A bicycle odometer (wh0cl t :f8o mb-y69czqeich measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch whee emylb69:cc t0f-qo z8ls?

Suppose a disk rotatesd lzdy 5.wg5 h9(+acxc at constant 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 tangecd.5x c(h5 lydaw+g9z ntial acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the.5 4s x-czo,t a.xzyub angular velocity $\omega$ Explain.

Can a small force ever , wc:p;81 iau 6i)shlglk a:tqexert 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 your hands behind youxcf+cfr-p (pu mo 46,or head than when your arms are stretched out in fro (corp6,o fx-c+u mfp4nt of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets all tjkl gr:h+bgfc* kd:070;bt the rear wheel and three at the pedal 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, ad tlkfjb7l0: ;:gb l0 crgk+*h small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fles4*s 4 arzgqi+dh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of 4ad4q*+irzs g rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carrrp/a3t alu21tifo s* /y a long, narrow beam?

If the net force on a si2p1sur 1;bna ystem is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zero?n1bs 1 ua2i;pr

Two inclines have the same height but make different anglesra d(-u q, uan/53q6r.yziiuviv g78 z with the horizontal. The same steel ball is rolled down each incline. On which d7 u(vuqizy,3/i gr5i 8qu-z6av. na rincline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from r/ekmbjc rf -s; e4.0vdest) down an incline. One sphere has twice the radius and twice the massrjkc m 0efb-4e/.;vsd 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 radn hd -kg)*t * s2q f9l8w6cpzryjka6m)ius and 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 total kinetic energya 6*c2 )hq*spymk9)fdj lw6 kgtr8 -nz at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentl ymed 4b bi3h35em9m5r 0/vyzum are conserved. Yet most moving or rotating objects eventually slow down and se ybrl/ 0mzeh 34y9v3mbd5 5imtop. Explain.

If there were a great migration of people toward the Earth’sdxq6 f2rz.du2 equator, how would this affect the length of6ru.dq2 fz2dx the day?

Can the diver of Fig. 8–29 do a somersaultz p0r1b 8kwvh1 without having any initial rotation when 8 vh0pw1 zbr1kshe leaves the board?

The moment of inertia of a rotatingqe,/rpa+ gs;mf+ l7xn,.. chmnoun o9 solid disk about an axis through its center of / posg9oq,cmnmf+nex; r.u7 l,n. ha+mass 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 stool holdw8;e te)s u,qfing a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular vequ ee 8sft);,wlocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. bjv;m1e c.1q jHowever, one is hollow and the other is solid. Describe an experiment tj;vje.m cb1q1o determine which is which.

The angular velocity of a wheel rotatim:y;:4nqqci kbjf2 x p./w-g gng on a horizontal axle points west. In what direction is the linear velocity of a point on f:mq :px- wjybgn; gqi./ 2ck4the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rota8)cn lt mqewwcxv h.;:w6:w 1oting turntable. What happens if you walk toward the .clmwwh68 twc)eqx:n ;w1:ov center?

A shortstop may leap into the air to catch a ball2z us8pvpiwo 80rr,xu:m* wb. and throw it quickly. As he throws the ball, the upper part of his body rotates. If you lookzpwu:28.bv,i8 *wr x ompr0su quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law ofwy spk b2 .sjhk5w29-j-5 goduw7 )wtcznq k-, conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can od 5wz7,n- oj w9quw-2k ps.g5t2bwh)-kkysjc perate to keep the helicopter stable.

  Express the following angles in radians: hw md-,kwn9s6 lz.o*zznw 62o (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. Cal 7on, ovl0fuv*culate, using the information inside fovou,n*l70 v 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, 380,000 km from vg8g9**f xw/w9zdkhaEarth. The beam diverges at an angle/kvgxd*9z ww8*9gha f $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender ro8ywn -u1yl8 zz40j wkjtate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down? w j8w8y -y0jz1kuzn4l    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. +n*:xcfpro6 xIf the ball makes 15.0 revolutir+ c*f: xnx6poons, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutiop6 d xow-am)l1ns do the wheels make-pdmlwo1 ) a6x?    $rev$

  (a) A grinding wheel 0.35 m in diaiihae /biu-3 y-3cuq)meter rotates at 2500 rpm. Calculate its angular velocityiuey i3i)-huqcb 3- /a in $rad/s$ $\omega$ =    $rad/sec$
(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 (F u5f vg(c s77stpsax0(ig. 8–38). (a) What is the linear speed of a child seated 1.2 m frctssv (pf( sa77gu0x 5om the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of +0vtn2j .naoy.5e7 hmeuw q :nthe 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 point)ajnw/il;b80t* xj7 ccrmg4u 0xu-e t t; y3rl
(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 particr8xb/ezxzp ;) kepx/ +le 7.0 cm from the axis of rotation is to experience an acceleration of 100,000xx +/ez 8kb/exp )prz; $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 2f4 eyt1/j pq2f80 rpm in 4.0 s. 4f1 jfep /tyq2Determine
(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 radiuss c o.sfh1..md:o.e*j l /ynztsk) m3x $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apolloafs8 i*tykbst5(em96 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 to 1.0 rsmt ke8ti 9y5as(b*f6 evolution 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 8 3-hjj:bu(b4zorn tvin 220 s. Through how many revolutions did it turn in thb8h(4 - :tnz oru3vjjbis time?    $rev$

