A bicycle odometer (which measuresoku /1b we.nccn80-ke distance traveled) is attached near the wheel hub and is designed fork nc.o-/e01u8enwckb 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at ii wm50r,gs87 qme3brx(ys *aconstant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration gbrxs0r387sq, y*iae m 5imw( change?

Could a nonrigid body be described by a sing epgnxie).0w*1od 6vcle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torquhzod.o;zr 5f ;e 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 l be7(;i1,ddluu ery(y/zx.qd cda47n when your arms are stretched out in front of you? A diagram may help you to answer d7deyd(y.i4l x bd;7zr1/e q,l(u uac this.

A 21-speed bicycle has 7ltuifg 3a)dz.b ,qjmq6ycew ) ks-2 .seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a m3tek.wq qg) lf2dbz-7u.)jc6 ,ayislarge front sprocket? Why?

Mammals that depend on being able to run fast have slender lok40a;a5 d f 0nz472fu3lxm0dsxsmk zrwer legs with fleshxzf 0afdmx4 d20z;7k lam5rsnu3k 04s and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8(k; 8- aiizzlc/. gpsj–35) carry a long, narrow beam?

If the net force on a system is)abk,s6ftds*ofk;k5657s9yx: g wu/m jqjz z zero, is the net torque also zero? If the net torque on a system is zero, is ju9,x7:m sk*ssgt/fbkyk w; 5o )6d6qajf z z5the net force zero?

Two inclines have the same height but make different angles with the horizontal.f,ta9c0a)w x.i2 5ifirqy: jb The same steel ball is rolled down each incline. On which incline will the speed o aq2x.9b a)tj 0,c5iif:yfriw f the ball at the bottom be greater? Explain.

Two solid spheres simuij x7n1il:m 3yltaneously start rolling (from rest) down an incline. One sphere has twice theni :ly7m3i1xj 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 kinetic energy at the bottom?

A sphere and a cylinder have the same radius and t v*iu7n 2ua xytr2yv-.he same mass. They start from rest at the top of an incline. Which reac2nir y.vx y 7-a*2tuvuhes the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most zyv-0-lcn s) wmoving or rotating objects v y) --lznwcs0eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wou pt c ):+qlbzf*bbx3y/ld this affect the length ofbb zlyf cb/) :*qxp+t3 the day?

Can the diver of Fig. 8–29 do a somersault without havin hs-0,gay6q h8ai dqw idv+-d(g any initial rotation when sh6qa+ g wyi-h a,d-d0(sv8 dqihe leaves the board?

The moment of inertia of a rotating solid disk about an axis throud)oo -wf9 7quegh its center of mas7) dwofu9 -oqes 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 sittingvh6tivm ( /w3o m,ism+q4zkx7;e yk3l on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angu iv46mvtk;,3q whmmkelo(x+yzi3 /s7lar velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and hagedj. t9+l m-msgc d4nf.2 ,moa)tz 0rve the same mass. However, one is hollow and the other is soliddgcnam. +09,rl-zdf4.s2o gmj )ttem . Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a hor3wlelin m n7nai.fel btkoq 5;hw** hl9r2119izontal axle points west. In what direction is the linear velocity of a point on the top of 1 lme7.w3lf*in2nlr haetkh*bl 9;wo591 qi n the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large ev+2zxf5f:t q freely rotating turntable. What happens if you walk toward the center:vtfe5x fq2+z ?

A shortstop may leap into the air to cat .vhxvfizk3c y/1, )vzch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and l,v/.zix3zyv h1kc vf )egs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of wv4 ;sw ah89jhs6k( htangular 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 the helicopter s k;j9v aw6h4w8hst(hstable.

  Express the following angles in radfnotv 4nlj,8l4. p tf+ians: (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 becau4 6ftiqv+vc*(gtk9n ose of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon,toc9k ft+ qvg4*6inv ( as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The bewzjdjdc6 9io1.(dvk8 zjz+ n8am diverges at an ak(cjz8 8d.z 6 zondji9v+d1 wjngle $\theta$ (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 turne/ garybvi+c.0j- 5zqbd off dura+5j /vc b.-rqg0zy biing operation, the blades slow to 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 another ch/*a*sgsisl4 :ecm6 :a5u 1ik49qivzq) r bqrhild. If the ball makes 15.0 revolutions, what isa:iib5 sc4l/ra*r uz1 ih:49m6 qe v*)kqqsg s its diameter?    m

