A bicycle odometer (which measures distance tra -c1nga a92yc9g-dw qwveled) is attached near the wheel hub and is designed fora-99n12 - q gccagydww 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant anguladhou: b2n :afx0 1oycl/zo btz4n-n(;r velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, doedx o/bb ynu:12o az(-zhlt :o0fcn4; ns 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 lfp*ow,( 9nt t9;jw tra single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greategj2ng;/sypqcngk / ls7e9 55er torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your head tha qkdcx0oz76q(wlf ,m9 n when your arms are stretched out in front of you? A diagram may hel6w0o ql9cf,(dk 7x qzmp you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three8f ysum4k (jha+p d7/h-icg y* at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large fron 4yp 8(*ckm-jihasdgfyuh /7+t sprocket? Why?

Mammals that depend on being able to run fast har.nhhr .+kv)g0qp6m kve slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this h) r+pqkh 0 .vkm6.grndistribution of mass is advantageous.

Why do tightrope walkern 8ivch:5n69 bw3bqn+ ksjn re -)jx*qs (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net tork ohj80tny 0y-)ge+nlzx*p2 coh8 6ncque also zero? If the net torque on a system is 62n*o )+hk0hz-ynytjcg c8p0n x eo l8zero, is the net force zero?

Two inclines have the same height but make different0zpuvup5a-(vx 1qpk2 angles with the horizontal. The same steel ball is rol0x1uvk2pu - ppzv(5 qaled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from resr4a jghr(+nia 9nlimz: - te2)t) 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 the greater total kin-n l )natr4+m:zjriihg9 e (2aetic energy at the bottom?

A sphere and a cylinder have the same radius and theulbrj z f ;:aoq/s)(3h same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater spee /)ahbu( r :jlsfo3z;qd at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum a7he cc i gkgce.m3xn:)y-53jxp 8ixm f8*d,afnd angular momentum are conserved. Yet most moving or rotating objec83) i7xie caf-,8xcg3j m5x:nd fpg .myhekc*ts eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, -5ab4owcil/3 q3 ;b x;pynfs o:gd1jwhow would this affect the 4p iodb -g wyaf13nl3;josb:w/cx;5 q length of the day?

Can the diver of Fig. 8–29 do a somersault without he ,-puro: s6mzaving any initial rotation when she z:srom 6,u-epleaves the board?

The moment of inertia of a rotating solid disk about an axis through its cented4 lr* mrgu-t+q3 vgp8r of mass is +* qrl- 3tumv4d8ggrp$\frac{1}{2}WR^2$ (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 sittiny+gxcay(76 .bypz v h;g on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the mayg7a.+ vcy ;pz(6byhxsses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look ide*m *1db 1rogko vmt0 9bj-gjo+ntical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to bdjgb *ork*v1g +m- mot1o 9j0determine which is which.

The angular velocity of a wheel rotating on a horizontal axle pointo 3 y 9sleian+(ec:qr8s west. In what direction is the linear velocity of a point on the top of the wheel? If the angular accelerqleoir n:as98(ce+ 3yation points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Wh (6ywwyg ea 1*st6cnm-at happeny 6m sen6-g t*a1cyw(ws if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it tzg/w)gy(at : quickly. As he throws the ball, /( g:)awyttzg 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 confwax7c8k+ 7 iwservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep axwk787c i f+wthe helicopter stable.

