A bicycle odometer (which measures distance traveled) is at4l 4c c/xux:cjjvs+*o tached near the wheel hub and is designed for 27-inch wheels. What happens ij ocvccx4*/l4+j:xs u f you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular veatf g:2hkdfk5nb r: 6rn7l:;zlocity. Does a point on the rim 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 th6ranl 5 r7: g2fbzk;k:d:n feither component of linear acceleration change?

Could a nonrigid body be de* v2p72k pgskq kh3 ,)z0fbewl7b+d liscribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exehg2 yi3.t5crbx*r cfr3 gf) (urt a greater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with vy8qkjk- xz1 me7l:6megg 1 *myour hands behind your head than when your arms are stretched out in front of you? A diagram may help you to ansv kmmx: zq *gyjl8-k61ege7m1wer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pep8o2 zwfp6ga+ dal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small frontg 28+zpoafp6 w sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fastqv:pm vkgm5 ,3 have slender lower legs with flesh and muscle concen5:m vm,3gv qkptrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–)/a:oy2ciq wfn) z owgjw; 1f)35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net t g)ohqul a;.etc;c (0oorqueou) hc;lc 0.etq ga;o( on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the hoeyl4m07fsf + v,uv: yerizontal. The same steel ball is rolledy e0f,:+l4fu e7svmyv down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. One i +j8:rga4k25 y,g5s e hmlzqksphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the b2+:8h5gk5ms,l 4qkrzie ajygottom?

A sphere and a cylinder have the same radius and thk ( jtaqlc5y;-d5dj (jv( 6alre same mass. They start from rest a( dl5a(v ay(-dt;jj5jkcrl 6q t the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conservkc9- y: d7* m vokw)b8m.yp,h rq/ssqded. Yet most moving or rotating objects even7*hm-sdw /:bdqc8,ko qv.yp) m rk9ystually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, 2 xz. ztos8hr4zctl8 rqpz8l/3;9okr how would this affect the lenzr /t lopx8s.9zqzh2kcl8 4tor; 83r zgth of the day?

Can the diver of Figiv)jrb6,*wam89e(dv eld2r ,qkm y4 d. 8–29 do a somersault without having any initial rotation when she leaves the9j4edam*q2dv y(blme )6 8rivkwd,r , board?

The moment of inertia of a rotating solid disk about an axi6 ,vdlxw 4vqc.s through its center of mass is qdc4v x.vl ,w6$\frac{1}{2}WR^2$ (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 holdiw,mh, bwb,pu) ng a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity inbbw ,,uwp) mh,crease, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and txzau52 x4),3d n esokyhe other is solid.yd a)5x sokuz2xn4,3 e Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontkyeshh-b* f4ut4 ;o .lal 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 thbes ul h*;hky4.4 tf-oe tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Wh brwly6 psts)/9( ch5*ylr ;hrat happens 6rcy(swp)l r; 5/ tyslbhr* h9if you walk toward the center?

A shortstop may leap into the air tug h 0abwt nm;(tynyx u3)j190o catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite directx ;ubtt0(9y n3j1ya ghnuw0)m ion (Fig. 8–36). Explain.

On the basis of the law of conservatiazvmy -)/y bc)on of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Disamb v-c)y/z)y cuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians0 lx fj)voutk+6p8- ha: (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 9djs,l/n* du tzsr;2 bof an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in ra 9z;sj,bl 2*dndustr/dians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divi+ s:8 i8we/eo1 y hmgh7cudj,erges at anh+miu8w 7j,8:yhdce o 1gs/ ei 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 blender7+ 5wxkn;xvs0hzyjs6 rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. +yjx ;5sz 0n7h6wvxs kWhat 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. If th:ww m*bwfcy24e ball makes 15.0 revolutions, what is its diamfb *ymwc42ww:eter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Hcg;6i:hzs x/ eow many revolutions do the whe cz/x 6esih;:gels make?    $rev$

