A bicycle odometer (which merug 3-1 4a*t9wxk cb zp b6tdigddy57+asures distance traveled) is attached near the wheel hub and is desigt r1xt*d4d5kp9g6a zcb big y7-wd3u+ ned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotatd: w,tu8(k pjpes at constant 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 : 8kpw,d pt(juthe magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of t6 v cct6yfea2/ypvezg*,w 6;dhe angular velocity $\omega$ Explain.

Can a small force ever exert a greater i lu;mz 8nol98torque 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 youre we2-xr(uv c; hands behind your head than when ve- exr;2 (ucwyour arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the reaq+8t kt,eu6kreu+7 ie r 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, k+e,ut u r+8et7i e6kqa small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to ru0ua *qdyfa 13dn fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, a fdyud3*q10 aexplain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow l 3; ea+f8euvmbeam?

If the net force on a system is zero, is the net torque also3s4, ufn6kbkc*i u6wa zero? If the net tou6b uka,f6 sic*3w 4knrque on a system is zero, is the net force zero?

Two inclines have the same height but make different ang +*3) gszw kzzdc6r6osles with the horizontal. The same steel ball is rolled down each incline. On6*czo swk3 r)6+dzzg s which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from repd1e,cxc6myk l -8 +(t u)nzeast) 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 to)tcem 8l1d,-u6c + n(kx pzayetal kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass.rbcw/v 8ux k+* They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has th8/* ucb x+kwvre greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momeng4fa. ,nx(r/2 v9zkxu1nalos tum are conserved. Yet most moving or rotating objects eventually slow down a4lxr(1 ,uvn .kfoxn/azs9a 2g nd stop. Explain.

If there were a great migration of peox 6 durpph569gn4x0ytple toward the Earth’s equator, how would this affgtpp4 r60 6h yn5ux9xdect the length of the day?

Can the diver of Fig. 8–29 dnq 3cnp-dkg64e: ggg xdl8j z; ..kj7jo a somersault without having any initial rotation when she leaves thegl8p q d6 dge34.g-jkzjnnc7. j gk;:x board?

The moment of inertia of a rotativ+3 p6 fa(fuu) lo *kj a-mzl:oq:+rszng solid disk about an axis through its center of mass+ao* oja s:r)3+kzu q: -zflv p6mfu(l 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 a rotating stoopeiid.m,c/ wp n yn;60l holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decreaseiwdi n;,pep0y .c m/6n, or stay the same? Explain.

Two spheres look identical and have the same mass. Howevh1p2 iic*c4oq4empe7er, one is hollow and the other is solid. Describe an experiment to det7q2phop4mee 14i c c*iermine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. I,n p 0 yxr tj4ub)2f htv-rjk3*y+cp5wn 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 accelerati*xrfctjkh ,)-+p 2t ny 3rp u5y04bvjwon 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. Whl gs9vfv yg(+9at hg9 9v+(sfvlyg appens if you walk toward the center?

A shortstop may leap into the ag++,qcluy ) aija*d)+0xumxdir to catch a ball and throw it quickly. As he throws the ball, the upxmixjq+ l )c+ua,+y uaddg)*0per 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 conservation of anguljj 53;nbw -bedb azq-)ar momentum, discuss why a helicopter must have more than one rotor (or propeller). Disc wnba;eb b-z)jdj35-quss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30* s:ipj7aaum a,,qf/y $^{\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 coincidence. Calculate,8 uqq9d/rfi g6ems+rx;8(um 2wr/xnnlpij *, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and twfepjrnm, m9r x*2x/8iuulirq d(6gn+ 8s /q;he Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divergpq;t- w4 pp08ecnf +fses at p4pn-tf8c+0fe sp qw; 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 blender rotate at a s o3w2gx mihnb,a i6z5l 9531hdm ;kzorate of 6500 rpm. When the motor is turned off during operation, o5whm a sz 3gm5;ni,3i1odh2lk6 9b zxthe 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-c+ fb;3mgnyu .5 m to another child. If the ball makes 15.0 re-;+ gycm3bf nuvolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diam,+ufb/kri8 cheter travels 8.0 km. How many revolutions do the whrf+u/b,k 8h iceels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates a s)v//x+zc81n7t stq7fbu rbgic) 1 rw6jmcj -t 2500 rpm. Calculate its angular vtn-rt mj8v/rg6ius)qw1cz/x71 cs)7c j+ fbbelocity 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 shy 2 xjkgw0gs2y.1av, (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the center?gsga j hvx2,2.0y yw1k    $m/s$
(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 its1 sqao( zt+zy8 orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed): vdv4m*jdn2k:hyz n of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a i13jam3u x-fl ii p;x*particle 7.0 cm from the axis of rotation is to experience an ac- j3i;1p3u*l xfmix iaceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center *3ydre9 qjyp;.cyn+kf*k + fffrom 130 rpm to 280 rpm in 4.0 s. Determrpyekffd *kjc +.+;39f n*q yyine
(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 radiusjwk88wh 5zdbb ba43icvv5 r). $R_1$ 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 Moozm.w 5 b 8x*m*5iemxujl3;uuin, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their.35 ej*;lixw *m5 8buu zimmxu trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 * /eckbqv84qt s. Through how many revolutions db/tv* k4qqc 8eid it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 sihzo8faqhd- ic*q .la+8.w-as3 lz ;u. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the str 4nghz uqqqnt6+c n.k/b,-rf)esses of flying highspeed jets in a whirling “human centrifug6b.nf q, rqkc4/hqntngu z)+-e,” 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 rpmrjy.4b udwq7sh)uy,9 in 6.5 s. How far will a point on the edge of th4yh7)wb qsdj9 y.ruu ,e wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/mil x0klto2q 7e/1em*c3hrxz9 un It turns 1500 revolutl hc0*zert/ xe1xmqul o2k739ions before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 rexf kqv;,k e).vly .sk4volutions as the car reduces its speed uniformly from 95vkqy 4ex; v.)kfsl,.k km/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