  An automobile engine slows dow(1kzd8j yfs9i n from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whieij8fci9jq-v j ec3 d t8p,o/rj1d0u x0f5e:jrling “human centrifuge,” which takes 1.0 min to turn through 20 complete revoluj3 i/j, f19vjp8e5xjt0 jc u- de8r: edc0ifqotions 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 uniformly from 240 rpm to 360 rpm i):e*y5nrbmc,nga po) h5s vj3 n 6.5 s. How far will a point on the e53c:g, aoebh)smp*yj r5) nv ndge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turnshf sc0og87 )t61h cqya 1500 revolutions before it comes to a stohtg)1a7sq o c8hy fc60p.
(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 reduces its speed unpb iju8rrmawz39nwbf 8 : 54e(iformly from 95km/h to 45km/h The tires have a diameter of 0.849:rb5w n(3 uwmria 8f zbje8p0 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 regf: 9trip 0c)zlc,x0ivolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a dipxf t00icc 9:)irl,zg ameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbiw- xi4daab68c a/j2 ldng a hill. The pedals rotate in a circle of radius 17 cj286c-xba iwa/ dld4am.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What ixyl-y((u(t3g 0ona: e rud 8fis the magnitude of the torquluuda t- o yx08((grnif(:y3e e 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 the wheelt ncc, uy8g(l6-y -nuxlpd(0j shown in Fig. 8–39. Assume thatd-u8-l(,ucglc y ( tn0p y6jnx a friction 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 n9hcn)jz9 8f, e q)k6fmnhy q)the 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 yn8) 99khn h6jmenf,)czq)f qtorque on this system.

