A bicycle odometer (which measures distance traveletu2wo o+ cs t-mh;w.o-9le;1 g8rm ngmd) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it oht g +cu.2m o;;g9t r1w -wenm-mls8oon a bicycle with 24-inch wheels?

Suppose a disk rotates at constant.i f oacaq2aq(30eb,l angular velocity. 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 either component of linear ac3eabaqcalf. (,q0io2 celeration change?

Could a nonrigid body be described by a singlzhk61t:v )fk h2rg, yee value of the angular velocity $\omega$ Explain.

Can a small force ever e;3dbg;fhhc1y5 /oh l 07ick 7ax9wqmsxert 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 scro85,acm kpts2k:n8 it-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you tokoa n8m c8r k2c5p,:ts answer this.

A 21-speed bicycle has 0eyuv(yg( z.w seven sprockets at the rear wheel and three at the pedal cranks. In w.uv (yyge(0z 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 able to run fast have slender lower leg6o6 of0u*h,mh qyrm- ds with flesh and muscle concentrated hdqrufmyo ,mh0-o66h * igh, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, nar(ch2zed uwm,fd, ni// row beam?

If the net force on a system is zero, is the net torque also zero? If the net todik cwt0+rp (8kaiyg m9:i*-prque on a system is zero, is the net fpgkmti9-+ ipacydi08kr :w*(orce zero?

Two inclines have the same height but make different angles with the horizonta;);kn*pzf j+ 5to zzkml. The same steel ball is rolled down each incline. On which incline will the speed ofj5zk fz+m;*nokp)tz; the ball at the bottom be greater? Explain.

Two solid spheres simultana f87hr14u atnieg7f 5cdu6o, eously 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? Which has the greater speed there? Which has th 4orafaf cuuh7d,e17n5t86ige greater total kinetic energy at the bottom?

A sphere and a cylinder have the same7gslkkfgi9cb/ 5+bdkg ,p y m1a-*0kb radius and the same mass. They start from rest at the top */d0gy 7bk+ k91gs-gckfb 5 ,bk imaplof 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 momentumj ofoagagyc3f15aj; 6(x:1vol s*g2l are conserved. Yet most moving or rotating objects eventually 2 36o;*fsvgag llca :yg1j 1 (ofo5xjaslow down and stop. Explain.

If there were a great migration of people tow;/btndlk: qn2 :z)ec xard the Earth’s equator, how would this affect)zxdl:en tqkc ;n/ 2b: the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial r w)1e5wyon*4vp q;1 5 ,st2lv hpyyenwotation when she lny tqos*1n,)2yvh1wl5 v4wyp5ee;pweaves the board?

The moment of inertia of a rotating solid disk about an axis thro.os.yno z o/kp3;y cy7av:w (augh its center of ma7 ; /3cs(an .oo:yzvpy ayw.koss 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 sittipj2mqjb xyc gy(p)(-1ng on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the yq(gpjpcyjb 1-x 2m) (masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identi4i f,zd4wo2xt b+b+mxcal and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine whichi,dbmxzb +24xwf4to+ is which.

The angular velocity of a wheel rotating on a horizont-xccguj9 9cr4ca8.ko al 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 co9grcj4c98 -cauk x.the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rot/b4ji8 rahbh*ating turntable. What happens if you walk toward the center r ji/8h4hbb*a?

A shortstop may leap into the air to catch a ball and throw it quicklyckp)2 34zonl m b+r8u+cu9yzg . As he throws the ball, the upper part of his body rotates. If you look quickly you will 2o+zu 93yr k )c8n4gczm ulpb+notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of cmv- (*xmoapm* onservation of angular momentum, discuss why a helicopter must have more than ompmom(*va x-* ne rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in rau0xi i t*d:2zmdians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calc.h-g acoc .w/qulate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as se.ohc. -w/g qcaen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. Tu*w)eeyu7z8l fw9 p k*he beam diverges atl f7e)z*9wwp 8kuy* eu an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a raw*a .q794wxwq:tc1q1 dvt;bqpx ru /p ,gft(rte 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 arb(tpa 7u.d t4w:cp vq*tfq,w wr1;1qxx/g9q s the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor) i:ud/ldd)k2 7ocapaz ae) tb,w( 9lo 3.5 m to another child. If the ball makes 15.0 revolutions, what is its di27al po)a )9l,/d )tad(zb doeucw:ki ameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How manyhc k-rmn2sbc)o -4y/bt- hqmig3) a.mpk+tx ) revolutions do tt hs .kph3bxn)-)+y4bma -og -/ 2kcimtrm)cqhe wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotat1q4 lpab r4;lh dxqmw68d4atcq 0ma -6es at 2500 rpm. Calculate its angular velocity in;q 0t614 xd6dlar ah 4mqa-lbq8pm cw4 $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–38) x buwfo jl360r-6d/ej. (a)xr-fluj 6o0b/36wejd What is 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 ofv:oq a;axk 3+gw g(r,8p2cq rcxfj +/f the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poc4t)+vsy /kashyyu, im- ld-1 int
(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) mu1ed/9blrty7kt9 uo / kst a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 119tk ubo yrkd// 7e9tl00,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerq 0of q efn22:etr3ig m8x(j+iates uniformly about its center from 130 rpm to 280 rpm i j mq8:efeg(0rxi qni2+o3 ft2n 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 radiuszdxth 3xeu koa /r) 33b9)a(tz $R_1$ 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 abmh7ihnead 4kzcc)4bc-g) ; :woard the Apollo spacecraft put themselves into a slow rotationakm) w;e4cn:h gc d 7cbi-4)zh 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 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 acceleral bs2w4:/vxccc-f9w btes uniformly from rest to 15,000 rpm in 220 s. Through how c/cl2xb:s9 cf w-4vwbmany revolutions did it turn in this time?    $rev$

