A bicycle odometer (which measures distance tra:875simjdznf,n8l y3cwhm 0)pc)nm pveled) is attached near the wheel hub and is designed for 27-inch wheels. What n)yp midlnj 7 :8h)cw fm nmz50,8s3cphappens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point olfd cayh0yc, r3l3w+6 n the rim have radial and/or tangential acceleration? If the disk’s angular 3dy,3l warcy 6hflc+0 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 describq8q4py0g; qnod 5/)jtgfe25 k/trmj e ed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger bfm)o-i w92qk0 w).zxm xxj:dforce? 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 yo(hrr56h p(w r (es:zcaur hands behind your head than when your arms are stretched out in front of you? Ahh zc65r:ear(rp (w (s diagram may help you to answer this.

A 21-speed bicycle has sevepf9uh z1/o6( wx ghdfk/y( n)l si+sr6n sprockets at the rear wheel and three at the pedal cranks. In fzdsxroskhu(( w+lh/i6 1pf9yn6/)g which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being vk(:f0kw1f fm2my3c 7f,tpen able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is akv yk70cw12f3m( fe , tfnpf:mdvantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bearvszoby*.7uh : 7r:fdm?

If the net force on a system is zero, is the net torque also zero? If the net 8hu*+pu 2a:jgqmrf iu61rj d/torque dp6r i2 j+ f*:juqh1mar8u/ guon a system is zero, is the net force zero?

Two inclines have the same height but make different angles witzcke*i )bvat7h201y8f: 6 fz ) jvfniqh the horizontal. The same ste18q : vy0eackiv fz7fhif))tb 6zj *n2el ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneou h9)0iblk.y9rqbssw. f pzk3 (sly start rolling (from rest) down an incline. One sphere has twice the rad .flp9qk k b3ry)h. 90s(wszibius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius ag dt*:3uzw+. wvl vcj7+zmwl4nd the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater totalv u:m+wz37*vg+w .cjlwt 4ld z kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular:0b-vogr9 hejc *7ve u momentum are conserved. Yet most moving or rotating objects eventually slowrcb- vjue 0o*9h7egv: down and stop. Explain.

If there were a great migration of people toward the Earth(s 09zm vna4wd’s equator, how would thizsw dm9vna( 40s affect the length of the day?

Can the diver of Fig. 8–29 do a somersault with.hg +3 s16ix gc4kjznsc g+h/mout having any initial rotation when she /g +hk.smzn +cgjix46sh1gc 3leaves the board?

The moment of inertia of a rotating solid disk abk0,s2qujfwm/k7v+ 8q/j0vwtgcl oj + out an axis through its center of mw0fk 8umj/jv+sg cqk 2ov /0lj+tw,q7ass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating a/a5 et1woygz zqy5 )g2(oz(pstool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease wqz/o(t 5y azaeg 15oy)(pz2g, or stay the same? Explain.

Two spheres look ident na2)kh+r4,utn:ce +fxtwp f4ical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to deteru+e,f nncrk f2w4:t)+xahp 4tmine which is which.

The angular velocity of a h2hc(4prnc 1or4pu+n7 r uw4swheel 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 whee(c7up41nuh2r4 woh crp+4s nrl. Is the angular speed increasing or decreasing?

Suppose you are standing 0m/t 1n5zmq . fz b;dokm-bw1o: gfro3on the edge of a large freely rotating turntable. What happensm 0q .otg3ozmfk ;-zdrf1w1b5omn/:b if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw opw2.ojdf87j+ x* qu x5qq(dv it quickly. As he throws the ball, the upper part of his body rotates.(pj+.dqwoj*2 7dou xfx 5 q8vq 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 conservatiwcmwn9q3y-i t u. er2qat5e 8(on 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 k-et(t mw.8w3yq5i 9eqacnr 2ueep the helicopter stable.

  Express the following angles in radians(s s*or )6) ou)vxxrkh: (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 becaq huom7mm* +,guse of an amazing coincidence. Calculate, using the inforqu,mg moh7+*m mation inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380q1- d lcrim/v9i;/dzj,000 km from Earth. The beam diverges at z icjm;l r1q//-d dvi9an 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. When th39yuhg/x ifr-rp akv l4b4; v9e motor is turned off during operation, the blade9-9ryhvfp i /; ub g4xlv3k4ras 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 b fq0c9:mebo +ves-f4 floor 3.5 m to another child. If the ball makes 15.0 revolutif +-c eqfbbe 4o9mvs0:ons, what is its diameter?    m