  (a) A grinding wheel 0.35 -a0.dg-zpa yfm in diameter rotates at 2500 rpm. Calculate its angular velocity in g-0fa za- dp.y$rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. hq k7+ql1)chxn yferj c4m:aup/z9z8w y 1* (f8–38). (a) What is the linear speed of a child seated 1.2 m from the centerufzck lj4c(8 h:xyhr1+q z/ae1 n* 9mqpy7 )wf?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of t85m ,iqvve muj.*rdp9he 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 of8 j0h(u -e()pl1ruyev8ycqki 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 tjgt1qcj2 q t+(oa9jh/ he axis of rotation is to exper qo1(jhg9 tj2/j+acq tience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelero6.)k tu we+t7jkhrz/ates uniformly about its center from 130 rpm to 280 rpm we7 o)khuzk+6tj . rt/in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiusr)rnk3b xun 67/nok4byh., kd $R_1$ 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 aboartrg8t+vgj3wtll ;zf7w+ . u3 td the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation tfv8 g3+l;l. 7tug3wjw tz+trt o 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,)0j4:fcec ltb ai36ys1 qfw0 z000 rpm in 220 s. Through how man1 f43 y:ibt6lf0c0 qz)je csawy revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 120m lxj,3/ul*1z ir5qn y6xfwq3 0 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 highspeed jeq(q ,k /q+*d9/a advjlchi)d yts in a whirling “human centrifuge,” which takes 1.0 min to turn dda qq)ak,cyq +*//v ihdjl9(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 dia kyywg; pdv83;meter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s.8dpy w k3;y;vg How far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it isqq /* 2 0evd;yvqf6qen running at 850rev/min It turns 1500 revolutions before it d vf*2vyq qq0e6ne;/ qcomes 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 mg0 tm x81r/qv k2wzll,ake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diametew/01 tlzgk m v82,rqlxr 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 revolutiongtv.v8uij ek r:m( + b6oiq;*is as the car reduces its speed uniformly from 95koi*q;+iv8vj(egi.tk mu r :6bm/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all bv1g po(t7c,w her weight on each pedal when climbing a hil7pb 1g,v t(wocl. 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 ozb7ikms.x k3;oe( 03lishbd9f 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerdl03khso(b;kxe 9i z7sbm3 i .ted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in0e.qgtnf2m ,t o g(p*j Fig. 8–39. Assume that a frict(gfpqg,j2* .mot nt0eion 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,h+uapg bxiq46sfd vp7,/+g h 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 t,+ g sq+ufvaig pp,h7xh6b/4dorque on this system.

  The bolts on the cylinder head of an engine require tightening qc -ve5y(rlu1to a torque of 38 ru(vy5c 1-lqe$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 z61z2n0 t-gib fpep l *qqku/9g c7e*dm when the axis of rotation is u1tcl* *9gzi 6q2kg zd ep0n7/ebp-fqthrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia or4p9ap/ng0v9 ++e qg:ib ci nzf a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 + 4r9pgpiqbniv/+ 0ngeca9z: kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball onaxfw1** ooxyi/a7z(w9u q l8x the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m.9lxw (7 u 8zwxofi1**xoq/aya 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,g h)/dl+dzdpa3fn/begh2rkgy+ s5 4 constant angular speed (Fig. 8–42). The friction force between her hands and the clay is bd dp,deg gy r+/h)+gn f/slazk5h2431.5 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 inepwly k9un0c r vwv9s ng;2;4(trtia of the array of point objects shown in Fig. 8–43 abov;cpn ; gtus9vw0y 9k wl42(rnut
(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 whose total mass is g )s+q1fhd;6ml y/5 y rlkwk9f$5.3 \times10^{ -26}$ 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 cylinajieamz8:st1h: e ,q/ /br (gfdrical satellite spinning at the correct rate, engineers fire four ta/ta q8fji,/1:bzh( se ra:me gngential 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 radius of 8+0kfpl j2tbr1; 9fbfp.50 cm and a mass of 0.580 k9 ;jkfp 1f2+pbtflbr0g. Calculate
(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 ru y(xqzxt/+j0s*1xtio76 q hmest 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-gotudu4)mw+j3a2 o;bc ai7 vpb8 -round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. i)aa jvb 7wmbduu+28cp t3;4 o$\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventuall.f:cuzzb.r4;fso; qorwv3 4zon y3i +y brought uniformly to rest by a frictional t3yz3z boi+rnq zf; f;w.: ooc4s4rv.u orque 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 7 3:bq:bvba*pzphc09 w- v rd 4o$m/s^2$ 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 bitr9i4*7o ;ivvkc2 jk10b w naction of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fiiv;jkw 4vb 2 01c*i7tnoirbk9g. 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 convr-ba bns97-g sidered a long thin rod, as shown in Fig. 8–46. b-v9g-b as7nr
(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 tzh9 ,ty) 6wdkcwo 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 (gxk / 4c/mob;cas;u:3-*x- i bbknl cyrevolutions) and relxlb c3k4y cu /-k;sb-bx/*anio;:gmceases 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 bkdwi4 ))w ka:jc)/k8 dwtd; pof 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 develops a tor+7y 4l 5zqlq5oo,uuv2cm/wn 2 6aqivj que 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 q vlc:95aa(r43frc7.d zhjxc (tc gu.cm rolls without slipping down a lane at 3.:(u7zjvcafcc3dg .9 5rx(q ch ltar4.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as theofa -03 +l b*5 a:srqjtoc*qoq sum of two to*3:sqbq q+*5 -raaoto0 fjlc 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 kg and a radius of s ap/oi2:v r/kz 1 w;ebcu( mf+ya*4hw7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution p*mway r/scafhizeu k ( po/42+wb; v1:er 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls without eso 7x;;pvl kzaf7 s/v1zaj*f55y5gj slipping down a 5 *5l gzjaj7kpze7fs y1v/sf a5; ;ovx30.0 $^{\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 k.wy b;sed.58p8mhsptip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energyem s885;.wpsk bpdhy. .]    $m/s$