  The bolts on the cylinder head of sk t,0cdp01m lzqir ++uskfzt3h0 0z*an engine require tightening to a torque of 38 zqt0ht31rzsc ,m0 kf d+ 0 ul0i+zp*ks$m \cdot N$ 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 rad9r * hyb,e2z8g xkux(yius 0.648 m when the axis of x2 r,ke* yub y8x9hg(zrotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bip9q:1 mrnwcr.yko 1 m8cycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1rn1rm1pc8 y9 w qk.o:m.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, light rod rx92t xupukrqt4m:kj0*s /2 jis rotated in a horizontal circle xp9muts tur/*qj0kr4kx:2j2of 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 wheqa+*b8 scn e6q( d1s6qcuq. qhel rotating at constant angular speed (Fig. 8–42). The friction force between her hands a6.q qq de(+ b68*nshcscuq q1and 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 inertvz2 0tw3s lg4h 4e *e/uj2eefiia of the array of point objects shown in Fig. 8–43 aejz /2tguvfw2is l 043h ee*4ebout
(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 twu 9 e6gsu-lbl7o oxygen 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 :i6yc)x tegmu)r 5ku5 spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and ag tcemi)u65)y u r5x:k 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 8.50 cm and a ma-icg o7s rbifa +g(j0,ss of 0.580 ob,+7rgsf j ic0ig(a -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 bibpxx n;) sx+2dy)v /xat, 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 tangentitxlgga 3lf+1 ;ally on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the me 3a1gglltx+;frry-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 rotating at 10,300)j7 ;zvtsirv- rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.2 )jv7s;tivz-r $m \cdot N$ 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 -g4cj*2xq kuw 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 a*sucurdn0o418 5drz of the forearm, which rotates about the elbow joint under the action of the triceps d08oznu 15 drr4uacs* muscle, 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 q ; 7ks2tk6kyy:be ha)be considered a long thin rod, as shown in Fig. 8–46.7yats; )6:e khqybk2k
(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 twan9i 5k)cx ) tcmp/t 7i8mimk.o 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 hammc g.r+kla**wl er from rest within four full turns (revolutions) al*aw c.kr*l+g 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 iqo s-+ g( 1m8tr7sv;jfusa lo;nertia 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 to2gruc-90 pygh* jhq0 orque 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 s3- gd6rqqi5 iia uw);9cdpd8ilipping down a lane at 3cd ia89dp ; wq3d -uqir6ig)i5.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Su)0 z;6f jao 0zii -uamr:miit7n as the sum of tir )i6fi :i mzo jau00zt;7am-wo 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 radius of 7.50 m. How much net : xqmt7g ,uf.1-lg.mtcdt,glwork is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid lgm1 ,.tx tc,gl mu7 qt-f:d.gcylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts f/;owwq(+fsuhxd o8 z0rom rest and rolls without slipping down a 30. zwf u+ hsx8o/w;q(do00 $^{\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 itbb ezs(,u wi, 8g1 ;0tpv.prjvs tip. It starts to fall and its lower end does not slip. pi .ub8spr0b;g(1,etvwj ,zv What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rorkfv93od.b8b tating on the end of a thin string in a circle of radius 13ob9.8dkbf rv.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentuyrl4o1(+j1-8z c meezb nbs3im of a 2.8-kg uniform cylindrical grinding wheel of radj1z4-enrz+m ib(b 8 1 esylco3ius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on ,49 n +d-uk:j oiuaapaa platform that is rotating at a rate of 1.3rev/s If hejup,a+ : nda-uko 94ia raises his arms to a horizontal position, Fig. 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 eatvmy8f cp0js2 20lqgf,d 1id(77ymone shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If 800dt fm(jgva7 l,dfq2 7miys21yc pe 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 f+g vpoqi o .;3,s:4wjbqp0fy wrom an initial rate of 1.0 rev every 2.0 s to a final rate of 3 :p4yq03+ qo sb,gij ;ww.ofvp $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its centezny dwg/v:zmvs20d t 8t*gl74 r at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5n:t 7mv*/0 zs ly82gdw gdtz4v.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinni5t/bcwc*td- p ng at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Ed c-6kdm 6r.vr4) imqoarth
(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 jbk:fl+d/awaq9 7c t3jpk43y of inertia I is dropped onto an identical disk roy7: c j3akp w4/f3ljqbt+ak9dtating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.7)xdnn1eu9a ;c k(zvq4 $rev/s$ 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 ce;;b *icou )e,hltq9iynter of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 920 qy;;9,cbuhtle )i*oi $kg \cdot m^2$ 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-rounu(6gt 5rg7k4xio. uasd is rotating freely with an angular velocity of 0..ig6gu4trao ux5( sk 78 $rad/s$ 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 dwar+sn r2i s.y,mhf, 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?(nm ,.ysh s2ir+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 windqrp4m3 jm e*9hs 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 pn:n/nrdv;y9wdune- k797v o + g 9drq$ 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 rotate freely w 82 e1xc d*ttpfc-dv,rithout friction. The moment of inertia of the person plus the platform,2*c- d1e xc tdvt8rfp 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 stands9yd/4dw z bkt. at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inerti9tbd4kzw dy/. a 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 grounldw+idag80ss6 m10 fw ba0wa(d with the end of the rope lying on the top edge of the spool. A person grabs the end (d6s0 8aw w m al+sdfia1wgb00of 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 the same ov+mefi*st*m-d5) p eu-:rgd 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 latter case, treat the Moonf*+evur:)mg-es id5p- t*md o as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates frot6vge)0m r g(uow.q6t m rest 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 cylindx 7u18 3h(/n 4rdwaolk7zvvbser of radius 0.20 m acquires a rotational rate of from rest 7kb1l sow3 (vvu 4/xrd8naz h7over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of twonjeuf8e:jk 2-pwju9/k g hy7g.,7vd l solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameterk /-gh,ejj.u7gln2p7 9kyjv ued8wf: 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 from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the ang0 gvb fc6e:0g,+qe- p 3iycyng /fkyb;ular 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 kvo k,gtw a6zhoo*//xq3p*z3 rotating at a speed of 1.o6vp/g*k 33/hkaqo * zwt,ozx 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 off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-posqvkpy +a2jp :2sq/iv /3/6rm6 uetulllution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should vm /ue/qv/+py q6362latkspri: s2jube 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 al2b p0wn*2dtj n $H_2O$ 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 (hoo/du-dmcg2j2l;n8wk 6j po(xwp) 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., wekz24ety *:jdbg b t/k.fkth/rj*z3.b ignore friction) aboztjhe*/d.y fkb2kjt4 gr/.tbb *k3: zut 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. [Hint: See Fig. 8–21g.]

A wheel of mass M has r9a*wujr8+ nny8y kgy-adius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step a9+ngy*k8rnyy8w- u jagainst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling :y74ezl 7fzu,kul 8 -aar3dhrwith speed v=4.2m/s on a flat road is making a turn with a radius The forces acting oz-3u7arrey,ah87 lul zf d k:4n 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 0.50z*g7)5 sj)go1 f9dawib hppi *-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and wheregsz *g f)h1pwo*9p7i5jid b)a does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thih g*oowfcl 6*4n rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tigloc*6g *w4foh htly against her body.   

  You are designing a clutch assembly wk/f10kjk- r( scxqq k(hich consists of two cylindrical plates, of mk10ksq/ck-kx(rf jq (ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 az.x fnmazd *-ex*k) 1bx0ks+vlong 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? As*ek zxx n-fb+*xvz .1 dmsa0k)sume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but pm nf; v4xj:5h7xj6rddo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as th ad( bddw3ti*v7og;l/ e car reduces its speed uniformly from 90km/h to 60km/h The tires have a diaavdld( o7tbd*w ;g/3imeter 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