  A bicycle with tires 68 cm in diamet;wb ;h/bswb,ebka ,l (er travels 8.0 km. How many revolutions do the wheels makebeswa h/ (bk,;, blb;w?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate .q-vvd yz qjczpp31z, :v:ao+ its angular velocity iz j,v1qy-3o p:czz+v: dqv.p an $rad/s$ $\omega$ =    $rad/sec$
(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 completj*zw b+b0/ig kk :6-p7k zxnbqe revolution in 4.0 s (Fig. 8–38). (a) What iszi jqgpz/n bw07b6kkk -b:+x* the linear speed of a 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 kjz/* xj38zwe 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 9 p8 r.q(qad0bot;z vg9dfi,fa 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 tha+oh h.a kp9.de axis of rotation is to experience an accele9 o.hhakd .p+aration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rop(,1wz l m3u1fx o/nrpm to 280 rpm in 4.0/1r x 3 wolupf1m,z(no 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 radiug3l ge.x8p(l res ph *cpg6q+9s $R_1$ 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 Mo6/u7tbfr ; ar/nnk.h fufd /h)96ogdron, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their /b/frrrak.)6d 7tnnu hdf h6/;uf o 9gtrip, 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 220 s. Through bkn(4kv e25vy f (zn6dhow many revolutions dk(kfe5n v(4n z62 vbydid it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rshjxc4fsb a9h r+9 4/ypm 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 highspeed jets in a whitfg ) uj 97wv vrar+:9p/y2qafrling “human cent 9:7tyq u aj2+ f9pw/)gvrfravrifuge,” which takes 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 diameter accelerates kp 8flqdd*7un+(z,o auniformly from 240 rpm to 360 rpm in 6.5 s. How far will a poiua+ z8*,l( 7kdndqo pfnt on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runnin o5i ypn+nh(c-g at 850rev/min It turns 1500 revolutions before it comes to anin+p ch -y5(o 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 revolutc0 wz t2c8a0dpions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have 0tzcadw82p c0 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 th1el yi*.oms et61mwc (e car reduces its speed uniformly from 95km/h to 45km/h The tires heci 6ysw*o (m.1etl1mave 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 pedal when clid 2.urx -abm1xmbing a hd.rx-2x1m ub aill. 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 force of 55 N g2 h/,y*o xws,( 6lu gkbwq)iuon the end of a door 74 cm wide. What is the magnitude of/i ),6h bulx,o uwws(2g*kqyg 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 the axle of thc;lp8 f7v/y the wheel shown in Fig. 8–39. Assume that a fricc yp;/ltv8f 7htion 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 thn o fi /jl.h cr-xnuivy3dr(/bu(w13:e 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 net torque on thisvbj n/ nxuy w( 1i:clhi.3-fu 3(r/rod system.

  The bolts on the cylinder head of an engine require kt)r2fr (;( mcjnm/ pktightening to a torque of 38 t;/pcf( )(m k2mkjrrn $m \cdot N$ 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 inerti 3,zyah1 n;uqbp 1r2osa of a 10.8-kg sphere of radius 0.648 m when the axio 1bs;zhu12yrqn, p a3s of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of i cz9mt:7bhm8.g: tteznertia of a bicycle wheel 66.7 cm in diameter. The rim and tire havee9g . :zzbmm8c h:7ttt a combined mass of 1.25 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, lg.n5ry+8xg qo ight rod is rotated in a horizontal circle or5+g8 nyq gox.f 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 on a potter’s wheel rotatqa5 we 1e r(szac:zwijki.-6 1ing at constant angular speed (Fig. 8–42). The friction force between her hands and the clayae eszwir5 iw c(.k-1j:za1 6q 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 zw:xzasxp;+ +the array of point objects shown in Fig. 8–43 zxz+p:w + xs;aabout
(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 atozv x :8 2z(6qrzmkvln*ms 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, unifoxn2mih h9,d*0d+ nbfa rm cylindrical satellite spinning at the correct rate, engineersbfi x nhd20+9,h*m dna 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:mza: ynh;ajx y b4,i9 radius of 8.50 cm and a mass of 0.580 kg. C4mnb::hxa j;y, iyza9alculate
(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 baiyldtz opv8*;y-er 2bfa5u 2i-exn pw*bx /8)t, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round ani9y3h7f ;uq exd 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 andf 9xhiey7q3;u 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 w)fe a5:f rrj /x)o7wbat 10,300 rpm is shut off and is eventually brought uniformly to rest by a xof5r))re fw:/b aw j7frictional 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-)d o7 n y+mqsazln9ya:-d0sfn xo91r 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 solemh6mtak8 b (8jly by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscl(8thkmmja8 b6 e, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considerednto8 8bfl zzsk14c2m ; a long thin rod, as shown in Fig. 8–461ntbc8mo z2z kf;s8l4 .
(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 consistab2 zhdmp/u)(fny : k(s 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 accelevo xr0 j;ayg e*3czjka5/z9k/rates the hammer from rest within four full turns (revolutions) and releases it at a speed ofcr0k/*kox59; zzj/ g ayveaj3 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 inj: 0weo.wra vs quiw,.as76 2rertia 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 develops a torque of e l1*k1gdz.m8m pbgx+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* ltxe3nl;j*j s without slipping down a lanl tj*3j*xlne; e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with resyb vt *y knb+rt(j:r,(pect to the Sun as the sum of tt yr+v rnkb ((:b*j,tywo terms,
(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 radif,ihcydfq 325y8jfz4us of 7.50 m. How much net work is required to accelerate it from reshij 3yz4,qfdff5y c82 t 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 mass 1.80 kg startql vm,omw:i5+ s from rest and rolls without slipping dow ,q5ilvo: wm+mn 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 starts to fall and itsm q;h i;y0yabvf w++x2 lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground?2q+0biavmfyhxy+ w ;; [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of auz4fg ;st dqf/ -3.gw 5ecnnv3 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 c3nq-wgtd4f.;z5fe3 us/ngv m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a l 1:-omncw jwqf.a fxt7* d2f/2.8-kg uniform cylindrical grinding wheel of radius 18 f w/xtac.n mlf *:jod71-f2wqcm 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, hands at his side, on a platform that is ro5e;nu 2tajp8b1h; m qhtating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0h1a b8j;eut 5qmph2n ;.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 inert*/g3a 1fb. 7yorlxs qtia by a factor of about 3.5 whenbxq* a/l 3t7g.or1sfy 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 rate from an initial rate of 1.0 6nx0.q4 b 1x5oxckkryx:t7ca rev every 2.0 s to a final rate of qct046xkcy b. xon5rx:1ka7 x 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 rkuvpcz yywz gugb b867q-80wo4* 3i z2otating around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotati0-yw8 *v zgu68zw u p27qi3bbg4zykocng wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum hteom: hhal-- 5(x8hi 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 angulawepc8: 77p2t l ql4cfzr momentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inert/t phh22n+4w5ymzp5n;q qa kxia I is dropped onto an identical dihp2h5kq nym 4q+;n xw2ap t/z5sk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atpe7f0oq:h s70 uwgp.e 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 a+g t ;piin+3kfye:q7ht the center of a rotating merry-go-round platform of+e+;gh7 :3 kniqitypf 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 a4fnksc-jf+ (8tl 1e c+mp1egfngular velocity of 0.8fpm1nce8e1fgcl++( 4-t jsf k $rad/s$ 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- gzlq) -gi :fd; (zrh6c0z g91y tmt/m*kxjpu 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 momentum, what would the Sun’s new rotation rate be?(round to the nearest intt-r mu)9 t1-yizp/cdxjfz g k*;l0hgmz6(g:q eger)$\approx$    $rad/s$ (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 zjzd(g(drhnni . 7h3 *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 w-gya6b pft6)o0 hyz(9d p5wi$ 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 rt sb1+bsxb6i 0otate freely without friction. The moment of inertia of the person plus the p s6x+t0bbsbi1 latform 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 b8rn-lxe2y 8j stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a momen8-r xe 2l8byjnt 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 e5--3qsuqhp 5t(-k: g axaza wexxl/ i,nd 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 t,xih (sgxtlz5pu-a x:5e3 wka qq-a/-he spool? How far does the spool’s center of mass move?

