A bicycle odometer (which measures distance traveled) is attachkdnao/ tr0xukze/b.3 3+h2 pved near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bi epbvar/u2.3dhk+/30 zt n okxcycle with 24-inch wheels?

Suppose a disk rotates at constant aip2bj,mao)g wr(+j y-ngular 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 ac 2,w a-yjbm)jr o(gp+iceleration change?

Could a nonrigid body be ci n87aarp6pp6bt-k 3described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a labvf. +:dfj6qij6dte 0rger 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 your heax ((3xpq6jrqk(m1+u0m rrfe p *a/fued than when your arms are stretched out in front of you? A diagram may help yorpru*r6f(a1meq xku/j xq((e0f+ 3mp u to answer this.

A 21-speed bicycle has seven sprockets ateea :hfyl -m:7 the rear wheel and three at the pedal cranks hae7l-:me: fy. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on q.( 8ih,rnge hhxb6.ibeing able to run fast have slender lower legs with flesh and muscle conih x,8ih6. hq .rengb(centrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry+1y xmveb8)93qgjn7) mq0 l tm/boax9nh 9iwy a long, narrow beam?

If the net force on a system is zero, is the net torque also zerjqag nc2i w4h8.m. sopfwh 8;5o? If the net torque onwhm nca.2f s.gq88i4 j ho5;pw a system is zero, is the net force zero?

Two inclines have the same height but make different angles wi fot:0j- )u/ggy.cd3n4m sj7fyo ;wmsh l ri69th the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of 4i f/3fc-s)ny6djrj7 t u;l y .go:9os0wmghmthe ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from res,ig(4 0()hac (axkmk dnk 7grwt) 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 thed0kck )( magigx4 h(akr7(n, w greater total kinetic energy at the bottom?

A sphere and a cylinder have the same 9)q; iip*qfmshr u2d) .6scwsp(/aooradius 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 kinet;fcd owm.) u hoqs9r2/ppi6)*q ias(sic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most mo0v(o 1f yixr l0m+y)akving or rofoaly+ 01my x0( ki)vrtating objects eventually slow down and stop. Explain.

If there were a great migration a ijy-g7d22inx) azhdirb;14d4 mu. lib/vr / of people toward the Earth’s equator, how would 7i/gz m 4aubh.nd 4lib diyra2x-/) j;dvi1 2rthis affect the length of the day?

Can the diver of Fig. p :h;-gki kl ne3g ;na)aej33a8–29 do a somersault without having any initial rotation when she leaves the boar )3ln -pen :3haa j3;;kkaegigd?

The moment of inertia of a rotating solid disk about an axis through its cent6q7kp3fe3k+; zf g unger of mass is ezfgk336 n ;pgf q+u7k$\frac{1}{2}WR^2$ (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 wk; /rtse b3ip,h62sb-,grc g mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decri,ks2hpt ;-err6,wc3 gg/ bbsease, or stay the same? Explain.

Two spheres look identical and have the same m ) sr(ebz j/3doow/1bqjna(m-ass. However, one is hollow and the other is solid. Describe an experiment 1dzsj)o/jem n((/rq3 a-owbb to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle poinns l( j/q*gsojkr07*ots west. In what direction is the linear velocity of a point on the top of the wheel? If the an ooj 0jks7grl( ns*q*/gular 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 edg..*f ;depjlz8a9 jqltrc9rj g7e9:k ae of a large freely rotating turntable. What hap98lr : lj7a*;9jr k azef. 9qcjed.pgtpens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. Aso /v*inn tak;(+rkep- he throws the bkkn-ot r ;/ie (pa*+vnall, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conserkdqzty u(gz+6oopoi eyu- x:8 g76 1e,vation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more way6yig+oeutoz1 7(y-do ue8 6g pkxq:,z s the second propeller can operate to keep the helicopter stable.

  Express the following angles in radi2 cpv:kzw.l8 r2buf/ )7juh5ry,ewdoans: (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 ofk 4-r o e yhffwo05vl;(pwh;:f an amazing coincidence. Calculate, using the information inside the Front Cover, the angular 4oo5-f; 0frvh(w;: yhekf lwpdiameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at5:pxj fjmof b k,;+.vs the Moon, 380,000 km from Earth. The beam diverges at an angb m+ ;x.fsv opfj:j5k,le $\theta$ (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 omv; +qwhp 7ashz1p,k*ff during operation, the blades slow hvmpk*w ,z1sqpa+h; 7to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to ano z8 n*(yrmzleu l26f(4pke-nurxa4y9ther child. If the ball makes 15.0 revolutions, whly8ke4-r znzuaf2e4rmp l *(un 96(xyat is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutio;z 0*vf p0xm8wi8fs aba q9y8fns do thi 8wm0azf pya089svf qxb*8 ;fe wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotatl7w7p bgmexx;wp - 5:*e xdx+pes at 2500 rpm. Calculate its angular velocity ig x*pmw-p+xl;bxp: w7 e7dx5 en $rad/s$ $\omega$ =    $rad/sec$
(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 comp,r:) +p.nst p.kv02;fcqmlvuz3nbu zlete revolution in 4.0 s (Fig. 8–38). (a) What is t ptvu.2:c;nr) 0.sfqpkzzum3nlb ,+v he 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 angular8v :.1 q6qyhjcq w1lnt velocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speevjy6*2l:zc x-)v qia od of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 s8t, 3 yl2z jxmk*sw)ql0xf s0cm from the axis ofzxs, ls0y)*kw 3mfs tq208xj l rotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates untqr)fz.3 k/k7gjtb) :k 2bsnyiformly about its center from 130 rpm to 280 rpm rk k7 :f.3q /jbnt2 k)byzsg)tin 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 radiu0k ja307xid enz 5e)qis $R_1$ 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 Apollo 9kz4osmpv 1wj,p2 7despacecraft 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 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diam 94kmoz,d epvswj p217eter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. *:1kxpqjv5v wj (arc :+*le/2 jjgm yuThrough how : jjuv1xge2(jm :5qkl cpa+r y* vw*j/many revolutions did it turn in this time?    $rev$

