A bicycle odometer (which measures distance traveled) is attached near x wg2 +d/p6u/b01ej0hgmdnebthe wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle wd/21e6gw+jumehx pn bg0/ 0dbith 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the gll/19kqa1:x-q , ttm 1hwiq hrim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acq i /a19q-th1:wgqhxlmt ,1 lkceleration change?

Could a nonrigid body be described b.v. kzp*,kn mx(vwxe cij av71 7kc.h,y a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explg )o l2ys76ddldxb cr5;p5bb*ain.

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 to do a sit-up with8ewgag j22/ wz your hands behind your head than when your arms are stretched out in front of you? A diagram may help you twaw28 gz2je/go answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three6oa 0oe(v 3j:f*nq dhb at the pedal cranks. In which gear is it harder to pedal, a small rear s nh bfo0o 3ea(:q6dv*jprocket or 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 to run so/,to i1-ha(batbmi ()p s;h fast have slender lower legs with flesh and muscle concentrated high, close to thetos h h;aom(a1b- t()s,bpii/ 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, o;vo e* ttoq41x( d+lz )cli6w wpw4f2narrow beam?

If the net force on a system is zero, i6a +ztpiknp ,.i;+k dvrop +.cs the net torque also zero? If the net torque on a system is zero, is t+z,p6t.cop ridip k+; a+.kvnhe net force zero?

Two inclines have the same heigh)*aqs loh7 x6tt but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be o7xq)6 l hsta*greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclinezqep0;pb *qs2xp rm*r-/do y ;. One sphere has twice the radius anxpy *-mrqesq2;p z0/bo p;* drd 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 energy at the bottom?

A sphere and a cylinder have the same radius and the same mass.bg8- jztx9s-c13eb ysq; r)zo They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speezt --)jcq;x b9ger b1yo38sszd 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)q+mb, vck kp) momentum are conserved. Yet most moving or rotating objects eventually slow down and k,bvmk)) cp q+stop. Explain.

If there were a great migu1u-st2gyi4oqi cg 4s80vbu1 ration of people toward the Earth’s equator, how would this affect the length of the dqg04i1yo1 u sbtv2c uu84i-sgay?

Can the diver of Fig. 8–29 do a somersault without having any initial rotap mves72x4. xjtion when shs pvx 7ej24.xme leaves the board?

The moment of inertia of a rotating solid disk about an :u iyg-(3 xn;sztqs6aaxis through its center of mass isnsax ;y i :g(3zt6qu-s $\frac{1}{2}WR^2$ (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 stool hold xqzz(:hk87n k7vnx4a ing a 2-kg mass in each outstretched8az47kkn :7qx nx(z vh hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hox6ls:8-.y te7(z7xpf dcm2-xtgf hx yllow and the other is solid. Describe an exxz8pe (myl. 7x: sd2hxfxyft -6tcg 7-periment to determine which is which.

The angular velocity of a wheel rotating on a horizonbm wsri pep 8 ,-o5tgx.yb)d6,tal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear .i6x 58ptsbd)- mp,wygorb, eacceleration 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 rotating turntas((p.t ljmo 1tr v/qy8ble. What happens if you walk towar(l(r t pj1./ 8qvmtysod the center?

A shortstop may leap into the air to catch a ball and throw it quickly. dpsl+g8y 6gq-As he throws the ball, the uppy-8pq6+lg gdser 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.

On the basis of the law of conservati dx24rju zgffu9+4ik0rnd, 6t0u 3c geon of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicogg9i, +t xz04e fn6 cd30dukfurj2ru4pter stable.

