^{\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 y:l4yk c ) ,xxgd)jvgxz) ou5;amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the M yg)lx)vj z 4:5ouydkc,x; g)xoon, 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, 380,000 km from Earth. The -n1i ;h0y p8kond0pnwbeam diverges at anyw o0 1p- nd8ph0ki;nn 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 rpmotej ( 2ycms/tgb9 u/*. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleratiumcst 9t 2b jy*(/ego/on as the blades slow down?    $rad/s^2$

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29#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A child rolls a ball on a level floor 3.5 m to another ch7 ,1vw) :b:2azst pyjbq : xx;f*cykalild. If the ball makes 15.0 revolutions, what is its diameter?fks qvlty12x;bpcx 7 )zw* ja,:yb:a:    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 diame/zri1l uit 8 7r(czoy,5y-d ggter travels 8.0 km. How many revolutions do the wheel7,d 1(8uliiyrzgzc g-/y 5tr os make?    $rev$

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31#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) A grinding wheel 0.35 m in diameter rss vn9lvzvn(v3b+.4votates at 2500 rpm. Calculate its angular velocv(s ns9vvb. +vlnz34vity 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 revoluti/ khmn) uarhw3.x.hh+)rfwm . on in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated kmu+m) rwhn3.). .rx a/hhhwf 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 vewtlqc2 iakt5*l m i(t32f.(jjlocity 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 p0d va6 y kx:kxx*pasl01lqn;/g+ g:tjd5u6d joint
(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 iff9i ty uk-: mm(j,fxv:96eub*ra;sb o a particle 7.0 cm from the axis of rotation is to experience an acceleration vejkfmxbi 99*-rf;o bt u:sy(,ua6:mof 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 130w va d4eo+w.*trhdl(.5b io;clq;ov/ rpm to 280 rpm in 4.0 lo.w (;ch+d/l oqerd.5b ;av t* ov4wis. 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 radius uh)kcf / 6u(koa8wm98qz nd3z$R_1$ 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 them7 l ;5ycc3b,gnm*ieqdselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0b;*micqg y3l,ne57dc 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 acceleratoy g2z4 6z4rk+ep :nsk)wjh.ges uniformly from rest to 15,000 rpm in 220 s. Through how many revoluti6 yn)g42:kze4+.r pgjkwso zhons 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 450 b*fj3b +js4zz0 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

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41#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Pilots can be tested for the stresses of flying highs2k(bm t.:e qj a 0xbnx3.dv-xepeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 completee0.bq md xnxxk3(t2. v:b-eja 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 uniforml62qxnu4rbu/ i y from 240 rpm to 360 rpm in 6.5 s. How far will a point on 2ix4 /rbuqn6uthe 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 runnc:y-m/fn ym+ 06enxxr f n7ta/ing at 850rev/min It turns 1500 revolutions before it comes t6/c/: r mntx0na -nxfyme7yf+o 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 2j3rzdxj.g7hp/yh h sf*iv+5ca) f.ospeed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m. g.5x2p y+zah sv3ijjh/o h7rff )cd.*
(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 revolutionsd7 zx trsd2reijk736* as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.8jk *2tddrs73r7ei z6x0 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

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46#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 55-kg person riding a bike puts all her weight on each pedal wh6f gkpg5 1se6aen climbing a hill.f 56 1pkegs6ag The 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 therg p/2 yoou,xe,76sub.mw* si end of a door 74 cm wide. What is the magnitudwupe6*/,7 2sbyxu g,.somorie 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 r*u4zg tetun2g 58rij( rk35 mof the wheel shown in Fig. 8–39. Assume timrg( zr3tu2jneu 5gr5*k 84that a friction 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 jh(zkbviohrc o w4 .*lj-n50/ m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal posiv izj-j /no *oc4.0l5hbh rkw(tion 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 cyl::sj ;alrj o6 joubi,n;e)f:oy g7de,inder head of an engine require tightening to a torque of 38eaoign u,y :;jj feo,bj :o :;d6r7s)l $m \cdot N$ 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 we8ueyd)qqp+( ec l,h(lc,e 2 3a yby:lhen the axis of rot(lc: c3e2qhdeyp ee),(bl,q+a8u y ylation is through its center.    $kg \cdot m^2$