  An automobile engine slows downk02o5 0h 5nqia;skqvx 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 stmnet7 uy)ea2( r a(oe:6: xujgresses of flying highspeed jets in a whirling “human centrifugn )yagj(2reautm6 (::ue x eo7e,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm ir3(w+7)ou5lug qr gcan 6.5 s. How far will a point on the edge of) u7growgc(35u+lr a q the wheel have traveled in this time?    m

  A cooling fan is turned off when it if:tkn 5u fh5wj86gy1ls running at 850rev/min It turns 1500 revolutions before it comesn6f5u hwtg :k1 ly8jf5 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 its spe+vtmuv:(+gazd3 a 8- t)yrdjhed uniformly from 95km/h to 45y+)zhd3(: guvdt-a vj m a8+trkm/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 cb2 yr2h nox:9the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.9yh2xn:o cb2r
(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 p5+bik,yp s vn+/o c*rputs all her weight on each pedal when climbing a hill. The pedals rotate in a circle of * ypsvb,5k/cno pi+r+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 onl *,r5ld55dgu wz2upq the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerte,d drzulu25 5qlpw5 g*d
(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 whrpa b*2ss9r9, cd9dd aeel shown in Fig. 8–39. Assume thssar*9d p9,cba 9ddr 2at 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 kts0, qn +;cta,,cvlf the ends of a massless rod which pivots as sk t0,; ncsqa l+ft,v,chown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head ofk+2e -u7yk5.tcyfxh 6lbvtf7 an engine require tightening to a torque of 38+ek. ytlku fhtf57v762 yc-bx $m \cdot N$ 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 spherwn :wej-lsib5. io2h /e of radius 0.648 m when the axis of rotbs .5i :e/-o2njl wiwhation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rimvd5u483tv p. m* gq:b dgekw+m and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).d*kmq8.md+utg34w v v5:be p g    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is cnp (hm8u47jo y3mpv.7kgx 7rrotated in a horizontal circle of ram3yn. v(pcpgm4o 7hj 7u xr7k8dius 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 rotating at constant apvz 87 t nb0k4b9vs0knngular speed (Fig. 8–42). The friction force bkbbnsp 0n7 tz4vk0v 98etween her hands 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 the array of point object.mbjnpj,ufng1lx pt07v 6 i0, s shown in Fig. 8–43 p, tjj ,n0lg7pbf 1mv0inx6u.about
(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 atd da39-t 7ng2* uvxnufoms 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 spinning at the corr4ev 6t1d(f ck-f:2cq vkpxbr6ect 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 if1k6 eqx2:fc pkrvdf-v (b64 ct 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 wiyc8*l n+puni+a 8m,lbth a radius of 8.50 cm and a mass of 0.58ca8ml+nl b,u+ yn8i p*0 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, acceleby0bj9i z4 es4rating 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 hfb5ezw g: *jxji4nvmuqe; , 5.and-driven merry-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 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. Calc4ev5gqj b5f:m . w,zix ue;n*julate 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 rpm is shut off and is eventuallymr)ijau7 y, utu6: a9k5 bbjq7yd 1vx7 brought uniformly to rest by aa7bb9yk 7i5uqy):tu jum dx, vj7r61a frictional 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 acceltdz a 79e.k:+y lcyv1terates 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 acsz3 v+67onrv mrm,pvf0/y7i/i:i f ql tion of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45+sfnz p/i m7miv67/0qyli,fro :vvr 3 . 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 shown in F:k01bycovpi6z 4d10u dqng ys;9 dmb*ig. 8–46.9zg pdc dykm0 :40osu n6;bb1iy 1*qdv
(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 mabmz5732mhya4zk i zz8sses, $m_1$ 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 hmk s3oy/3fazvk; datvp*i8.n2 x,g3 tammer from rest within four full turns (revolutions) and releases 23 s todaa8f33 yxtg,vz *vkkp/; .minit 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 inertiacdk *i6dscf9 fw 2q09g 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 al zn /zh5fjadf/f;+s7 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 sr 5jmz r()4audown a lane at 3.35( 4ajm zs)rur $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the cqi u,*/;j6nnj,uexcsdz )6mEarth with respect to the Sun as the sum of tw u j z,cdiemcs*/xu;,6nnq6 )jo 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,*a4jsnr(hl c swd,i- a mass of 1640 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.-d,s r lc4*(sihnja w,00 s? Assume it is a solid cylinder.    J