  The Moon orbits the Eq*mzznf ,0 fy:arth such that the same 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 latt:,zyqn f0m zf*er case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest8g6yh *6x)z 3bczm acm at a rate 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 rcy u:4w3r, uqcadius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque deliv4w3cuu,c rq y:ered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and di rvc4b ,5gopy oj-1z,sameter 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 when it reaches the end of its yz p,b 1-so ,jrv4go5c1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, ho ol52pw h25g0e6eg2o5k ar53gyjbubow is the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotatbojgda 2*ztq fc:3d8:ing at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries oz *otbd3: qgcaj:d82 fff no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it+intae6ez4 2( mm- txr to use energy stored in a heavy rot-+4z6 2mn i(teematrxating 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 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 illustrateslkl ye9ol :96c 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 hol3:9 e ca;:mhg kuvjy+algs*-rizontal 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 leng tme:hbx 93gwch ;8-8grh rrr;th L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of relebrc; hhrmwg3hr txg ;e98r- :8ase, 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 e . dr750ii skhuikd6(standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will c 0krs.e(u6iihi d k7d5limb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with stwk1 e 3/oo1qs/3ruly sfx2+ypeed v=4.2m/s on a flat road is making a turn with a radius The forces actifoq sx21yrlu/yts o+31k/3 w eng 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 o( mq8 d7iqeycmf6(:p m and begins whirling the rock i ye(q8q moc6(mi:dpf7n 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 as a solid cylinder ae6zl n5*k:za:j)xiog2 sg/ts nd her arms as thin rods, making reasonable estimates for the dimensions. Then calculate sjkt /:zggl5o*n:s6)ix2z e athe 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 w(h a4t:j 2ebj,9sqjdqmb/n/ ghich consists of two cylindrical plates, of massqjs/,bhbatnd 9e /4mj gj:q(2 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. lkf5jrk8q5rd lt kue;a(x; 13 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop 5 ux jtfe;3lqkr5( l; dk1ka8rwithout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, butnbz(;nnt8ax e75y h -d do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduceu8) nqn8 /cc4+;3vay can;cld(v k rd8 lw3bqjs its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire?bav8c;r8nc(4n;c8vd n3kq/ldu +qyl cjw 3a) $\approx$    $rad/s^2$(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