A bicycle odometer (which measures distance traveledoqol v 8 b0t5z 1 (4jamiks4h4)c+ejpm) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle w(o5bs4tzkq)4 08c4m +1vojalhm peij ith 24-inch wheels?

Suppose a disk rotates at constant angular velocgsetjeav c r1uj gzi7 :a9w-1q ; ze:6l3w*x(rity. Does a point on the rim have radial and/o caj rgt ir7u*e- :zg:61eq1lsej 3wwx9zva(;r tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velocityxot h)c;.v/2v1vhbfz $\omega$ Explain.

Can a small force ever exert a greater torqueqx*yyu0f:,4zq 7lc ym than a larger force? Explain.

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.

Why is it more difficult tox xhxq; 4 o.-bc9+yjyms3q/bg do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagyx4-o.byx 3gcshj /9qm qxb;+ ram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rez+xvz2yfq: n *ar wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or vz zfnx:*+y2q a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able .9 s(wbv8c k1jk5mt nks:rp*kto run fast have slender lower legs with flesh and mu*mvn8(cp 9jk:ksw1rbts 5 kk .scle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bfki05u0j;ear eam?

If the net force on a system is zero, is the net torque also z * iv apg(pf6v28bmoc(ero? If the net torque on a system is zero, is8pi*gv6c(2 mav ofbp( the net force zero?

Two inclines have the same heiw 5jyw9l :wxlb1y-i3xght but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the spe w9x3ixw -blj1 lw5:yyed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from reslz*q5- r8ebf:jz2 fr(uov2rut) down an incline. One sphere has twice the radius and twice theru2lfbvu8 f-*rzre qjo52 :(z mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same m5 rxc -8 g1akfd4tvs1e8ls-+nm kf/csass. They start from sc8t4 cfms1sg 1 xkvkad 5/ +fle-8n-rrest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Y rn k4+hn.z.+iegh mi9et most moving or rotating objects eventually +r h4 9inhei.m.zgnk+slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how xqy,b ;ao+z2o would this affect t ,+;oqxz2abo yhe length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rots8ya )uw1: um3xsm9eeation when s1auw mee8u sym: x93)she leaves the board?

The moment of inertia of a rotating solid disk about an axis tch1 f kko /t8ynjz0 i)/t3exgrg95ct1hrough its center of mass iz8 n1xcck0ij1/5tf 9gthr)g3 / kotyes $\frac{1}{2}WR^2$ (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?

Suppose you are sitting on a rotating-l+d fd5hbe4obdfhu kh b0o xs*8 4o,+ stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity incred dbeobh++okdo 08x-,fsh 44fb u lh5*ase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one t (se srakt-c:k8 uhneoi2.77is hollow and the other is solid. Desc- 77etknk( sa.ruh c2eois :t8ribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a hor,a b1vc3(zkc t5;pjnu3zhxp- izontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, un5vz3t bp(c1k 3- ch;jpa x,zdescribe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotah56ivgft/ sd 4ting turntable. What happens if/6t 5 gd4sfivh you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As hev)s jzy1n c70d throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and le v c)1zj7dny0sgs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conser whs)/xop2hn*0x 1adf vation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propelle*0hah1df/ s2n o)p xxwr can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 3:x+q51z aj:. p jdodpq0 $^{\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)    $rad$

  Eclipses happen on Earth because of anxy55,u1 erz f1-hf7qqwcprm*i: bn:t amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as sen1p c5t bw:fhi mu,5:x *1qr- z7feqryen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth;n*1 ciy47gsr zvwbr7 . The beam diverges atzg 4bs yicrn 7vw;*1r7 an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. Wet(u -fjx)v6 ihen the motor is turned off during operation, the be fx(j)-tvui6 lades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anot7 wdu1ll-x7rpher child. If the ball makes 15.0 revolutions, wl u7rw17 -ldpxhat is its diameter?    m

  A bicycle with tires 68 ct ,t;bd joc71 r.*vtiam in diameter travels 8.0 km. How many revolutions do t1tic.at d o j*vb,7tr;he wheels make?    $rev$

  (a) A grinding wheel 0.35 m ix9gdysaqb)r(gko ) *v 4x.o t-n diameter rotates at 2500 rpm. Calculate its angular velocitsrgb.x ogaqy k( -9x4 do)*v)ty 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$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–38).v:3 qcpafg3-f v3r2r/u a)p xc (a) What is the linear speed of a child se3 3p:xcv/caru3rgqf)vf 2 ap-ated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular veld1nhvn pvdpz2/+ 7 xx4ocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poifl zyfx-q h5-4 o4.nldnt
(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?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm wkx/j,h x:zd2 y9byz 8from the axis of rotation is to experience an accelerat /:8k ybd ,xxwz9yh2zjion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceler2+5/zfx grfckates uniformly about its center from 130 rpm to 285f zk 2+xcgr/f0 rpm in 4.0 s. 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. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiuoal7vg2/;sk/ y+h o)pn nxb0fs $R_1$ 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, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts l 1 n7,k)lddhjaboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenlk ,dhj 1)n7ldly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 2.3)gqk i 3ifc5 ihjq)b20 s. Through how many revolutions did it turn in this time?q )g53 iicqhk fi)j3.b    $rev$