  An automobile engine slows doz50unjh5 as x6wn from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for zwh np 8ubpkkv.5mtm6 , o(dv,b7eu3, the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reacvz6,uo 7 bmvpudew3,nh 8 pk(b5,.mtkhing 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 acceleratemiw4f fsl ,4y.)fcgy(s uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the ey4c(s)glfmf wy4.f ,i dge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 r,)xa9oa,p xqmevolutions befop ,qx,x 9a)amore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car re 3 :xl6x-qf5itafyoiq5 yl(/z duces its speed uniformly from 95km/fx :f 3-tqiyzy(axqo/l55 li6h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its0t 2-5l tvyyks speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.t0vkslt y25-y 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 we9ewx wwpy rgi s,mm/,,b19t(y ight on each pedal when climbing a hill. The pedals rotate in a circle of rw9se (tm9rmyy1w ipx ,bw /g,,adius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide.+,xev1 cndf9w- + fr6-c/srg ojjj 7sz What is the magnitude of the torque if the force isw 7 c -/1sjfecvdr, rojxfj++gnzs96- 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 tht2c zay8(hs+le axle of the wheel shown in Fig. 8–39. Assume that a hz+ca t( 82ylsfriction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attachedt9l:ov6a z-7 ox l9r9yuy4yrd to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizont:9-yry6luv4xo 7rdz9y9t ola al position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an ence t2id25mhg 5gine require tightening to a torque of 38 htg5m2 2e5dic$m \cdot N$ 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 ozc.qpz-h 0wb/r9+ ez1btz1rs f radius 0.648 m when the axis of rotatpz-+/ tc0q sez1wr9h . bzz1brion is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 c gqqspv(4j0+ym in diameter. The rim and tire have a combined mass of 1.25 kg. Thej0pvg(s 4q q+y mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a xq oh bi:3 qxx0 )ed9+mk z9drvknae68o /v85uhorizontal circxxq 8q+kvir eb0 do z9d):k/5no3uhx m9 ea68vle of 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 ro2ae+m/enn;un()8 ju hu(d 7p; kkue kztating at constant angular speed (Fig. 8–42). The friction force between her hands andz)dk(uumne2j n+8kan h;upee7/ (u;k the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig. 8 4nqs;*7s7x,4 u rnbvjif pyy0–43 ap yrf4b *;7ivj40 7,snsynux qbout
(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 oxygenkq6vu1bl u -7glph+b92 svdmny8q6q9 atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinnina) ahx),velo ;2wcqq:g at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm ioe2lq)h xa;:aqwv), cn 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 s zu6.tgn )(qy/: vlvecm and a mass of 0.580uzlysn6 )tqv.g/(e: v kg. 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 rebh*svzd/2s*zu6 v w8 sst 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 nl e7zdm59e) 69*q +lsy r8trvh :eecemerry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in e6:el *n8mreh t9cye5s9v zrledq)7+ 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. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatinfz0 5(/;uugw l kjer-wg at 10,300 rpm is shut off and is eventually brought uniformly to rest by a fr- f0 u/j ;lz(k5werwugictional 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 i x:elcv yp:lb-6kgl*wp7,2jk2o ne+ a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of tswnhi19(9a zo he forearm, which rotates about the elbow joint under the action of the triceps mu1a99 (owzsnhi scle, 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 considered a long thin rod, as s/ 0mal5sw+q nyhown in Fig. 8–46nqs 5m0y/+awl.
(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 gh(ru6dqzfas y5go71v,,w-o consists 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,:huwog- )ltnx zfhe-q6(5wx turns (revolutions) afh()que:5t zwoxn6- glh,wx-nd 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 moment of inertia(vyypi3zb at1-qe4zs:sc, a0 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 developsoy/ t7igdc2u/pk 1nn. a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping down aa2tlcqlup/(*q( *u mu lane at 3.a(m/u* t cpllu*u 2qq(3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth 6zwv re0f; d5dwith respect to the Sun as the sum of two terms zf65wd;e0dvr,
(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 8ac5mj5jio ip cx8 q2igjyd do 324)3y1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume itpiiaij2y g52qyj8 oc 453)dodjx8m3 c is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg am( iwxkx.,z; : io3abstarts from rest and rolls without sl :bmz ikaio;a3,xw.x(ipping 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 its1b7 3l w mgibs)7kedlkt5:gpu2e6lcr8; 9ykg tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before wpgl k5e rt d71k2 ; lys7ck l3i8gg69b:uemb)it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momenxqpsf:2); t3t w7wi*axxh wp 0tum of a 0.210-kg ball rotating on the end of a thin string in a circle of radiufwq7x )as i0*t:hppt2;xwx3 ws 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniforg4l . iu(9 v tms3puxo0 zar38fp9jz8jm cylindrical grinding wheel of radius 18 cm when rotating at 1500 rr08uzm fj.tz8a9u9ij (3ov p3xp4sg l pm?    $kg \cdot m^2$
(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 rotating at acmoay x )4+q s+c*fcd3 rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 4 os3+m* )+cqfa cdxcy8–48, 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 moment of inertia b)is5 :czrlrz6 ye-m* qy a factor of about 3.5 when changing from the straight position to the tuck position. 6zsq-mer*)zl :c r i5yIf 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 99/y0gg:lm qr c :jjdlinitial rate of 1.0 revycl/9jm0::gd q jr9l g every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotatind)fsqi, ;c riy.0hd- mg 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, mycs.) , fi0rdhi;-d qapproximately 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 angu pkjj pp2px zvc1377xe7j qz(:um6r -clar momentum 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 momeix6r zqaa*zm- ux:pq7a+:r c0ntum 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 ota/met+na 4,z l2ukzot nca*z --jy**f inertia I is dropped onto an identical disk rotatino*n-e-2lu t *a zm*y t ,nazz+tjac4/kg at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at-p .ujjn 6j usrkbv 1jv)1ne5/ 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center f3v-v52whtz, wyhs e- of a rotating merry-go-round platform of radius 3.0 m and momes f --t vz5,hehwyv2w3nt 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 ang 1-9prbu i2oat;fznn0 y8 cd0vular velocity of 0.8rboz80 f0ni da 1;c9pu-nvty2 $rad/s$ 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 dwarf, losing 3k-nryv*sevs.; z +t rabout half its mass in the process, and winding up with a radius 1.0% of its e3r;k+ez*.vnv s-t rsy xisting radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involbphe8,i l.d a)lz -v86p vudq2ve winds 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 x n)y-sa7vpzj9 kz++x$ 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 plakq6/dbh go wc25 us;paki171ftform, initially at rest, that can rotate freely without friction. T5qfs2u;/ak7i6pdh1w bkog 1che moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameterbuozv+ozg ;-tse1so188 xl-t merry-go-round turntable that is mounted on frictionless bearings and has a moment of b81gz-tl; u1s x+8ov-ezoo tsinertia 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 rct,1t gw 8yp6bolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far doesw,16cbt8y t gp the spool’s center of mass move?

