A bicycle odometer (which measures distance tr:;fjctwg z0ty (6 3uaraveled) 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 wheeljz;t: u 3yf( tc6wrg0as?

Suppose a disk rotates at constant angular velocity. Does a point on the rim .t onyxe5sb. s9c:9s ahave radial and5e: b cotnxs9.asys.9/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the ana. 77(dbvc07 dgbigog9f ,.s xoc)fhtgular velocity $\omega$ Explain.

Can a small force ever exert a greater torqa ae*2rjn2 s1due 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 m4k0cb/ovi -*o f g30sn0scrnsit-up with your hands behind your head than when your arms are stretchk-00 /f bon m srsocgci0v*3n4ed out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the ped a ilb :- agd*ttwn/hg09eu)j1dh;x 3zal cranks. In which gear is it harder to pedal, a small rear sprocket or a lar jd*te; 0ad3i hhb- az:x )tg9wugn/1lge 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 ab;o)wheg6t 2i/d g+ swole to run fast have slender lower legs with flesh and ;wto )sh/2o+e 6wgig dmuscle concentrated 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.dwhv,ubr, x87 8–35) carry a long, narrow beam?

If the net force on a sy92f-zpel4 l3bqws 74n lz5kasstem is zero, is the net torque also zero? If the net torque on a syst2ls3l ez44pf5 k- qwnl7as9z bem is zero, is the net force zero?

Two inclines have the same height but make different ang 7qzswqbc92 ,mles with the horizontal. The same steel ball is rolled down each incl 7w2cs qzb,qm9ine. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously sxo +ah he1gmyw*w) kftv78*o(tart 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 haeyhkaf*gw+o1oh ) *(vtmx78ws the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same tao t edd/lje+89u:/q (ou 6nmradius and the same mass. They start from rest at the top of an incline. Which reaches the l/o6 (/ o+tne: q8djduaeu9tmbottom 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 momentub wn;e, jdfr-k;wg gom;cr0++m are conserved. Yet most moving or rotating objects eventually slow down and b wre wngg-ok;; md+;c0r+fj, stop. Explain.

If there were a great migration of peoplf(t4t 9)fkkcee toward the Earth’s equator, how would this affect the length of the dayk9tk4 e ctf(f)?

Can the diver of Fig37yp kf emp8-f. 8–29 do a somersault without having any initial rotation when she leaves thp83yke7f-p fm e board?

The moment of inertia of a rotating solid disk about an axis through its centerq5 k7 kv/p-ngf of mass is kf5p/gqvk-7n $\frac{1}{2}WR^2$ (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 holding a 2-kg masf gpkclrl ;r;uo*9,; bs0z1gis in each outstret f, ;s;* zgg9pb1ul irlc0ro;kched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow qte yl/;a+-tqgp8c3;6fhgb q and the other is solid. Describe an experiment to a pbg/hgclq y8+ ;3tq6e-qft; determine which is which.

The angular velocity of a wheel rotating on a hkx2vd0etk0mvybu /8 * orizontal axle points west. In what direction is the linear ve0myu8te kk/ *0xvv2d blocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of zxfb:lzom1-sn ; y 20ea large freely rotating turntable. What happens if you walk towab1n :zyl;ms- 2z0xoefrd the center?

A shortstop may leap in,t;e2nng x( vmto the air to 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 directionegnt2, nm;v (x (Fig. 8–36). Explain.

On the basis of the a8.hr:d j4leu ;9v1xoxd/5 zvy7vum qn;ulw( law of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more walv/8 1uzhqo(x9drladvm x ; u 45: wv.ejyn7u;ys the second propeller can operate to keep the helicopter stable.

  Express the following angles in radia2fud pfmn*5bhhz0 w7 - cua1+xns: (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 a/zggfk l.ip9hn 3)9s( ldwp m1mazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as m1g wi h9gksl dpf.9)p(l/z3nseen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at t2wnddl ak1l)zxfh z .m) 3j4b5he Moon, 380,000 km from Earth. The beam diverges at z )ln1a2 4md bd.5h3fw)ljzxkan angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is turned z:ebk p+(b /m/i;gn 1zfv ple9off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow dow;b/veg b:nz1p kp9/e+ zim(fl n?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another c mi2 b-lz w9f 6xcpeh1h5qf mslhoc;84w//fq8hild. If the ball makes 15.0 revo f4-8lp/eoxzlh 2/c51fqhfc 6 wbwhs;mq8i m9lutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do vs)q lme5 0/j+ rlaum6ob(0ip the(vbl)jui0sq 5el+op/amm 06r wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rot*lxlfo2 *rvm9n;u jn+ates at 2500 rpm. Calculate its angular vfnu l; n*v*xlom2jr+ 9elocity 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 (F9 . 8c7eeucume4q5mp1o gdy1gig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the center? u.m dye4 e1 g1pe85cqgcm7o 9u   $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (aqq vj1u9igv0olg3+p7gcr - +cz 5hv/b) 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 8j97rs1uhsb+4k scx fl-(zd ipoint
(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 th(6vsz. c1*9dn :mlpfezyk*/p d vdt g*e axis of rotation isf *g k 9vyt *1d*lzvdz cespd6/m.:np( to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accele4lxf4 rn 6kg0srates uniformly about its center from 130 rpm to 280 rpm ixrnk4 4gls6 f0n 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 radiuyut228i*v wpa s $R_1$ 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 Apcukb3 .w7 iwft(.g( *g,xmrwt1red. jollo spacecraft put themselves into a slow rotation to distribute the Suxecmfdt1w(u.ktwg(ri ,* 7j.wr3 gb.n’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 accelerates uniformly from rest tutwfqth304gy( 3:qw g o 15,000 rpm in 220 s. Through how many revolutions did it turn in this ti3qy uw0f4qg(gtt:3h wme?    $rev$