  An automobile engine slows down-w)b 123a4ey sj1q y,g aybjxy from 4500 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.    $rev$

  Pilots can be tested for -n,onzxr8g -t the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complett,gz nr8 --oxne 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?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly,sny0,wrd4pem mx yd2wd 2)t 2 from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have w 4d,rsd mde)w2y2xny2m,t 0 ptraveled in this time?    m

  A cooling fan is turned off sfq o-o0 6(k5b,b crhhkfm78pwhen it is running at 850rev/min It turns 1500 revolutions before it comeso, cf7 khb-ofkm(sr865 bph0q 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

  The tires of a car make 6zahbnv a3-niq -)3( db5 revolutions as the car reduces its speed uniformly from 95km/ava()i3b dzb--q nhn3h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car makhd3kf;ry 4)8yu vnc h-e 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The 3uh-)y48 yhv ;nfrdck tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight 1u19wjr x4r ppb+-m 82cu rlknon each pedal when climbing a hill. The pedals rotate in a c2cujl1nw m+rr-pbr89 p u1k x4ircle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. Whati3 hq4r1krc /v is the magnitude of c3kvrr/1h 4qithe 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?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39m5 )k-3o6tcjr( rg blm fg/:nq. Assume that a friction torque of o)5qknjt mg- : /3 rrgfbl6(cm0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a masub8e 0;pj)ggd sless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitudejude8b gg)p; 0 and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requaum97 go,+sks ire tightening to a torque of 38+ 7o,susk ga9m $m \cdot N$ 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

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when the g2dac160(q lfywxz; z axis of rotation is through i;6fl wzx0c g2a zdy(q1ts center.    $kg \cdot m^2$

  Calculate the moment o0m.uw2:zkq p;/omyxwf inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (.w xu/qwpkz: m yo0;2mwhy?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light 5ype1k1mnww- rod is rotated in a horizontal circle of radius 1.2 m. Calcw-1yk m1we5 npulate
(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.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angu4m; 4 cccatk+/4nmrmof8 aq *jlar speed (Fig. 8–42). The frim4*qm+ca4; fonc /m8j4 rtcakction 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

  Calculate the moment of inertia of the array of point objects shown in Fig. 8f95hbpm7zso; –43 abou79sohm5 fpz;b t
(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?

  An oxygen molecule consists of tw(*yc34pac8fer kxhah;t( g :bo oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correcasn:h 5 6-rjqt dfkv:2j8 3)lm(jlabyt rate, engine2bvl6s :rnj t )8ad-5j:hqym alkf(j3 ers 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 reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a rad/9a:er g3rmzv hk a dn3c2u,8zox7rj4ius of 8.50 cm and a mass of 0.580 kg. Calculate4 /gm7vknaz2ra u3,djhr:xoc3re8 z 9
(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。    $m \cdot N$

  A softball player swings a bat, accelerr3fb 0p/ idr9jating 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.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merryj*( q*oso39 jexq rxkp ,p5nc0-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 ra0p3, xocron 5*j qp( *qse9xkjdius 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

  A centrifuge rotor rotating at 10,300 rpm is shut ,qk)s5 zq.gasp4l 49xkcx /jtc:+zud off and is eventually brought uniformly to rest by a frictksx+aqczp 94gukx 45,t czjq/ )l.: dsional 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

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball at d4tfn+x ; l8lx7ltwe27 $m/s^2$ 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

  Assume that a 1.00-kg ball is 6bte)*6ihnmqg 1 bnku v 4b8o8thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10v68nu8k g)b16qbe* bhnoim4t $m/s$ 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

  A helicopter rotor blade can be considered hjgst u s 52,l;gl9zf:a long thin rod, as shown in Fig. 8–4t;5huf szl l9s2j,: gg6.
(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?    $m \cdot N$

An Atwood’s machine consists of t,dwgm4 a 2lbm;wo 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.]

  A hammer thrower accelerates the hammer from rest within four full to1+r3oe 8eu r9n2ehg-dx/xz yurns (revolutions) and releases it at u9e3-g1o dn zer+ex h2ory x/8a 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} $

  A centrifuge rotor h b bv2 ts5w6a4um.2ebhas a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine n5fzd9mso1u5 develops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping v(apbuua:,d q v 7l,3ldown a lane at 3.3 7,aq du,ba:( v 3uvlpl$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of tq z;- v gsuznidl eo3j5,yy:rc5c221ghe Earth with respect to the Sun as the sum of two terms, y iozvd2-e3;52u c ,gs:lcg ryzn5 1qj
(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