  A bicycle with tires 68 cm s ,xa fr)je(egp2* )skin diameter travels 8.0 km. How many revolutions do the wheels es2rg(fasep,*kj) ) x make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angul80 dnspcb)w:ranw.f j y*pa7)ar veln08ab j.fwsdcpr)wnya p*7: )ocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 ymd2*3fwl0 * qo0pkj ks (Fig. 8–38). (a) Wd 20*j0kfylqm * kpow3hat is the 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 vexr d loinxc891x4k(uce6 y)( blocity 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 speed of lw tm k9;s-ms ,p4ds-fa 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 cm fr,u;r w i qzn;883ddyq3ilio3 vom the axis of ;iuqo,;8 rn8yi3dzld33 iqvwrotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center fow2:0; a-p8)nndjokkpj 8qbdrom 130 rpm to 280 r );2pj:bo -dj pan0k8dq8 wknopm in 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 radius*uixqss:o8ef s-m. s0 $R_1$ 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 spacecrafs- g7l/fza i7vt put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no r/z 77alvfgi-sotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge acceleratj9 z:mi6-hsmh6hbnx e ui3d-8es uniformly from rest to 15,000 rpm in 220 s. Through how many revolutionse -: hmxuj3b is9iz-86h6 dnhm did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcrezuqgk2a9i01;rzlzo:1 k(jtbi am); b5( p eulate
(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 ipq(eeww8b1b( )+pa t+mj;j e zn a whirling “human+p (b;bt+q1 e)jz(w epwjaem 8 centrifuge,” 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 ihr tv1di4:u1e n 6.5 s. H41eh: t riuvd1ow far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850revf;u )4u9nvhh., yjzgv/min It turns 1500 revolutions before it comes tozhfn,y huv.v 9;j4 )ug 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 rh;xk krc6wyvsaenxma7:, 5 3/educes its speed uniformly from 95km/h to3sna 5mhx7y,v wce;:x r6/akk 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

  The tires of a car make 65 revolutions as the car reduces its speed 7ug r4 ov06xrltv/)s/o bkf u4uniformly from 95km/h to 45km/h The tires have a dia4r )v sgob ox/0t76v/fur4kulmeter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when clii6ydka67lsko f 5 fn0+mbing a hill. The pedals rotate in a circle of radius+o i0k65nafkyd7 l 6fs 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 wid9.;upsh430xzr y hcf9 xmpk1ye. What is the magnitude of the torque if the force is exertedhpm4zh 3rfyxx;cu s0 9pk1.9y
(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 Fub 6,q2 jye(ojig. 8–39. Assume thato,6(jbu qey2j 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 the ends of a ma7k 41f3 hupiu a(/nqqcssless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude a 17nqaic3u4 h (fup/qknd direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tig7jm -uvhdhy 1 v ox rtj2/.s4b24m;eashtening to a torque of 38 vo u. j-bv 4/4tje2sr;admsx27 1mhhy$m \cdot N$ 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-kk50. , ou9 amkf+yb7jzsq 5gqxg sphere of radius 0.648 m when the axis of rotation is through its center5abs .ukx fo 7q+q5z,gymjk09.    $kg \cdot m^2$

  Calculate the moment o ci(my8zw9h:e9l5z wt f inertia of a bicycle wheel 66.7 cm in diameter. The rim and tirlw5e9thz c (wm:9i 8zye have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of+q ..erxt8hdn a thin, light rod is rotated in a horizontal cit8x+e .hqn. drrcle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating ;z b*z4o9atz mg5 nrz(at constant angular speed (Fig. 8–42). T4zb*t ranog ;zz mz59(he friction 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+8i3wnz a kts,. 8–43 aiwsatz3,8 +n kbout
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose totaoq4w+*bo4cu. ,w ay xqt+l) oel 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 cztffv4 l*yry()o x/z j 86x)nyorrect 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 s )fn )/yoxzt8y4rlzvjx( *6yfteady 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 uniforqz n,5hhyz1ezyi, p/gbi4-x: m cylinder with a radius of 8.50 cm and a mass of 0.580 ky, ph/5xiqh ,:n bzz -1gyezi4g. 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 from rmb.f6zhl y1,7e (cg baest 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-rou8p;6l u i )6crtceh6uand 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 muuaci)t cl;h666rp8e ass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10;m30axdaok wkc*:rj pg jurm r33+0c8,300 rpm is shut off and is eventually brought unifor0rgcoacm8d jp r03:awx m* r3k3;+ jkumly to rest by a 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 accelerates a 3.6-kg bal *pa mpym)m uc 4v.)z.+c htg*(cly(vkl 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 act ;mye) s fjy-uc26uo gb6,svxya e*a;3ion of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rm x 6 2aaj)fgc3-eb*; euyu,os6vsyy; est 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 consid v3n): 1j x1 xmwm+hjig+pbai.ered a long thin rod, as shown in Fig. 8–4n1+v.i bxg:3impj+ )a1wm xhj6.
(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 tn1dq4nhp-7 0/apusdi+zh (k t*jruv2wo 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 hammew 98fbhes( 9efr from rest within four full turns (revolutions) and releases 9ef9f(h bew8 sit 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 inertia q /eiz6ivq b7-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 tog89qj m(0gbe crque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of massk h rdwz*)*k4p mtb:s3 :evd:k+wwg(d 7.3 kg and radius 9.0 cm rolls without slipping down a lane at 3.e r(d:twk* pgbwm4*zk )::+3 kdwdvsh 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Euev/c5e9ksd..j; dp; o m1afo arth with respect to the Sun as the sum of two fm/o;ks5ua.v9e1jec.od d p; 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 radius3hru -mis4*l m of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolutu3im*hlm 4 -srion per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 .ib xjv/w65hy kg starts from rest and rolls without slipp/x yvb jw.h6i5ing 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 to fhq.(( yjryc y3all and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energhy r(3cjqy. y(y.]    $m/s$

