A bicycle odometer (which measures distance traveled) is attached near th-oem bf fs8,9j+oy2w ve wheel hub and is designed for 27-f8vebos oy,2m +jw f9-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. kjeylrryxk* 4 r3)q;. Does a point on the rim have r;r j ryrq.)ey4klxk *3adial 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 acceleration change?

Could a nonrigid body be described by av)n6c,3svxdp1 mxg u- single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force?hpulk2 v3 s76j /+ zbyd2cfrh1 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 to do a sit-up with your hands behind your head than .zp 9zr shk0v5.e:fuwwhen your arms are stretched out in front of you? A diagram may help you to answer th f.9shre0w5zz vkp: .uis.

A 21-speed bicycle has seven sprockets at the rear wheel an 5/avdytrw 3* t*tlzb9d three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocketv3d/9 yal*rw5*t tbzt 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 m;kv5m6f 6czr *m6tsj being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On tht5sc*m66j6v ; fkrmz me basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkeryd *wry u t+):6sslg xigabs 0c(+g9h8s (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net mpycqf82osp*m*xe:5.fc x uhji ,y.) torque also zero? If the net torque on a system is zero, is the nm:.c, oq uspy*p*cj8 .iyxhm5 x2ef)f et force zero?

Two inclines have the same height +ly-wl 9 9rh6 yw.v mma7sbuz6but make different angles with the horizontal. The same steel ball is rmylryl6sau.-6w vz mbw79 9h+olled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneo8mvbdrbh:d; qv1x24 lrzg1 8eusly start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Whxl 4z88v;rm2 rd1hbveq:b1g d ich has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same r (pg)kjy 1d /)opmt9f9rc/i qaadius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the gr(q1k9pd/ /9f r) cjomtygap) ieater 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. Yet most l o8 2lsd5reje8hj +2xmoving or rotating objects 2he r5xoejls+l8 j2d8eventually slow down and stop. Explain.

If there were a great migrat)1lc0r csnbq5m n-2nzv -: yuvion of people toward the Earth’s equator, how would this affect the length of the dabs y0zlvqc:v- nn)25nmc 1ur-y?

Can the diver of Fig. 8m)i 7kz 9. l .4o3vk iy,g3yynf0gh/z bnwma,q–29 do a somersault without having any initial rotation when she leaves thek9 fm 0yz3bv ),y4.gk.q3m l oz/ywhii ,na7ng board?

The moment of inertia of a rotating fs)w0g(( . a;bwa qqhrsolid disk about an axis through its center of mass is gqs0wa)hb fa.qw ((;r$\frac{1}{2}WR^2$ (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 sittingxotcg p vp//() on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your ang) xgt//p c(vopular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howev)il. aim6k d4a;(iw luer, one is hollow and the other is solid. Describe an experiment to dealiui.;l k(wid4) m6atermine which is which.

The angular velocity,6gwjjqe ay2) of a wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angujqa,jw6 ye)g2 lar speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turnta,szplu xsv:** ble. What happens xv, **sp lz:usif you walk toward the center?

A shortstop may leap into the air to catch a ball and throwmjo mxstzcb;ml9/s n)zzqv 4)( /3u x, it quickly. As he throws the b l ,tn4bcxj3xsz); z9(smvu q/)o/zmmall, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discusm 4vdnctizwb(0d: +t /j;sw:ns why a helicopter must have more than one rotor (or propeller). Discu tw (bd+wm;cd:nzv ji4ns:0t/ ss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in +m7qcguzv htl2+- e:d)ndg8y 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 becauseoeuf01. nj5- v;w 1h*cysxz tx of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters j w5* fesc 0z.-utv hy;oxn1x1(in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at t/ s3oim,c q) znwvd5r9he Moon, 380,000 km from Earth. The beam diverges at an anglecv / wmqsrd)oz9,35in $\theta$ (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 at0:umf jgvit9 (:- otcu,4pl pd a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration u p-0:(tg9:j,u d pioml4c vtfas the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If t o: (*w0 d4g3zmumxggche ball makes 15.0 revolum cx0(gg:o * zw3gm4dutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8tq2+lwvnd;h5 .0 km. How many revolutions do the wheels l; qwhv25t +dnmake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotatesxf1(3 ;zfijw o at 2500 rpm. Calculate its angular velocity in3f;wj fx(ozi1 $rad/s$ $\omega$ =    $rad/sec$
(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 (Fig0n)r ) w u eskocnn,frn0)v .p1x,xgg(. 8–38). (a) What is the linear speed of a child seated 1.2 m from thecno,1p,u)fsn)0rkv nxxg0(r.gw) e n center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Ea ng8,eelv kkj*+7u/lmrth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed qxuzo* 08e8km-e8n f n; chky/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 at 2lzt,j8a,fvxo)5sn6 u zex 1 centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration ov8 s ,)x165nlxtjf eazut2 z,of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm tow73o 0ifm pi-xkp.pz 5 280 rpm in 4.0 s. De3fk i- 50p i7opxmzpw.termine
(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 radiu)..*s ajqi9k 7 npzllcs $R_1$ 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 spacecrar3,eyeg xjry3p3- :eaft 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 during a 12-min time inrjry:gpee ax3- 3, 3eyterval. 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 i g .j :4+8kjenlt 3 dj7wkfx9ke:fhmp4n 220 s. Through how many revolutions did it turn in thff9kej3n48 j.+jk k7lep m t xdghw::4is time?    $rev$

