A bicycle odometer (which qr50g pos;x2a 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 r;o0 pgqsxa2524-inch wheels?

Suppose a disk rotates at constant angular velocity. Does axf/g5 jk 0g2s. 9upwxn3i e)cg point on the rim have radial and/or tangential accu/ p2x9fgckni wges )3gx.5 0jeleration? 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 a3ta y.ono1bmuoq3b8* single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torquees:5u2 htt5bb 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 /y3v4sm gwvnw+ js(e5sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer +v 5/wy4veg(s3nms j wthis.

A 21-speed bicycle has s-or .lb2cp lk/even sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rl-/k2. poclrbear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run t/o7g66k+o iyn y2vzgfast have slender lower legs with flesh and muscle concentrated high, tg i6y/+7z6o on2ykgvclose to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Figu6o4jny3 kklz+4 s y:m. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the i3(j t;f azroww0ug: l3v z*q-net torque also zero? If the net torque on a system is zero, is the vwfwal: iq0 ur tgz-3;*zjo3(net force zero?

Two inclines have the same height but make different abod072pkoc p4ufy )gy*k (pv.u5)mpj ngles with the horizontal. The same jp gcpbm( y)fu d)54o2kvy0ppok.*7usteel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously star)6 y+lvg lnx45g tsq*rt rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has r)+*yqt65l gv 4 sxnglthe greater total kinetic energy at the bottom?

A sphere and a cylinder hay*ccdkh2s x5 o9**jrdve the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has *9c5djr kdc *xho2 s*ythe greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yeem5h;* wudg9 mu3je 7zt most moving or rotating objects eventually slow down and stop. Explain9mu7; 3ud 5*jhemw egz.

If there were a great migratlq65kk;(j 2wofhcd,pqcl 38 hion of people toward the Earth’s equator, how would this affect jo 35wp6 h,chck2;l8 qldq kf(the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initi*r55:kne::s 3u* x xi u:9/d5gics py jwvntemal rotation when g e:*vrpyec s/ 5j :imkxi: 5s*utwnn95:u d3xshe leaves the board?

The moment of inertia of a rotat 875 (d;zzr* lmohz:cdml8bbhing solid disk about an axis through its center of maz;5 zhzb h:lb88r dmdom c7(l*ss 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 zse i*9k 6mpx-)emv(oa rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity xokzi-s*em e) 6pv m(9increase, decrease, or stay the same? Explain.

Two spheres look identical and have the sa59ymffa9 *d lome mass. However, one is hollow and the other is solid. Describe an experiment to determine which isyo9f9ml5 *fa d which.

The angular velocity of a wheel rotating on a horizontal axle points westdho z windgt2f2ky,.i8 +g(5f . In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is 8dng,zkf2ghi2w+o.(5 f dyti the angular speed increasing or decreasing?

Suppose you are standing ov5zi ;p/ol7 mkn:10a) jl mikun the edge of a large freely rotating turntable. What happens if uk zm;pa vo0il/: 17)nikmjl5you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it qfmn/ao )2pkuo /47vpj 0)oec kuickly. As he throws the ball, the upper part of his body rotates. If you look quickly you win)24/f/pak moe k)70oojuvpcll notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momehla a 1x70sm**hkp)mt ntum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopthlh am*mxs 7p)*a tk01er stable.

  Express the following angles in radians: (a+91mm41(u booz vdtfqa wn)e/ ) 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 coinci0h)qcc 7cu(oss di4x)dence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Ea c)uci)7 sx cqosd0h4(rth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from9og+j86a).wcpq yd :a0h pqu v Earth. The beam diverges at an anj0cov.d gay+:q p968hwpaqu ) gle $\theta$ (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 pzuga/phazz::jrw h.6h (d* (m d.;7fjmjp4h6500 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(:h*6/gphu.za7jp mj(pdfr.hhz daz:;j w4m slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chig )h qczhh85xz:rcvy46x,d4 xb5n x2rld. If the ball makes 15.0 revolutionzv 4hgybcz 4n :x56xr xdqx8hr5),2h cs, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How o)-fao yf,q 2ymany revolutions do the whee-ofyqa,)2 fo yls make?    $rev$