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52#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter.fejy)oy( 2r(geb v:/ j-6/pmsfd,veu The rim and tire have a combined mass o-y/e :/) rj(de jf(fguv 2,spo6me vybf 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 /s 3gf pukjf7q8a s92h zznl*4horizontal circle of r*9nfszjzs87khg4lfu23apq / adius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

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54#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A potter is shaping a bowl on a potter’s wheel rotating at constant angular speegf6dk ui2q1 tnr+ i;3pd fu3;1ip igqt kn+r2d 6(Fig. 8–42). The friction 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 obj 88 gmzs9uwd2cects shown in Fig. 8–43 about gd89ms8 cw2zu
(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 oxyg,o7.fryl x/ogen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

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57#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  To get a flat, uniform cylindrical satellitqu:+ /m0p.bkziel qg1e 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 rocket if the satellite is to 0mequl z+k/bp.g1 :qireach 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 btb4m.l yuzik3,qc:/ a mass of 0.580 kg. Calbmqbzy.,: it u4 c3/lkculate
(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, acc 8rq3c: afgjl1elerating 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 a1 *+wkr xez2co small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the 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 prod o+c wkx2r1ze*uce 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 ate 8(1a lhyj2ej 10,300 rpm is shut off and is eventually brought uniformly toaj j1( 2hee8yl 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-kg 9 zqxsu162f lo.b zlg: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 baxp4hi i4-s akg089 .hv1pmq rfll is thrown solely by the action of the forearm, which rotates about the elbow jo1pfk g m9- 4qs48i.x hp0viharint under the 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 considered a long thin rod, as show5258hqdpf5 v-f- q0qu umbwhpz+lg ; ln in Fig. 8–46zdhl5 qffvq2ump;g+b wp lu-55h8 q-0 .
(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 consismgr5w109 rzsk ts 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 tw itlxm*s z8:bf.i 13full turns (revolutions) and ml zwstxibf:*31.i8t 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 moment gwa5; xtic q6ic6:bs8n trse1ni 37- xof 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 devj1 v:zy ;q54f xuhuddh(w ;g-belops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

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69#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A bowling ball of mass 7.3 kg an .vdo xgnswl+5;cl-e/ d radius 9.0 cm rolls without slipping down a lanlld/x.gs v 5co+e w;n-e at 3.3 $m/s$ Calculate its total kinetic energy.    J

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70#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate the kinetic energy+lv4cvtlew/( :7 njx-ru *b hy of the Earth with respect to the Sun as the sum of two t :w -n*t/cxl jvrv7l4he(u+ yberms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

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71#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A merry-go-round has a mass of 1640 kg and a radius of 7.50 1z,v4lng1 q lye ;nh2pm. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution p1lpl2nn yhzg41q ,;v eer 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 r/xc,r qdt.fc6qzb :k7vwl ;+qg2bm o/olls without slipping dbtbq.qr+ :ovqx67k;m w,c /gcldz 2/fown 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 stard y85sk cgwe byek:9;*ts to fall and its lower end does not slip. What will ;dkybc*weye8 :9gs5k be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

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75#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the angular momentum of 1 oxwad42p( yla 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an anguldx(wp42y1ao l ar speed of 10.4 $rad/s$?    $kg \cdot m^2$