  Express the following angles (* *u 8p1vsdu+)o: feymaswyi in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coinciixsi, 1;+fq 4ae5.uaqmlbtfux* s ./udence. Calculate, using the information inside the Front Cover, the anust;exqsf 4ux iuif.*5 +b.1 l,maa/q gular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directe: (mi5sz uqt7zd at the Moon, 380,000 km from Earth. The beam diverges at an ang(5: zusmit z7qle $\theta$ (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 6b,+ss,xteptq0 vf7g,5* /sc 3 ea /biyat-yuh500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. W,s h3atqvcb70b5/, se/sit-py*eyx u+ ,tfgahat 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 another child. xhyins;u: 9e8 If the ball makes 15.0 revolutiesy ;8u 9h:xnions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How mmaf c-td 3 4-e +sd7arjkm73pjs(h8qeany revolutions do the wheels maejq-t3e ahd3+jmas c87s7 (r-kfmp4d ke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotatesd:pnzzmd4 -7au;0d wk at 2500 rpm. Calculate its angular velocity p4-zzddw:dn ;mu ka 07in $rad/s$ $\omega$ =    $rad/sec$
(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 3r3d.9dg) ii(etpxkcin 4.0 s (Fig. 8–38). (a) What is the linear speed of e3dc3t) .p9kdx (riiga child seated 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 velocity of t. abucz6hv rpv*x;ix*3 en89fhe Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speu6 f bm lpsv6p9g4z5p,ed 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?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axxd9k ;+ic2w/bdsp wjxi1 ocn45e3i1 xis of rotation is to experience aiosi x1 dic94+3b5xcdk2n/e; 1xw jw pn acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly ;:cmw qw h6: z3xaplm0about its center from 130 rpm to 280 rpm in 4.0 s. Determi03hwlm:z6p: acxm;qw ne
(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 radius kimm2 13u-cuqef es- 7$R_1$ 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 aboard the Apollo space4w qmgmxj2v 1*/gm6nw craft put themselves 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 durimmwx6 m jwg*4n/1v qg2ng 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 220 s. Tpj8f*5mer0 tk-gdr6b hrough how manyd*f0r 5m rj8ekb6t p-g revolutions did it turn in this time?    $rev$

  An automobile engine slott4 p4i-dsaw -ws down 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 the stresses of flying high mdqzea/;k1n (speed jets in a whirling “human centrifuge,” which takenka/ mze;1q (ds 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?    $rpm$

  A wheel 33 cm in diam qs.y24wj9z9 shw q-bu)d +xkjeter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of tk-9u4+s9w.wq xhs jz2jb yd q)he wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revolp rs 6.rnwar3 c3:mxk.utions before it comrkm .srwrcapn:.x33 6es 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 65 revolut2y) g da/made0-g wsw4ions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have0dysgewd- m 2w g4)aa/ 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 make 65 revolutions as the car reduces its speed un bk4m- agyny9 )7vkzpwst*4)riformly from 95km/h to 45km/h The tires have a di7g9m4zwtv*by py ka snrk))4 -ameter 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 on qe9x l)kdg 4orjvk6 2)each pedal when climbing a hill. The pedalsk qjdr2ko )x9 ev)46lg 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?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is the ma3 yalisri ;4z+4fn6 sygnitude ofzsr443iyiy;s nal +f6 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?    $m \cdot N$

  Calculate the net torque about l-xe :;gf-b;un wke,w a)w x2ithe axle of the wheel shown in Fig. 8–39. Assume that a frictiox w;w-e:-ba2 fk, nl)wu; gixen torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to ther hl0oo8 m*(we ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the n ehmorol80( *wet torque on this system.