  (a) A grinding wheel 0.35 m in diameter r4.l cxvsu e)0wvr+a2sry -qx;otates at 2500 rpm. Calculate its angula4q)vcelra0; +rsx2-swyv .xu r velocity 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 revolu5 /k4i w,lfhtb1z+e cup1bd(ltion in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the center?,p(id 14kfczewbl l+tb 51/uh    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around the S(p*y x7xv s*pbun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed f5*6-eafje 0x . *n6mhmddv4 i luf/yoof 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 ceo2 hn0 hsgo(vx3kd*ev40b p3dntrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleratio d xe3 3 0b2kopdong0sh(v*4vhn of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its c5vrj;ll, s-qyzk mz: )enter from 130 rpm to 280 rpm in 4.0 s. Dek5)qm- zz,jv: r s;ylltermine
(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 radius vovft- p vk.t6)9)jf t$R_1$ 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,w+;k 6fy qkjb+k7u mf+ astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a dia 6w+f+ u;7q ykkbm+kjfmeter 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 rpm5xlvdlizxe369c70/ d obac 4*b ifq(f in 220 s. Through how many revolutions did i(vx/dl7 cfq6db*f4l9 bzci5 ei0ax 3ot turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.0 5u i x+5 xjuowodx29-iyvbt*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 t5i26xtok(io+ l mv )ithe stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutio)x tilo6+ kmti 25v(ions 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 ex2fke2f uu+nm25)tjqt ys +7yo*g*dfrom 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled e7 y nj2gf+ )2q f2m*ut xys*tk+uedo5in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revolg ijo+ -wivx;)utions before it comes to +;wji g)-ivo xa 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 rev 7j7vfx7xpn; solutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires haf7pjs 77v xn;xve a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car r-kmd5v/9nbwp5 pd tx2educes its speed uniformly from 95km/h to 45km/h The wmn/tv dp5p 2x5d9 b-ktires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on eacho-oeodybfa r c:(.3u* pedal when climbing a hill. The pedals rotate in a circ :-cf a .o*boe(3yruodle 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 cm wide. What is r w5fn52-(5j q;zgrv*2-ga iufjcjtm the magnitude of the torque if the force if(t5q2c;r 5m5 a-uzgij j2r-nv*fwgjs 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 wheel shown in Fig. 8–39. Assumeryz28c5xn*z 8hjq, wnv, hdno0qed,* that a friction tnh 2o zn,x hdyw0dve58*qnj,8qzc,* rorque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attachh+jakzuz; cr+yhsj q9:42t 0 ued to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is helh khqu0 tzu9+sc+2zy; :4rjja d 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 engin pd ja(ts;c;hnc3uc(3w 9pp i7e require tightening to a torque of 38adhtwc p (3j 3c(9cp;s ;p7nui $m \cdot N$ 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 iw*t9-zng (ulr z4 io7z(a a1oknertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotatior*- az loni(w(gou4zk z19t7 an is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 8ly w:z/qqh(i,bb7 xs66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass hw:qqsy iz7xl 8bb,/ (of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizkzgbaid :+(yuh k5zz*q nb+; 9ontal circle of radius 1.2 m. Cz ak9gbq*+;ykhin+z (5z : dbualculate
(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 rota 58qsz9ihl wm-ting at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 19m 5-zwls hqi8.5 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 o99 ufo e7c.qparray of point objects shown in Fig. 8–43 9q .foo9pu c7eabout
(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 consistb01a*fj/h.5tjnfn hdadg8u 7 s of two 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 spinning at the correct ra2 vdoou +ppewvfzne vn3-t-w 5l/am( mr)r.8( te, engineers /e-owm v5 8ndo2n3mw.p)rvuz (-fl(aetr v+p fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radiug-q,ng4i /k yf )hc-zus of 8.50 cm and a mass of 0.580 kg. hfg,g4n- kyu)c i/zq-Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it p s*, ti8ctvq:j s3h)xfrom 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 merry-go-.0j wdku:t +ooround 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 r:od utw 0j.ko+adius 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 rotat)*7a bi-ex qwmc,f 1iling at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional tor7 eclmx*,wi-q 1ba i)fque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.600ijqak2c xc 12m,p5a8l2zkheav 4f8s 4gigm-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 a932gh zi0.eax z iiije rdv3-dky9 l/0r/ iy,the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, -ikr 9i3eja0 i0d h yri/a.i/2g,zd9veyz3lxFig. 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 lon(s,adz 2eetln n/l8n)ek 0ii (g thin rod, as shown in Fig. 8–46.2ntils)zd0ie, na/ l (enke(8
(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 ma k0 sinf,e+vqw+c 2+e4qv+k flsses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within fourkf nt6n54vy7 m full turns (revolutions) and releases it at a speed o nn7kyv t6m5f4f 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 cc,0z y-q( ps6 q, inlkxcby.6of 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 k;0tcqqn5i *s97ov fd: :g2dxyjud.s280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg k (+j*yfatb 4zand radius 9.0 cm rolls without slipping down a lane atyjkf t4za*b+ ( 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sdwo46/ffa ;ir e1llzji83l g1un as the sum of twiw8af6llj 1 /or 1ilez4d3;fgo 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 net4: m 5i+fks3nn.eivn lm 7kuboe5f2 (g work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it ivm3kki nf7.leiumf s5 5(en2b4n:+ gos a solid cylinder.    J