  An automobile engine slcma+2 bgkbo: 2ows 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 fo -hh2 ), orxokwwzln*0r the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.olxkw,on-) 2 hhz0r* w
(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 from 240 rpm to 36-s2z*gf+r shr0 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this tifs s g*+rrh2z-me?    m

  A cooling fan is turned off when it is running adu;b*: gcqg e hp(7ko b:n3pgsloi0 6+t 850rev/min It turns 1500 revolutions before it comes to a 7gqcih oups p*6: g(n3gbb:0+d;kleo 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 revt1hgv1 x5 sgmh/sa3 qq( ypl)5olutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter otax/ggsh1qphy)m5vl( s 1q5 3f 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 m(v01us-zquc *ri jc a vr+4,muake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires *usq14z-vcuu0 ji(am+cv ,r r 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 on each py8wxo,wf/* gw p.t (eoedal when climbing a h /8 xweyt*gowfw,.op (ill. 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?

  A person exerts a for5zk )xsynswjln:u+/(w7z d6 jce of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerk/ j:+ x6)u5zjs7ns ndyzwl( wted
(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 axl d )4/zi :ni0*csnoxldw qj:w5e of the wheel shown in Fig. 8–39. Assume that a fric ndwcj 5i0/q sd* :nlz)4xow:ition 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 the ends of a massless rod wh1k;y us9*iuqp ich pivo9ysqup ;ki*u1ts 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 net torque on this system.

  The bolts on the cylinder head of an engin9u2.cfr chj/k e require tightening to a torque of 38 c./jcur2khf 9$m \cdot N$ 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 0umd :x2gdy ij +w4)fn2.648 m when the axis of x2:2 niy+ 4djw ufgmd)rotation is through its center.    $kg \cdot m^2$

  Calculate the moment rx bf+b658bxrx a5 v2qmjmt1p ) (bma8of inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 r x+tf2jm1ba8m(b 5 mv85q6 )rxbxapb kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lighdw g;6khn8 .he3boj-nj wx- 7)d06rbr yl hv4ut rod is rotated in a horizontal circle o.)neulhdrny3 wvk 74 dh 0xbo-68b-jhg w;6j rf radius 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.    $m \cdot N$

  A potter is shaping a bowl oww.a6f q4 ( fi0or 2fqp4sn+ndn a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the cla nfn0 4pdfa(+iq.ro 6wf4 2sqwy 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 inertr6 uj(s0:v* ttih3kuvia of the array of point objects shown in Fig. 8–43 aboujrutv*(:sh6uvkt0 i 3 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 two oxygen atoms whoq65;is9 y; cqzxh0rmi se 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 sate ow1j3(ugz,m ollite 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, wouzm,1 3wgoj (hat 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 ra d;(uu+3gtc x,*sv+m sx j*ua)immab:dius of 8.50 cm and a mass of 0.580 kg. Calcul)( m+3ss t* b,caxu: +;i* axdvjguummate
(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 tdy*l ;o + yxlbob-lv,,o 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 mxqy5k -um70lv /pq4g lerry-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 requi/xl0m5 4ygk q7qu l-pvred 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 eventually broughtbt-uv0,t6av rrd .;opurn s81 uniformly to rest by a frictional torque of 0u8 . as pov;uv-rtt6b d1rr,n1.2 $m \cdot N$ 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-k5ij m q:esuql uhsjl*n8 *ew6m+ k80v/g 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 ball is thrown solely by the action of the forearm, whi 5,5smt-eirp vch rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unifo s55-imvtp r,ermly 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 *4d.sip* 9rr6bwrayj v6qr (a shown in Fig. 8–46.*yrdr rpw a( b r46.sqv6j*9ai
(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 consistsjjkh+ y4q 5(gb 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.]

  A hammer thrower accelerates the hammer from rest within four full turns (re-dy kxa f5g0d;oui,1tvolutioyo1f0gi ,- dt;5dkua xns) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a momen:lv8pxh k/yw)p ob+/ et 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 developsleq70xm 32phzm8;f t m 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 makh 9w6gymn 9l1ss 7.3 kg and radius 9.0 cm rolls without slipping down a lane h k ym1wnl9g69at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect tc ims:u 5.)akio the Sun as the sum of two ters)ki5c.aum i: ms,
(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 716h k*ri4 dodu.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.0k1*di6du h or40 s? Assume it is a solid cylinder.    J