  The bolts on the cylinder head o5(q9aom 2zs zzf an engine require tightening to a torque of 38 (oz 52szza9qm $m \cdot N$ 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 ox e9,+0hw*2b tv+otkd v c,fuhf inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through +vc9 tfk dobx,*2he,+0vwhtu its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whem n2sblod.7,ik:z 2 3rxrio-cel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of b,n32-olo:mirc 2d7rs izxk .the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball ,nx 7 k:uzik7ron the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 ,ruxkn:77 izkm. 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.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angula)0 7ab x aeesgwx6.1lkbvr e ph8qo78.r speed (Fig. 8–42). The friction force between he7a ox81bqahx ep)ewes rv6.80b.7g lkr 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 26li2rafv9ptperp8el+,s u; point objects shown in Fig. 8–43 abo8ptve +e u2p;rsfl a92l,6ipr ut
(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 two oxygen atomsz8ogkn9th cp6vyzuoq0+-0 g 0 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 sp+: 7 7o vy2sh2ve bl+xhb2icnrinning 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 reac277oe :hirn x2cbv2 bh+lvys+ h 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylin1bvsb::2 dffpr36 .uuahz 4al der with a radius of 8.50 cm and a mass of 0.580 kg. Calculateb 4pv6u:hzf :f.s a1rd3b2lua
(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, accelerating it from rest to 3 bgffhp pcu-wk /q; 2j3+hgpv52 bn6k5$rev/s$ 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 m tm5sma- oewn7 at.l uo2+,az*erry-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 2uoweam* l.stz,aa nt+5-m7 oother 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 off and is even+ej27jms1ij48 sur0t rj ,ks d)bpa* qtually brought uniformly to rest by a frictism* u4jjs sdr0 jp82i q+bj7)ake 1rt,onal 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 hjjner21 1rgu6i qbt2s6 l:4e a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg bask* 2o o)n1l jpi,f hc/dfvz;0ll is thrown 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 uniformjc ;) / 1oskif,of hvd0lpz2n*ly 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

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 8–4;jj/ vs9v7fcwdn, ggnn)tzux :;xn0 ;ndug; j nvgf,0 j7;;:wx)snt 9zc xnv/6.
(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 two masses, 17-cop/xu e1 ee-3lo *c qrzsp$m_1$ 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 wir3-() nqgamf vthin four full turns (revolutions) and release3-r( mgv anf)qs 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} $

  A centrifuge rotor has a moment of inerti 8ragy3c(p9f+fmsd s /a 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 developig 3 q/lr7b zfh1q(57b,c ;wu)3qnurezo g9o ps 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 roll/gubx5 ;g(5ygkxrt5ot i(gghc-h 1w8 s without slipping down a lane at 3.3 oxgc1t;hg( ( /y5g-x8 55igw trbuhk g$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of r l++ mc ptz)z/yqm)tzyz: -oik3k;w7 the Earth with respect to the Sun as the sum of two t:ytz3zp+zklzq-/wyrim+c 7 tm;)k o)erms,
(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 t bda8 b ..t4d9)axzackg and a radius of 7.50 m. How much net work is required to accelerate it frd 9tz )bac4.a8at xb.dom rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and j8 ;gvgukgym. lnml(9le 2a)2 mass 1.80 kg starts from rest and rolls without slipping down a 30.nlm2;lg yjv. 8lg 9ae()u gm2k0 $^{\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 balanced vertically on its tunav3gn* t,hizy-5)u; 3 ;pdjih yl+i ip. It starts to fall and its lower end does not slip. What will be the speed of ti +uylh3,tan) ivun;z j y53h;*idp-ghe upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg bz9/pb nd tb :2p;fakf -)x:mrtall rotating on the end of a thin string in a circlx;r ) tfnd/bt-zap9f : kmp:b2e of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uov qqoltgy 6 mm4*jidn0 6 j+mi0q-c49niform cylindrical grinding wheel of radius 18 cm when rotating at 1500cmtmyj4vdnmil660i qj qqo g +o*- 094 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands r/7tnk*3fqe( s)yp 8 fhz(f/n6v mzn tat his 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 speedf3s(ynr) f/mz tpqknv8t7 hn*e(/ f6z of rotation decreases 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) can reduce her moment of 4v70huqz+u , c.vv r8gb,m zqhinertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular s mhr,zh87 q,c+0z.uvvu bg qv4peed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increa fm0kec;aag0cv o64fvs7:+;ke p 4xlsse her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate o: k4a0o lf4xcmes vv g7efs6cap;k+0;f 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 centedns706 0w+oadg vw+nor at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0gna60do+ onv +w0dw7s.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 o;lel *mp:dqq nx5x) +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?    $m \cdot N$