  Express the following angles in radians: (66jlx3 )3omr ne65yc 5gaaasva) 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 coincuh50 id exgefj w eb2zc38g149 hk,4roidence. Calculate, using the informabo0h53gejde4k,r1whfxiue 9 c g48z 2tion inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. T1 ;(gcia( g8tv+n/ca. zqc6h+ jlmgushe beam diverges aai+ s(z;.ta 8cgjhg+1nulcvc 6qg(m /t an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blen-k:2 t6qp xlmdder rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0p:d k-lxmt2 6q 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 another child. Ifx3x5wb;a9i;oabcr diyoi s84 n a(y,4 the ball makes 15.0 rrax(o,ax4n i;5 w8bd;o yiy 349isbcaevolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diame/p0rdpi cz4kac)7;,8tsbrm1bzv l p1ter travels 8.0 km. How many revolutions do the c7m /bp1p tvri )b8k4z adz,ls1rc;p 0wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates joyqj(kw1 q9e8t (cq+w 38cpzat 2500 rpm. Calculate its angular velq3ct8(q+o 8ycew9 zjqpwj 1 (kocity 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 r-a zu bhbh7u5 y h*iq1tyy+48in 4.0 s (Fig. 8–38). (a) What is the-7 4 yt8h+ryu1qubbai*y5hhz linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) inemfvg6aa8nuxln: 737: )v ybx its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point d -qi6 u v5jc18bzh4yi7tie9g
(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 rops0/m6cj;qv l7 pk bs8.s wxy/tate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,0csby qsppxw6 m j;k7v/l.08 s/00 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center4k9q z71db e4qlk,r,vom* kvk;j 0 vde from 130 rpm to 280 rpm in 4.k v0,zj1m7;4bdo 4k evq9q,ld e rvk*k0 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 radiu0*v dxg/)uk hn 7r1cnys $R_1$ 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 3:5fm ccfjo jd8o -*nxaboard 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 evf *3o5ofccj-d xj8:n mery 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 rb p9zjn87y7yd5i kl s+est to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time? l 597zynp+i y7k 8sdbj   $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculattrc otl1* q+7ze
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “h,)*rakyiky h6q2ry;s 5qu ,bguman centrifuge,” which takes 1.0 min to turn throughr5rq a) ,,ukykg* y 6ysi2qb;h 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 in 6.5 yt w3t;6e ;d9gvdk1nps ;vpk;1dte6y w n3dgt9. How far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it i7:nyo pw0b.pgf/,nrz s running at 850rev/min It turns 1500 revolutions before it comes to a stop 7 /p0:,o.pwn fngyrzb.
(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 redu e,qn n3k1v*dw gbxv,-(oita3ces its speed uniformly from 95km/h to 45km/h The tires have a diameto3v1( ki-n 3*, vqndwb xag,eter 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 revo r(8y;yd iifs0lutions as the car reduces its speed uniformly fro yd8 rii(;syf0m 95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal whebiwlr/4jc1 y tr2e ,-4rzff a:n climbing a hill. The pedals rotate in a czfta4rw4 /- yrf :bcji2r le,1ircle 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 7tojq7z8h r9qp*jo8.h 4 cm wide. What is the magnit hr7ojt.o* pj qq988zhude of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8fzkum,yl(3*cg a2w 2jyy 2kxmi-f8 e-–39. Assume that a friction torqueykgica j*u8e2xk z,2ff-3wmy2(mly - 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 3rvak+ mi0qx - zibw xi71/w.pthe ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and the b.m0z p-kv7 wa1/ ixwir+xq3in 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 torque of 38 i-rbzaq0.0ls4ck o4b r i0 cq.4bsb4-k0oalz $m \cdot N$ 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 s6.d-k2xo/mr)bu y:scu iwr;yphere of radius 0.648 m when the axis of rotation is through its cent ) y;romu/u6xwb:c s- yd.kir2er.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whb4 g4fph5 v n/u 3z*cop8pgx+seel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. Thevbg5c8n/up+xf4h gp *os z34p 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 isg od x*rrsiv./a jhb6y/7*9n a rotated in a horizontal circle of radius 1.2 m. Cgx hjsr a/iad.rbv*6 n9/y*o 7alculate
(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 angulhq7pvj 2b6ld::c5h zhar speed (Fig. 8–42). The frict::2jcphdhvbl76 5 qzhion force between 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 objects shown in Fig. exwk+g5 nkgjf /09b f nej-01b8–43 abo 0ebk b+1gew0f / 5njnjfk9gx-ut
(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 coalocbvf 22gafi h4:(g1u/ lq5 nsists 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 rate, e+:zbpod t y+z4cj6l, bngineers 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+lpycb+ bd:j, zoz4t6 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 cylinde(:n vdp k,*+:dfne vri0jtk3pa6 s6grr with a radius of 8.50 cm and a mass of 0.580 kg. Calds+ptj6d* :r0vvpn6:g, krak3efn ( iculate
(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 qav ;l.u3nj0rfrom 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 mersy4kgm58vg 2r f82aw cry-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 282yr g 4wc vakf5m8gsdisk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotar.rb0qnd :7qmgjml )0 b x-.mkting at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torqm q0m.7rd: b 0nkrxjgm ).b-qlue 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 accelerateb 0jk wbgsb0 -bx8i1x3e /7jaxs 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 tvd1wzw90 bt6eot b/ pu j9msh044mpz3he forearm, which rotates about the elbow joint under the aczh0dp twe4o s9w40j1pvmu b3 6bzmt9/tion 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 thin r7g;*l p 8jc iss/whbv7od, as shown in Fig. 8–46.c/ vjpb*g7 i;7 hs8lsw