  An automobile engine slows down from 4500 pz8333juha7l0ec q3mcupa i 2rpm 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 1oodpzpxa(/q05)6oo t si(+z; hlpxjstresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 comple; zs p(x0ooxp ot i1+6jp()q5ho/dlazte revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates +jef x;8tzua00f v6rbe4:rjyuniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on th6b4: f8vr tjrf+ 0jxy0azu;ee e edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runniguab-ad+g* 5t)yfo4xtd +jo+ng at 850rev/min It turns 1500 revolutions g-bft++)aj 4tu*agodd + xy5obefore 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 reduces itx/o(xn vm;yccb:w4 p+*8q gwk s speed uniformly from 95km/h to 45km/h The tires hcp8v/ qoxgk;:+xbmw(*cn 4 ywave 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 revolutionskcnk .1phjh f1)7fnu 9c)mk*q el0; vzqb*ub9 as the car reduces its speed uniformly from 95km/h to 45km/h The tires hau 9nzn c;191*hb *m hqjkfveup .lf7ck0))kbq ve 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 ridin *n jan7(vsv l1iw:(:p7au gezg a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circn 7l v wsa7vjeu p:1*i(zg:(anle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 ( wmy5 qhysc1u6q-e3 )eeb+gdcm wide. What is the magnitude of the torque if the forcey6by 5qd)h3u-w qe (1mee+sgc 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 whed0,: ximju gajx5 yfz*l,vnp369j 5 fhel shown in Fig. 8–39. Assume that a frangp, 93jjdz 6 y5i0 : f,5mxvh*fxjuliction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massles ywmg+f ie.-.g,ony- ts rod which pivots as shown in Fig. 8–40. Init yg, -f. egyiwtn+m.-oially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a 2k;n*khtjcgb m3. 8phtorque of 38gtp hj*m3c8b2 .kn hk; $m \cdot N$ 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 3bhki8w u;peg;kxcs .f29nr2m when the axis fc ;bhkp;e2 u3rwx.8gi9 nsk2of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inezt5aymnl, p.8efw9leru*, u7 le n:/c rtia of a bicycle wheel 66.7 cm in diameter. The rim and tire have9ut.lp,u,yf/e7e a r5zlmnn clw 8:*e a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is k1, aqg :p l enc,3/jdmz51jjeygk3 4lrotated in a horizontal circle of radius 1.2 m. Calculal/je4 me,3j a k,g d5z11ql3n p:kjcgyte
(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 w72hw(+e a x+ 2nxnrx+vhxdx(bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her handsx++x d7 hwreh+vx2x n(w ax2(n and 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 t z*pf xq7tof02he array of point objects shown in Fig. 8–43 afz*7xpo tqf20 bout
(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 g3mq zi cf6qe-ba// f.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 satels2qryry0 pij.m9sl6 z7g ..hglite spinning at the correct rate, engineers fire four tangential rgmh i.9 pr qg2lj6 zsy.yr.s07ockets 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 8.50 cm and a mass of 0p4xxbbmo 6dwj;b) z1 6.58wxb4pxmd ;bj z)o616 b0 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, accel6zwaq 0e d 1n*g-hkadu0olg-o/e m3a0erating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven 7e 7 fvqsf.*apmerry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 7p f7q.f v*aesm 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 rphhr/ 4wqjs6 gfid*xs+c/*u* tz-i 8qkavw );h m is shut off and is eventually brought uniformly to rest by a fric6 s gvfi hrq8xz-q /w*hh)*utkw4 /;da+*icsjtional 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 7vyewr -.h6 lbrf l8c,accelerates 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 the forearm, saj p(+l00+/:kumtbvr w8qti which rotates about the elp tu/+vt0m+ rq ws l0kb8(j:iabow joint under the action of the triceps 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 be considered a long thing2 phe,m-cu :gm ub-w( rod, as shown in Fig. 8–46hp -u:mum,(wgbcg - 2e.
(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 two (p5dz zx)faj +wy4z-c7 opvu2lf)w47zxs-c jmasses, $m_1$ 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,3 yrnie ev0+ 8.nsper the hammer from rest within four full turns (revolutions) and releases it ate s8+.pvneyr 3,i0 ren 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 htl ,:h ug:t,hql*z5pv as a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 2f*sj n,2v( 6s5ybdtp i/v,pg j80 $m \cdot N$ 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 a l9/g6 -lz i mo+og.tpisa. /9-sp+mgi6tgo i lozne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum fdc io7r( /4n hld0d-wof two terms, 70 oc/ dirh w4l-ddfn(