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much n:h oz2t9t/y.o u9s kenet work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8. h9tu.to/:knzys 2o9e 00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts fc *u+1.*,j8ftux7r - e0qjt* oxw ncnkqs)mjdrom rest and rolls without slippingo t0n-km jnfc7u**q .jxdw+esc8* )r t1,j xqu down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  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.    $m/s$

  A 2.30-m-long pole is balancy +8ifs.63m; did xduped vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energyd sf8x; i+3p.dimud6 y.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thc 9 lw385 h)vyyzep/v6tzg-s bin string i-gsvlb /etz 5)zc wp9h 86vyy3n a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum ofpaaz2 *ctqm2hm. d8y56 mx*zn a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm?mym npm.zt*d2qza2 h5ca6*x8    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating4(ug:h j pdw;j at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreasesd;(4puhg: jjw to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29)kn. nne+c pk 7s9tjfy- :6,pzp can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s7fy 6en n,+ knps.pjk:t 9z-cp when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her sikbq))wj3ok) pin rotation rate from an initial rate of 1.0 rev every 2.03b w )oj)kik)q 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?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its cezji,r wdn a68j2 p;iw/nter at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg zww;ij6,nr8d2ija/p 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?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.5 1je ocynaq0x;3hqi1cs6g ,/y$rev/s$ 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?    $m \cdot N$

  Determine the angular momentum 2*rndi i sn/*t *.kpfbe9iek5of 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.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inert2ppfy yv-,1ju (+sq ojia I is dropped onto an identical 1( sopf+2 y,-pujqj yvdisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a,6ay 1ltlq5 udt 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?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round pfht5 u8 tg20halatform 5th0a28 gf tuhof radius 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

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity opniqpx 3+ wi/ka.d/ (gf 0.8/dn/qp.k( aiwxg+p3 i $rad/s$ 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)?    $rad/s$

  Suppose our Sun eventual,ngoj:-ge,xugzgvb8k r, 9* qly collapses into a white dwarf, losing about half its mass in the process, and winding up with a u,gkgqnx8*:jr9egv ,,gb -ozradius 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?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 12bhp juy/ (.*k;,ywxp y0 $km/h$ 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 }$ $kg \cdot m^2$

  An asteroid of mass bb(9e7d *z m gv7:dcor$ 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.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotatel2gn lcg0;+fga u1; oh freely without friction. The moment of i;agf;g ln1chu gol 2+0nertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-roun-k,1veu; mjd kd turntable that is mounted on frictionless bearings and;k-m udje vk,1 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.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying on the ye nnkvcjo,+;39: eoh 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 without slipping. What length of rope unwinds from the spool? How far does thejyvec 9,:;+ 3nneookh spool’s center of mass move?

  The Moon orbits the f*qs :vb5k8 itEarth such that the same side always faces the Earth. Determine the ratio of the Moon’s s8vb: 5kis q*ftpin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rafn hp+a3 0/wojte of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the idz(x*p( u3jqshape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at con3*pj(xd qi(uzstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg azdffr.u2rzt6 a:,0 y4e c /69+n ouya8wizgwand diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo wz.fwz o,:nz 28 rwyru/ueca+9g 6i0t 4ayfa6dhen 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?    %

  (a) For a bicycle, how is the angular speed of the rear wheel (u8. y fnz3(gpo$\omega_R$) 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.   

  Suppose a star the size of our Sun, but with mas6q,zq.(x-o c k xd3tsus 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 3txqzsdq o(6,.uck- x rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to ;jv;,lihw h0g14pjoq use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheiq0 g4vhjl;hj;o, w1 pel “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

  Figure 8–53 illustrates a;jurr +-xw6o 8kye47ag b9gf-/ ovbnln $H_2O$ 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 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rollincq*u,i-y hpc)g on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot fr6 i3odgnt / zavu)*dyx/is43 jeely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assu)3i*d ou gatx/ ji4ds6n3zv/yme that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standids8d ( 3 rbb:d)hg0bynng vertically on the floor, and we want to exert a horizontal force F at its axle so that i (yn srb0d )hg3bdd8b:t will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wilm3u fo(x;ald19 j +zith a radiu9a+ l 3x(1j ud;iolfzms The forces acting 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

  Suppose David puts a 0.50-kg rock into a slt)cgzbzax 1b. hn1m+x- 6r b vod(;3nping of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. Wznv31ax b (+)bpd-xtmgzob.6hrn;c1 hat is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cyli tn /u2ni/7aqfnder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and ni2qu /7af/tnwith arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical pl1oy adg,/ozm j+w0pl,is whv.2m*gm, ates, of mass mjz.lh2/+ yvaoo , g,d*wp0 smm1g,iw $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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?    $rad/s$

  A marble of mass m and ra.gjp.a: n+ sbrxy d)l2dius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the .)dl.x+2g as ybprn:jmarble 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

  Repeat Problem 84, but do not as;.5kjhqn7m;fv0bo y 9u9 fagk rp x42xsume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the rfxr2*h1. x1vt7h)3a cxc f4jfu-tkw car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration ch1xxv)2cf 3 rxkhwfr a41*f jt7u.t-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