  A sphere of radius 20) 7e wb-smws1r.0 cm and mass 1.80 kg starts from rest and rolls without slip ws 1-)rs7emwbping 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 balanced vertically on its tip. It startsyw9k bhte ; l. ntb7n 6wtj90bji5q4p. to fall and its lower end does not slip. What will be the speed 5n.6jly 07t iw9w b9kp;ttq4n.ebjb h of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentujyhic06h+9tomf9 j1zm of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 0 j1 9ijy+ofzhmt9 6hc10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniformn) qvk(raagg8 .m0(dyq/la -rcy0 1qa cylindrical grinding wheel of radi(0m). 81agy rkq nq ld-acyra(v/ag0q us 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, han;cb dt 4(uuh*.n;tx lg6yyd.vj )g5dads at 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–g)gt .vytlb6 u( xd; 4ayc.h j;ddn*u548, the speed 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) cvjeohfh5jk*xb5p20;:z;d j i an reduce her moment of inertia by a factor ofbhj2j jfhx p:v05*5 eo;zkid; 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 speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation 2w9(.2kidkl-ycfge mi9 ume z4lj- 6y rate from an initial rate of 1.0 rev every 2.0 s to igwej2lmlz9dmfek6-u4y2 yi k 9-(c.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 vbsqb2xta+ -z ;ertical axis through its center at a frequency of 1.5rev/s The wheel can be ;2 s+-xzbqabtconsidered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentumh,*uqp shon+6 2 tfy dvp-8jn1 of a figure skater spinning 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 momentum of tzxsv(s1cpfi9v-m:k) wgf)4 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 inertia I is dropped onto an identij15c+bd+rh8/ cwms azj/uh k2 cal disk rotating atz 2j ajhsb/c81 krhuc /++5wdm angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns algv41gz 7sb3 rpm(d+s t sx86at 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 standsj9m2qkfi75j e at the center of a rotating merry-go-round platform of j9qmjie 752fk 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 freel reuvy jz3/q:c;k2zrakaig . 0hg -8l+y with an angular velocity of 0y :razkaiue+j8 2kq lgch3r/ g.vz-0 ;.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)?    $rad/s$

  Suppose our Sun eventually collapses into a whiteq2 olqylnky7 .qyg ;96 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 momentum, what lgy 6 q9 .kq7lo;y2qnywould 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 inkl t7f3o7.sam 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 }$ $kg \cdot m^2$

  An asteroid of mass r aj a694owulq(h .xdnl 94 a)u-jafb2$ 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 rewdfq zt z+467ahrud28st, that can rotate freely without friction. The moment of inertia of the 8dfzrdu6w24+ z7qht a 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-rou *t8sps.z03 fgmprc( 25ljyty nd turnta(pjs*tftp2l3m 5sc yrg.yz80ble 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 ground wi) xu,pnry b l20,iyd(gth 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 slipping. What length of rope unwinds from the spool? How far does the spool dgpn(rli 0xu yy2,)b,’s center of mass move?

  The Moon orbits the Earth such that the s3 )j-otj id7wlame side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latterlwo-7jt)di 3 j case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rateptg q.kc8kix ,*m51x dj 3s,rz 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 uniform cylinder of radiut bhniqx+ 0hi8w /7w7ws 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at hw/0+w q7b7inixh 8wtconstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical diskscxn8n gnea*gr*.3hl / r eau5(, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate t3ncrl* a n*g ( g8nexr5./uahehe 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?    %

  (a) For a bicycle, how is the angular speed of the rjwf0t2fu a;3 lear 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 of our Sun, but with mass 8.0 times as great, were r*5ayz) zu mbx hpcfr)hv/ jd28i:5;auotating at a speed of 1.0 revolution every 12 daiuz)) bf hmacr8v5z2:/ y j5aphdx;* uys. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to 045ocmt8de/h a d:jhg use energy stored in a heavy rotating fohtj/5mc e0ddg:8a4h lywheel. 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 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 illustrates an pm wtewb/:;p6 p9 t8sf$H_2O$ 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 hor.f x b e27cbnl,l-gv*lfv.;zj izontal 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 freely (i.e., we ign- 5x szebno 3l(zp0y.hore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. 5o(e0zhp-.x y 3n zblsAt the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts 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 standing vertically on thei.qpg1, 7+) l pfjjxsb floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which .+7i qjglpfs)1pxb j, it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat roa7u) 9jo0 4na6jr hwvkid is making a turn with a radius The forces acting on thja4r)ihnvw 06kj9u7 oe 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.z88 ogk:cybbfr+v -isk/+ ;cm5 m and begins whirling thfc: / ib;k88sgrk+ov mcz-by+ e rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body w9)tk:rqf l,das a solid cylinder and her arms as thin rods, making reasonable estimates for the dimq9)fwr , k:ldtensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of tj+d/mlo i w6*fwo cylindrical plates, of 6o/m *j+dwlf imass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. 8–57:k tfqey ,:d*jriik1 5 j/vtv8. What is the minimum value of the vertical height h that the marble mustfqk1*d/ v ijk7 5jr,yei:tt:v 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 asw;sd nu;r,j .ly(ut5zsume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its sp7-6uit. 2 m2vuurspkoeed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular skir u67u .m -v2u2otpacceleration 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