  The Moon orbits the Earth such that the . 80-2phba rh8stuhp re-x9hezp-u j:same side always faces the Earth. Determine the ratio of the Moon’s spin hj-hxh2 t -rpb8ur p8e9ep sah 0u-:z.angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from fe pxzq1,r:-ovrg j/2 -j fy-drest 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 radius 0.20 m acquoh:gk-)s6y a rires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torq :6 osry)h-kgaue delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of id urm041 d)dsmass 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 the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released frm1u4drd 0)sdiom rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed*rf lt)osu ;qv*/jv;6xih 28knr3i rv 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 mbgk :1ju*w+d eca:gay(4s cn3ass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to ung:4c1d(s c3eg+*:abykj nw audergo 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 use e t* s g-6l(2f(xmmv d4ondj1xxo7mncnr6); tenergy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a unc;6(ljtg)7*xm2-dvsxr 16nd o4mnxft eo n(m iform 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 y2deku j2y3)gb7efp;y0 za6h 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 (hooppjqq;;3m0w)/kasrn a) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore fq3 f6xk *cch2ktre(o;riction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hit 3kcxe (2;chk oqfr*6nt: See Fig. 8–21g.]

A wheel of mass M has radius R 8uj n::5pmehy u.:fe/ve*kek. It is standing vertically on the floor, and we want to exert a h:p 5 :*uyj.keufe:nvekm/8eh orizontal force 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/s pctoo b1b 4 6:joqi9c(on a flat road is making a turn with a radius The forces acting on the cyclisop 6(:c94obio cbjt q1t 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 qz6nw9/uyp4 w1.5 m and begins whirling the rock in a uqwp w4ny9 6z/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 0ilh*4 -z8l hsx6ppdsas 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 spinning skater with outstretched arms, aldp0* z6pil sh4 -xs8hnd with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylieak gscr m2u),xo9ej. clu*;3ndrical plates, of ma egrm)s.a9xlo,e; j32kc*cuu ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. 8–58 nm0w(gtd/;/hu rqf2d. What is the minimum value of the vertical heig( n/gdhu/;2q0w fm rtdht h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume 8 :q(ixx9riq u6,;jq inia2da $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its sp3mfn *c 4 f00i.rfmjureed uniformly from 90km/h to 60km/h The tireju4 mnmf0. 0rfic3*rfs have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s