  What is the angular momentum of )v1mgio8:t, avtx 49uj s9qfh a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an h99gj )u 1aos f4vq8:x,vtmi tangular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum4vyh8-q 8dhyfuaak;+ of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at u8ayv4h - dfy8h; q+ka1500 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, onh 3te+hg ad17k a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fi1a etg kdhh73+g. 8–48, 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) can reduce her momen;0d5tznswj y: v tzcd,vv/f27t of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she mw/z0s7,:zyfnjd2 vt;d 5 tcvv akes 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 ratld8uk5j0nv 647p ni w,gich.de from an initial rate of 1.0 rev every 2.0 s to a finc7nj,p ni4 8v5igd hkl .u6dw0al rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axmh 2q/h pg)0qnis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the 0np/ gqqh2)m hclay sticks to it?    $rev/s$

  (a) What is the angular momentum of psle91ph/h2umbogo 2 8j:wx4 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 momenx/+ z h.xvavgzm(o, a,y e)w(ftum 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 inertia ) sa,1rf*q vusI is dropped onto an identical disk rotating at angulaqs a*fv, 1r)sur speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 d(m*-tcbenys (1o o9s$rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round platforiuz/4s7xiy257ww y pd;c j kw,m of radius 3.0 m and moments iwjdyxp k w u475y/ic2z7w,; 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 ang753ti e ,l96xqq bijdwular velocity of 0.tqx , 9j37i6ldi5qebw 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 white dwa3s*).wu kehi/o iuav +rf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radeaouvuk *./i3s +i w)hius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve windf:ld nnv41brfkfn kewc;a3 2q13h04 js in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass j8y./ t9yy4 myql87k a-;drcy mssk2w$ 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 ct(poze,n;8x jk(e9n4.ga hy p an rotate freely without friction. The moment of inertia of the person plus the plnh9g(x(ept k4p;j yn a e8z,.oatform 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 9c3-nouoce 6 mwin3d 3stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless beari 3ouine cm3n 6dwc93o-ngs 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 with the endmt5(0 f*wwgai tau9ls7wj h *aqa5) w- of the rope lying on the top edge of the spool. A person grabs th*5ai 0a-)mgh(wsu jt7 l5aw 9aww f*qte 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’s center of mass move?

  The Moon orbits the Earth such that t9 js9vbst.9ee a;.lgk hu:,lg he same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentueh;k ,s9 lvga 9teug9:sjl ..bm. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 9ttdcc j55k3fcb68uo 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*gwpql h 6mrz/( y6fz3 cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Cfzp3* (rq6/ywl gz6 mhalculate 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 andox0vxp, nkw8s/ f;h*g diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of x0;v nkh osg*pwxf8,/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 reaunzr, l qip*.s ej+,g1r 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 S1 skub dzf69w:5 gk;qyun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, wha;ubzd k6w kfq519s: gyt 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 use ;hxz6qy k iiwvf1- m(6il 2aq+energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cy(- kal6f mq2i1 + yvqxi6i;zhwlindrical 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 illustrates8+ rc2(xr yl2iwyds1s 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 horizontu4 : 5ywluc3,v+z czg)ayl;jq2fez g.al 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 ignoref;v,hwi-4fh e8 xi(/dkt wo1n friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear accelerat,ohit4(; wdki fw/n-e fxv h18ion 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 verticallytro5vd+rxn;l uw 2,vnoayi4 s/vo;25 on the floor, and we want to exert a horizontal f l2v5xtw/y;+n r 5undo iv4s2rv,;o aoorce F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/n-cj0i7w;xqc 5- jllqs on a flat road is making a turn with a radius The forces acting on the cyclist and cycle w-ci5q-jc; 0 jnxl7 qlare 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 1v9:bn fq7r(n13jf hnk.ttzt6 .5 m and begins whirling the rock in a nearly horizontal circle above nf7n 6vtjfhk13nt:b(q9rz. t 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 8zil -66 9-jusdickgf a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinc- gkjif u69s-li8z 6dning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists 7o:si3 u4zja:rt s:ut) u eo0dat+3lh of two cylindrical plates, of u 7 )sel:zhor:duia34 0tta+jsu:t3o mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 /8f s3dgp(kkxradius r rolls along the looped rough track of Fig. 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 without leaving the track? Afd3kp 8/ksxg( ssume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do e0irexl0lnwj3 av/3)awbq1m 4 lti 43not assume $r\ll R$ h =    (R-r)

  The tires of a car make+nook 78ywwt z r0cfw:- ;rh4s9awex- 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a dihwocs;xzfw-7 wyw +ern9 8rk-0 oa4t:ameter 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