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76#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) What is the angular momentum of a 2.8-kg uniform cylindrical g dzs9yls8ne5 1rinding wheel of radius 18 cm whenyes5 8l9s dnz1 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 hisiq cgy3 ;q88wb side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the spe8qqcg; 83 biywed 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 Fiiys)uqu:tz4zu,(w3 m g. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straimw,4zsuuyi: ( tu) 3zqght 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 rotati a1o1v(i-jckvq l 2/ieon rate from an initial rate of 1.0 rev every vj2e -oq1ii av 1l/kc(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 arv paw790bm/li9og +iround a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. Whalmpi 7r /oi90vg+ w9abt 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 spinh fh1 dz9sn4x5ning 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 momentum of n(,6mia4er 0l.unv e-ezk x:kthe 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 disgei8wm3 )mz m*k of moment of inertia I is dropped onto an identical dimge iw *)3mzm8sk rotating 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 .cbh-p) tuzi,acc -9 gv; 9lplat 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 kn7a;+5c(ognoaylzuz r 4 8d,pg stands at the center of a rotating merry-go-round platform of radius 3.0 m and mo ,4az u lon+za5coy(p;r7n8gdment 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 angula2b.bqex8+zvqs z7gb4 x 1jb-3 ynmuu/r velocity of 0.3qysbb1g u 8zx bm-n7b+/e.4zxqj2uv 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 dwhi(t /mcgdf()s3 7.9febkd rkarf, losing about half its mfc/( bsk.7f 9gie 3)khtd(m drass in the process, and 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 w /8sgi99z ;p1w ynavyjinds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

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89#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An asteroid of mass fv /q*b:djzjo) *ii08 zb8evx$ 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 can rotate freely wit*6nta-w;(l0 wor5 hvlsng- mlhout friction. The moment of inertia of the perssw-vw *o; 6r0-5mahlll tgn(non plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?
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91#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-roundl -iqe8h*o-e cco,ydo3-1aio turntable that is mounted on frictionlhaqc -o81co-ol*deo , 3 eii-yess 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 with the end of t w lc-5p2ixy/fhe rope lying on the top edge of the 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 w5-xiypwc2f/ l ithout 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 facj- x nin,vp+lztz)0y1vjj.t 2es the Earth. Determine the ratio of the Moon’s spin angular momentum (abtyl jj2-1t+z,i )vvzp0njx.n out its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

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94#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A cyclist accelerates from rest at a rate of i uyzmlo9jm;y /2l3 9f1 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 shacumcj b1w:.t e(( fmp*pe of a uniform cylinder of radius 0.20 m acquires a rotational rate((cptf:j m.mc web1*u of from rest over 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 cylindrical disks, each of mass 0.050gn8 mmvg,4yt: kg and diameter 0.075 m, jonyt m48:gmvg,ined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released 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 h f7yvf6c)a 2s(jy:esangular 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 o* 1c8b9+ltigrm dqa y(f 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 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 tbtqr*+li8m1(c d yg 9ahat 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 for it to rgpn,l: zqzl 3.: r;eduse energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 140 q,rzlen: .g;:lpzdr30 kg, uses a uniform 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 /iihzxrmn 4b9ra5e qj i.2 62oan $H_2O$ 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=/7yasul )f6e6o tnyfi:ezo0 33.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

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102#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A uniform rod of mass M and length L-put1qonps(l u ;;j(c 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 acco(pc-u 1;n;lq jsp (tueleration 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, and we *jzz r1bdzv24 want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8rdz* zb4vj z12–55). 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 on a flat road is making y e)ovjj*h19 7ut6lnng1ue x 08xj4kva turn with a radius The forces acting on61)4 7*tjn8x uynvhjx l 1g 9vj0uoeke 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 1z1*l abu8z a,w.5 m and begins whirling the rock in a nearly horizontal circle above his head, ac1lba 8z uza,w*celerating 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 skater’s body as a solid d :2ea ig/ 91)gvaforlcylinder and her arms as thin rods, making reasonable v iaefd)1o2lr: 9gg/ aestimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

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107#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  You are designing a clutch assembly which consistqrl k1tr;e .9es of two cylindrical plates, of mrker.;ql91 teass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ai +n,xqz.rz;vlong the looped rough track of Fig. 8–58. What is the minimum value ofi, vqrx;z +.nz the vertical height 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 assumev tm,u35-qctnavvto/ jt;u: / $r\ll R$ 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 revolutions as the car reduces its spe y 7tsb5h969ylrn8ea ted uniformly from 90km/h to 60km/h Thty895bt 9 7ay6 ehnrsle tires have a diameter 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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