  What is the angular momentum of a 0.210-kgxz uf d) /(a-ue;;hd*;ln tjeg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.ght)jau/;u;;*nxl-( dze f de 4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel on rd.t.cil00hb4wj w)r10ed of radius 18 cm when rotwrb10 n .0l)jt4ihdc d.ewor0ating 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 rotatito2b/*gz iej( ng at a rate of 1.3rev/s If he raises his arms to a horizontal position,/iz (g ot2eb*j 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 i1cm 11ei30/zqr9nsb3rxpsq 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 whr bnrszim 1xi9cp1033 s/q1qe en 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 from an*n2 zh; nsgv+ e,io4wxfl y.cxzt*((z initial rate of 1.0 rev every 2.0 s to a final rate of 3 vy(s.n* h,4xicz;z (o*fe2gtn wlzx+ $rev/s$ 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 ax eks2kp jl5y()-6a4rhwiquw0 is 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 3.52kh-wq)ile u 4yjaw p0k (r6s1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater .oa 0b21zbu hnspinning 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 angular7cdb) l1-t s-xg+xpnb 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 moment8ee;5ibz qlu i/1jn x9 of inertia I is dropped onto an identical5nx9qij/;b1u e 8e ilz disk 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 2.4yvc)n)2c6o py $rev/s$ 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 centn4( t) sv1jzj1g3 kgxjer of a rotating merry-go-round platform of r g(s jtz 3xkgnj)v14j1adius 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 wiw8cu 9ci el(ou9ngocg,w 6cld, f0 q+.th an angular velocity of 0.8 icgne 086u.u99c +dqog fl c,wo(,wcl$rad/s$ 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 eventnbo.p./ s.qsu ually 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 lostupb/.s .sq.on 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 excessg5e -c sph6nruhb2 ; hkyaq941 of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass b9te e 3l/ krg d0n4gxj7 a )y/:6d/zek7gtmti$ 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 r;8urq1j9yljd 4kx2bh9a ,pv + e6qvurest, that can rotate freely without xbyevj+arr4u p2qvjk96q u ,81h;l9dfriction. The moment of 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 stooe tizvg,)6l pcz3odh m 1()gl ;g7.yands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearini lhge 3l )1vcgg;mpt o o6dz)7,(oy.zgs 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 withhs+ wpcbfa q/1 0:f4jm the end 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 person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of masc0hjbfpw4a qsm:f 1/ +s move?

  The Moon orbits the Earth such that the same side alway pynv7fvt s 2 9-e6qpmcfi64a 1pc0 fw5)z,iaqs faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, tr)piv,-mc f5npv 6 ywq7eqaf0ip2z1fts6ac49eat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fromk /((gc wa odm5:qfqz- rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquire85hz ci+v+ bev9fky4;z t8hnyw4 (kpu s a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque vhuik8zhyeb c v 4pf;8 +ykw(+9 nzt54delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, t,fmfo9i39 )w1shl w h.z:nfmeach of mass 0.050 kg and diameter 0.075 m, joined by a (conc9f,f tms91: fl.3om iznw hw)hentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is t01ns;p3rv rv3h 8hngihe angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0:yu t +bxr:g*iipu to(2n2a*n 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 it(t pn2u bt*+*ui:r n:2ygxoia s 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 autom9epu obq z490f*yc3 sdobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km wifo0ub9 e c pds934zyq*thout 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 illustratec(;a;xssbx zv .b6dcc.)2bqn s 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 oe s fmo8r8.l y14-tk6q -abhspn 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 frggizwh q6x3f9le 9+jx9 m,p6r 7 godt7eely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then rele9f i3,dj69lqtxgoxrh z67w9p m+g 7geased. 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 standing vertically on9nw;xn7r j :8 1mhrpvp the floor, and we want to exert a horizontal force F at i1n9rp rjn ;m:v78pwx hts axle so that 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 ;nt( -yu5u6(j*q.l jrl knfd wis making a turn with a radius ;ul.n wuk*fynj j(drqt6 l( -5 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 0.50-kg rock into a slihbd1yd 3d tw*(ng of length 1.5 m and begins whirlih*b3 ydwd1t(d ng 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 torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, m r;es4gznh( j :0k.kteaking reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinne0;kr e: st4zgj(hk.ning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which l8,/jrna 1iuq consists of two cylindrical plates, of mas,/ jqu 8n1lrais $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radiz,(gpl,m 1cc ;xalgn( us r rolls 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 thlxa(l, ;m,pz(1 cn cgge 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 assume 9q,i3*e-cwc (twuae1h4hr6wbrs,df$r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car redu lg y3d8aau0)k 6hgtu7ces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) aug uy0gdta8 36)7hklWhat 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