(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 qk5jnv)r.e9mx :ciy-i2 mc1j masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer pt1zrl/z 3*hy from rest within four full turns (revolutions) and releases it at a speed of 2yp lr1*z/3ht z8 $m/s$ 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 m/x u5m u3jdsb4 z)t/xvtyq8-o -mdpgp4*b3 cqoment 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 q*+y iyir w l0w 5uei,bt/q.wb9uk q,8h sq71ka 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.wzfo y 2n2ch6,3 kg and radius 9.0 cm rolls without slipping down a lane atz2n , wfohc2y6 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of th48kr/v /hwxxaz3dd (o e Earth with respect to the Sun as the sum of two t8x o//4d3wxk zdh rva(erms,
(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 m0h p;optnh76k1m)ey 7x) 6vzzsq+ by7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? 6qyk6zn7 b pypx);o est+h17mz0h)vm Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rag sei:jbp3l1j900k q: 7nw iwest and rolls without slipping down p q0:ba sji nwwe0k9l3ig7j: 1a 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. I osd6lze( 1-oat 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 a(edzso1l o6- hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-b+ k 2og2xlhr0ghc z- hphd+u4z8e p+4kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 2z44h-p +h c8bk2+hzo ldpgx+re uhg0 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of adn+fonkfh1-:hm7 0pj* ei1m y 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotati*i0kfhdn 1h:fnem + -7 yo1pjmng 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 at a ri 0crn(hr/ t3zate of 1.3rev/s If he raiin/h0rr zct3 (ses his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inertia uri(w (8kmpja1;2 *xfsawq c.h5yx7y by a factor of about 3.5 when changing fromka xsrj1 7xayy* p(u m8; f5i(q.w2hwc 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 increase her spin rotation rate for) x-z6 krx7ujzlo ;;rom an initial rate of 1.0 rev every 2.0 s to a final ro z k;ulrr x-xjz)7;o6ate 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 aro bt)d0)+hx0 imsvrj8x und a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kgmv80 it xdbx 0r)j)+sh chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinnin w3c gf2cqld6551l /nvd9t dehg at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Ef+a w5h1 im7se0rvex.hq x35iarth
(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 orn(te*/ qnt2 jnto an identical disk rotating at angular speedn tej/nr(*2qt $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsl( /(l.ognz :ks,x63urd) 6ftlx eyh j 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 the center of*44 c q,z*nojklxc93z ap8vlwl1 o0up a rotating merry-go-round platform of radius 3.0 m and moment of ij zn1lc** 0,z olavu9ko4 c4x3w8qlpp nertia 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 rotating3*ycnh dck0t0 6 h1i+f5whkve freely with an angular velocity of 0.8 0 6nhv3fche d105 ktchwyik+*$rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf.us5k; i-tu 0fo nojey2ar4qz(i(r xs2;pvh4 , 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 4shfk0p syn 5a(uzoejorqr ;u4 -t(x;2v2ii.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 )qb)+d m 4v yqk;mzsj4120 $km/h$ 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 5i iy3w3meb+q $ 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 rotgzfd) k+2mq4y3ozulshc75-r ,lz pf; ate freely without friction. The moment of inertia of the person pk;) f zzl7 muoshg5q-lf c+z,yr 43d2plus 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 gzvm ivj(i:-3 edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of-iv(mvzj: 3ig 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 groundcr/ij;jq q:8v o kz.i5 with the end of the rope lying on the top edge of the spool. A person grabs theq z iv.kiq:;o85/cjjr end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. q*srin.lxr ls0 1+7tpDetermine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbitatnp7 sir 1sllx0+.rq* l angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of:.t o(x.f.dg2ytb rmg8 q/jzm 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 shapeshf1 6e(6o kdc 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 acceleration. Calculate the torque delhc6ksf e(od61 ivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kgwl71oed, 5klijz y*j0d (v 5io and diameter 0.075 m, joined by a (concentric) thin j kvzoe,iil5j1(ly05d *odw7solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the ank 3v*;0d4g te;dw a aaojuhy:7gular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun p4b8r7z lnzd7, 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, losi87br7 pzl 4nzdng three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use eebv0t/5 rl; p+p 4htz aqk8qz9nergy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 ;zp/ 8 e +zkt0tq blh5a4rvpq9m 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 illustrateskeui+9z3ov* p 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 hoka(epu-/ 5l0*u aht vorizontal 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 lengt-sgp/ n eyv,4x(1cioph L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally1s 4cvn ,ipy(xpgeo /- and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is stand;yy x)+ 4v0ayzg cgwy7ing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will cli)4yzy0y cx;g+y v 7agwmb 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 flatnx )x62sp*bdevulw7 2rmey); road is making a turn with a radius The fop;smxb*d e e7x 2)wlvu)ry6 n2rces 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 a 5 hmvg bdvb27*sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torh72bmvg *b5 dvque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thi+0pgv3n, jvk4ec l9 tkn rods, making reasonable estimates for the dimensions. Then calculate thet +9pk4jg k vnc03evl, 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 assep l .:qae agben82pheueb (5;*2zu* cmmbly which consists of two cylindrical plates, of mas hez n.*pg*58mq c :uab;(eeb2e2pauls $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rol ze*0,z;yn5wx/ spb zhc 2*qyugh track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is te/zzhw q02; c5,s*z l*yyxpbno 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 assue/k3elb (.w-4jfh x- )zyd-smyrblox7n me(( me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as ,/nrvzu:ny )cthe car reduces its speed uniformly from 90knur/:nyz, vc)m/h to 60km/h The tires 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