(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 ofrk: ) scnnc;n; 7.50 m. How much net work is required to accelerate it from rest to a rotation rate ;n;n kncscr ):of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20*u w532wdzup wh 9trs+.0 cm and mass 1.80 kg starts from rest and rolls without slippin*z +uhu35wp 9w2rws tdg 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 verticrell;;c s17eially on its 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 it hits the ground? [Hincrle1 is7;l; et: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating v5yd*zdtm y w +t;6x8hon the end of a thin string in a circle md5;hxzt8+ w6 *dyvt yof radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular 3xpoz00w*ib c0d;knjxxhv8. r41 tj wmomentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cz4txi0j;roxw j *8xh0b031 cvwp .kdnm 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, o(g3k 5* 3ywjyojjnm f,q9 5gsxn a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal positj5wn ,y35jx*jykfq 9 gmg(so 3ion, 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 one shown in Fig. 8–29) can reduce her mot 2odv t.u-1dbment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is hev2bu dd-to.t1r angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate todb/244 owdcf)0 obvfrom an initial rate of 1.0 rev every 2.0 s to a f btb2cd/0o v o)44ofdwinal 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 axis through its cen 1 sb ,m2i82k isvboc) p3l61assllnw4ter at a frequency of 1.5rev/s The wheel can be considered a ls43l)2s,m6sbnp1a l 1ci2 v b8koisw uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momvu8 lmdev.mw)o9/i *bb -0fnlentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of thz*ds,ptel1v 3 e 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,l7 fa+j)gxcy disk of moment of inertia I is dropped onto an identical disk rotating at angular speg+yjl) f,x7caed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.7 fksk.s7. 7i kua7lrj4 $rev/s$ 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 9)dxw pt(iv0yh p4 y8zkg stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment yx)p0w(idp tv8yh94z 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 rotatingfdf8: h:f/o dq freely with an angular velocity of 0 /fdfdoqf:h8: .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 t7w*vhc80 ge uwhite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the78*hgcev uwt 0 nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120f.5vqq b :x-v qg):vpct4jer2 $km/h$ 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 n75akn,u:w ku $ 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 can0;nvkkma4.kg h xk r6; rotate freely without friction. The moment of inertia of the person plus the 6krav .0 ;gnkmh4kxk; 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 diamdlc9mx ,zja 4-eter merry-go-round turnta lc-9ajdmz ,4xble that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the c4thp pno2nvm .br*-8end of the rope lying on the top edge of the spool. A person grabs the end of the4n pp8*2v bcnrho-mt . 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 side ali1w06n*6l mev/ ooysyv5ins2:d tsj6 ways 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 Moon as a partis21 0* i sm:6nl6y/iwsvo tne6dyjvo5cle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates frozt52 rv 1 d-erjrotvof6 :4r6jm 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 5a+1x 1 +, uc*x2qgkgfentuggshape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleu qgcnf xutg,+*+11g a g2kx5eration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, er9v)n xy2/ n: e)lotivkt-n5lach of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long stk v/)ltnyx2 ril9o5v) -enn: tring, 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 rcfbj+t 9 2uujb*qcy i6*mbp 3+ear 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.ndvzd28 be ee7ed 8-h0swa p,d/ -m8da0 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, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carrieeenbd08pd-e m,/w2a d7av8sdd 8h-z es off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low- ) x,uppd6z80jwrvx 1tpollution 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 flywhee p6 ,x 1wdxjzu)08vprtl 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 illustrateq)z0 yi 3we3 vx3shh-ss 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 hu2rhc/s i sw o4c2yl26orizontal 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 fr2h m(:a ,+;uu6f2wqflo mf znneely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of 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 mz2fu:2o+ wamnf6m ;lf q(,nu hass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. 70qefv6pm d7qvp;aq+xagz y2* t6he (z t* 9ifIt 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 against whicg+mqe p0y6(dz v* xteh qpqft af6;zvi*9 2a77h it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road ixvj:r3 l5u .m+f (-3edalscxq tw, ;kns making a turn with a radius The forces acting on the cyclist and cfxt3mx+e q:a 5;jl u-c(s3wd l, nr.kvycle 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 slim0ys t4r)u2w gwg)i ;ing 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 ir4)2;igstwug)m y0 w. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms asfye3ze9wrc4i:p b) kqvlu;g vmg- +26 thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinncqlig)v26 y+ 9v-e mzg 3pw4f :;bukering skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assfz 5nbvdootv8+8y 0 0rembly which consists of two cylindrical plates, of0dtbvor85 nz+v8of 0y 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 raf :g*b 2gq9p5nn 47gyoifx l9k+m1mfrdius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marblmf9l7og1r2 nf*fgy m k 4:5+x pgbq9nie 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 fu- (fk*ttq5xnot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revo5s.vdstn h1uur*m ):zc:y1 hd 92yy do2*q japlutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was)11.5yh*yun ad2d ysujc d2* p so:mthr 9:zqv 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