  A sphere of radius 20jn2p gtt*h 9e1.0 cm and mass 1.80 kg starts from rest and rolls without slipping2nh gj9p1ett * down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts t;eg-njhh-m 5go fall and its lower end doegnhjm - 5e;hg-s not slip. 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 lfp y+tumz14d3 w,,cr 9ar xi2rotating on the end of a thin string in a circle o, l93udx mtcf4rarpz,w1+2yif radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of af+z 6k:v3y3oq 1kdxst 2.8-kg uniform cylindrical grinding wheel of ra kky+fq1d3z3s tv o6:xdius 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 a platform that is rotating ai( u4vd+cgl1v uus (k2t a rate of 1.3rev/s If he raises h1+c(ulu2dsu kgv(4 viis 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 one shown in Fig. 8–29) can reduce her zd/l*kt/wid 3moment of inertia by a factor of abo/wkzi d3d t*/lut 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 angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increa1j3;r ) 8ddknk;tgdoqse her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate oft1rkq d;n8kjdg3d); o 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 freq9by+qqc un fuih34a+,uency of 1.5reqcq3,a y+iu 4 +hb9nfuv/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angul6l0iyodkn w yc14k o96ar momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angularixdf2qj: ff /pddl x2)qzv--7 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 an idn nti*)t:4:zjnqx 3fq-*p 6o8uvu djr entical disk rotating at angular speefv64rt * :d- j :3i8xnt qnuq)upzo*njd $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsen(-5txc r t0 ei6,gah at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at them6m3 o()(d 7gurzwnt p1syf8y center of a rotating merry-go-round platform of radius17) nwodmz( ( g8 3yfr6mpuyts 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity ;y0,hrjwvz/2:qo )6 hh nmrqe of 0z;q o 2h:6ejm nrwh,yqvh)r0/ .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 evenk-:dy3hds nc yq0,r9rtually collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of i9ncsk -rdy:3,0ryd qhts existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120 gqn/pi / v8wg unj0/0f$km/h$ 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 m7j 680svlz y.v,dzc+fqnkgsn0x( y5 ;gm fd7$ 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, initiomqivz zg3*10q , l:r2+jfckwally at rest, that can rotate freely without friction. The moment jm rc1 fvgqz3:*z+,liw q2o0kof inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edg qin1-)d ngccxvn 3qq7,*d3lbe of a 6.5-m diameter merry-go-round turntable that b-1ncn , 7qd*3 )dig3xqvlc nqis 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 end of the rope lyinb jlk d6b(0/ qxxc+u-xg on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What leklq /b+ u(c 0-xxxdj6bngth 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 always facn qt8cg: jm/4r7n, irwes the Earth. Determine the ratio ofwcnin7qr j, :/8mr4gt the Moon’s spin 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 hl4dl+(doijf+qrf9 9 at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of raetl*2nub0q(:be w bh3dius 0.20 m acquires a rotational rate of from retqe:b0 u n(b*w2hb3 lest over 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 two solid3pp x6s4okb)z 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 energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-longbpp6k z4xo )s3 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 angulajg sg/arc-a0 2r 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 o5ty,0nku7u fzr 2i3zb ur Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quartuzyr,5tb7n 2uzk0i f3ers of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stored itx t /uhcd76jw b,fb gm 2yz*2w,ag-8qn 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 247y6,8/wggmw2 qhf -2dt tax j,u*zbcb0 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates ae ( ifn;:7r-nqffh s4ggv5)lnn $H_2O$ 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 roh9,k hnm5b9s/g zce x(lling 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 i bc*au*y11q3h4u zsmugnore 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 rousb am**ucu qz1y1 4h3d, 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,0dbt y m mfp67j(f3w0b *afo(j and we want to exert a horizontal force F at its axle so thy tmjf3(0fj0 *7 (awopbb6mdfat it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is maviv(*z 8( fxclking a turn with a radius The forcesl*f8ci z(v x(v 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 0.50-kg rock into rp*1 eff2 *wwdgyk/.ra sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, acceleratr *wr*e2 pf f.dw/ygk1ing it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms /ut7t(. iy*xfrl0uet ;lpl3 qas thin rods, making reasona 30p qutl;. *lt(fxley/it7u rble estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindr nca5.dt .s5lmical plates, oft.clnmsd5 a 5. 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 radius r rolls along the looped rough t35p) gu 8ce0b fwdb,oprack of Fig. 8–58. What is the m3 ,) 8cg 5dbpewufb0opinimum 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? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not c8m( e*ejm*ap xm: 7njassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed 9 cfc d.*kmby*uniformly from 90km/h to 60km/h The t by.dcf9kc m**ires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s