  A sphere of radius 2a w-o3 lk-m+yb0.0 cm and mass 1.80 kg starts from rest and rolls without slipping d3+m- okl-way bown 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 ut u,6p1 cbq)0 b(dfxbbalanced vertically on its tip. It starts to fall and its lower end does not slip. What 1d ftxqb(6ub0,b)pcu 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 rotatisn; z7qsu5is+e; vlk7ng on the end of a thin string in a circle of radius 1.10 m nlussiv75k;zq +;es7 at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.tpxq7j) ;4kt qti (lvtl +l.x38-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? t)qltl7v.tlikx4q( + j;3tx p    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, han,ax3 + gr,y6oxyxco24e d0reyds at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreexxor 3rdy2e0c+ gy 46y, x,aoases 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 onr0w (hy.v mm97gu4hff 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 her angulahmh4(g9 rmf 7nvy.wu0 r speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial 6 fh*6t vlvymvoqm30 3rate of 1.0 rev every 2.0 s to a fvqv3mvo h *0yt6ml63final 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 center at a frelai3 0 pv88nljzrw/.lquency of 1.5rev/s The wheel can be considered a uniform disk l. rwp3i8alnlvj0/ z8of 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 momentum of a figure/fhhr b/nu 71c8g (b y4hns.dl 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*t w(;iq,4y2 4y mi vfkhx4vnv momentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto ao eab(l (w-2wun identical aul-wwb e( 2(odisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4jt:m r lhx g9q-h3ro 4y-)b:zg $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round)lp+zqz2k -yxyv /zc) platform of radius 3.0 m and moment of )y+q xzzk /yv2lp-zc)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 .kzz 8l5.2e7kgr bm dbwith an angular velocity of 0.8gbm2rbz57dk k. z l8e. $rad/s$ 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 eventualk;pi ru9x*.qgly collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angul*9pu.k qg i;rxar momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess od 2z(td zgt fa0e/hd3(f 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 6 kvh-q mq(g2n$ 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 rotl*s+ j:) epz +kn2mhs0 3lhykzate freely without friction. The moment of inertia of the person ke nph 0l jsz+km+)h :23z*lysplus 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 standshsnj-flug0 .- at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless beu0--fjhn.gls arings 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 elg/iyf7+5rc eoj53g,m r/(hd vatv 0qnd 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 per , 5 h/dfrj7cvme+5io/g3vl g(a rqt0yson 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 t7 y -3v+inhzodqb1c+fhe same side always faces the Earth. Determine the ratio of the Moon’s sp7qf1+3z oivc- bn+yhdin 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 rest at/8wafg8je nx1 y u0gf8 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 og 6tguj,i3a:bn*gzh1 f a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleratio3n*ab,ijgt6g1 z :ghun. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two so*u5osj( h.:owa*w6fuwp y ) r cue73qtlid 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 diameter 0.010 m. Use conservation of eofoht s):w*pea( 6 yj c5w.uwrqu *37unergy 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 angular speq k8n. eau-t kdx+9;v79p-amb- ajjkc ed 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 mc r) 7fp3m onf-lui11ysg:vt2ass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a l y um ifto-s3cpv:1g7 nr)2f1uniform 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 energy stored r oiz n(mpqh0-*)jy6m *xga2hin a heavy rotating flywhe-ngam r6* hzji20pm) hqx(*oyel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrat(/ h.-6 m /cks;ptyq zt)qcbties 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) i(b/xa,j 1 *df3upex ejs 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 frictiob9+bmyoct9h2 n) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment o9 b2ho ymtcb+9f 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 radius R. It is standing vertically on the floor, 5bf0:9 5st/e6r hjw ov65tu y,szhg jband we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has heightj5sb 6:zysutwv 0r/tf6 ,g59 hjb hoe5 h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is makinhsl**+r7x o jig a turn with a rad*ioshl x j+r*7ius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.8,np gm-zzbo)wvn mr c x6i,.y49m6p l50-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. Whatrnz4,pz-m9 x 86) wgy pn 6mb,.ilvmco is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s bs; d(yej,uls4x+ p -pqody as 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, and with arms held tightly aga-y qp e(s4+l,s jpdux;inst her body.   

  You are designing a clutch assembly whia:6.tqtix3vjjb /v u-ch consists of two cylindrical plates, of massv j iuxb.qj:/tv -a3t6 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 a0f7q)py) n7)jjnsh*msfu h0 along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the npyu )a70)f7 nh)qh f*jj0mss loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do gkq19bvkix r 6 i,7(bgnot assume $r\ll R$ h =    (R-r)

  The tires of a car mde;pvs6oxz:z /f nwz/v e5l;m* fde* 1koc( m.ake 85 revolutions 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 the angular acceleration of each wkl .p*oezcnf(od e :z/;5/;df6xe1 zv m*s vmtire? $\approx$    $rad/s^2$(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