  Determine the angular momenyz sr/sfnt4mi:89 f*btum 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.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inernh*jy w z *9bg4/uj3outia I is dropped onto an identical disk rotating at angz*o4wj*h nju ubg/y39ular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at ubfcc2+:2d gl0 b6 armx8k jd.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/gn)8ad)x ab1s un*aj at the center of a rotating merry-go-round platform of radius 3.0 m and moment ofjau*xas 1)n an /db8g) 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 of ir+quj4jkj2,* t0wom0.8 wirk*4j+tu0jqjo ,2 m$rad/s$ 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 eventually colla 2dqcp oejv-59pses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentvj9-oec q5 2dpum, 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 12pter 40a xg /cg*9dj0q0 $km/h$ 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 j;m mh- d7 .nmo4;vptfh1nw,w$ 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 placi3fi ; oy6+-h8gp pwltform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platformpi+-y3 pl; h6 cfig8wo 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 edt;*yw )t1ka-a nxzla a2eby)3ge of a 6.5-m diameter merry-go-round turnta ykn lb2ay a3t -));a*at1exwzble that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the 6srua(v(j u*k0 b: efvground with the end of the 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 without s0(sbvu vej6(: furak *lipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side alwa.ysm +x 5.vag 1 a.ka*bjv-ux y3)zqypys faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) ap*vaz xsg+ a 3yu5-y)xm.jy b.kv1.qto 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 ra8ht;y 9 6s6wbz/xyb vote 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 shape of a un0bgvp n8mczpj0h7 wh+y n+b9pr .v7. hiform cylinder of radius 0.20 m acquires a rotational rate of from rest0.pjn zh8097v b hwpync+ mrh+.gvb7p over a 6.0-s interval at constant 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 n;mj7;0mi 97trs g,bew0vl lkand 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 ot ,is;lm9 7mwv0rjb ;kngle 07f 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?    %

  (a) For a bicycle, how is the angular speed of the;pv+ yq+ckmb zcb.+:p 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.   

  Suppose a star the size g1. pn4 ipustg bxk*f)0ubt5-of 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 radib.sfgtni 1b4ug* kx)0p-p5 u tus 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.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for itidu-u3 ur /w/o to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should bu /iwu-ru3o /de 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

  Figure 8–53 illustratevqkcdo: b v-58s 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 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal s1hsb)k5 hp3r cmkq cptib((5 1urface 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 freely (i.e., we ignore fricto)w0*. ifmtvvu u+ol7ion) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of v 07*v)uw ofuo mi+.ltgravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M hajrfy)c2 9:iqtnx - jr-s radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The-2 fr9j)nr cx-tiy j:q step has height h, where h

  A bicyclist travelinaelr10,ujeulw s7 *)fg with speed v=4.2m/s on a flat road is making a turn with a radiuu1,ajrul lwf 7s0)e*e s 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 sling of length 1.5 m and begins whirli cz86g /lwda845g jvp2s9rrjcdi9,xcia q6 m 4ng the rock in a nearly horizontal circle above his head, accelerating it from rest to a66 vpwii rdg4dx8 ms9crcz 4jl5,a/c89 qjag2 rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cy-30d2j jxyj o, 5 ,hoxuzury8flinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds f, 320o ozh8r-jxf udj, 5yujxyor a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly whq6gdn,z te 3hu qd6t20nmz)6cich consists of two cylindrical plates, of mass 26zz)ud,m6 6ctqegnt0 hq3n d$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radius r rolls along the looped rough track of Fig. 8–p+ x0ai /hg+jl *7nkvv58. What is the minimum value of the vertical height h that the marble must dr7vx/ lihpgkn +v0a+*jop 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 akpxqs;+fj) q20 txghgt)3.h gbh 8x e)ssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolug5/7ss;*s rs.j dz6o u2swemmtions as the car reduces its speed uniformly from 90km/h to 60km/h The sg2 6se j5;w dm/u*msros.7zstires 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