  The tires of a car make 65 revolutions as the car reduces its speed uni 3*z u n3s.w(mrkk9yekformly from 95km/h tru*keks33my(9k nwz .o 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 weigjf4l uj0;+a pjht on each pedal when climbing a hill. j a;jfj p4+lu0The pedals rotate in a circle 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 the mag0 jp3t p td8hvn3e-m 4/0fppjlnitude of the torque ih00 jj3 n-p4p tpv/8p3tle dfmf 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 a2cw-d8 i(p bzdxle of the wheel shown in Fig. 8–39. Assume that a frictiozpb(d d82i- wcn 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 gja8iaeh0f6x 14y8vz the ends of a massless rod which pivots as shown in Fig. 8–40. Initial8 hjfaaz6iv4e 1g08yxly the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder heaq j 3b:*ihg ocf7ytv(1y/y8(spm 8dbi d of an engine require tightening to a torque of 38s:qydo fmvbpj78t/yihib1 3y8*( (gc $m \cdot N$ 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 ioku b 8e1a;9k-6mx;ypw + vfvmnertia of a 10.8-kg sphere of radius 0.648 m when the axis of61;ofav ;9 m-yxe+k pbuv8mkw rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in dianbnv.v,q 3ike87 qouuy)c8e z( fc;-qoa1 2oameter. The rim and tire have a combined mass of 1.25 kg. Te u(onuq8yn ai q8.3b, 7q;fozao)c - 1vecvk2he mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, li *z2legf*h6vxh v:rc.ght rod is rotated in a horizontal circle of re6rh2c: v.zfv * xlh*gadius 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 pottera( 7ea :038tq)efgds wd p.gtu’s wheel rotating at constant angular speed (Fig. :udtagtsf0dgqp7a8( w3.e) e 8–42). The 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 i,)cx ecd;vj7v)ja2 5m c;stogn Fig. 8–43 am) s; j jdg725co)a;vve, ctxcbout
(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 whosy(z7z8aus 8l vpp2wc7e 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 s)axdm 8 7rom)+r5x wkspinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a m dm+)as 5ox mr7x)r8wkass 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 radiusrtfm.s0gk j9 4kz,3mswj ni;04xpo.p of 8.50 cm and a mass of 0.580 kg. Calcp0j .rkzf i3p s. ngm4mw9ktxjs;0,4oulate
(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 5muits po0q67 it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tan2o+bn kbht2nz; g h3c0l) 8ido1/t yskgentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torqbb02htol)nn / z ; 1sio3+ 2tgcd8yhkkue required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually bro n0/ mio (ywjf(iea*2fught uniformly to rest by an (( 2omf eafiij/wy0* 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 ball xp mdso p8x3a:*e my/nr/*jp8at 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. 6 l0bk301wfa 6wou 4lxnpi(a pv-yof the forearm, which rotates about the elbow joint under the action of the tr0 w fa bipawx34o-lyl166.(opnk0uf viceps 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 rod, as shown iok2 3+ykrjx 5dn Fig. 8–46k2r3o+dxj y k5.
(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 consxe+blzga;ti60i hh *w;u: aj.ists of two 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 from rest within four full turns (ob9b-i2 kpc8smx4 n/ prevol/kixpnpms8b4 9o2 cb-utions) and releases it 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 mom qogq)3,4lpydhi;oi/ q: gu1h ent of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torquj8mg86gvc 9xem6 t;4moema) te of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without sl(pab 5 b2hxo)ve dh3we0w w1iwjx s,45ipping down a laned(aox pwxwj5 ie2vs hw w103),b5h4eb at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as thegq))5gxz :dkt sum of t: )dgtzg)5q kxwo 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 2 (ub 9h jfbfw;(irxwvdz3:t/c+q+cja radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume9+/q xwt f: ubc32(wrjbj cf vd(i+;hz it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls wit9k9iv+p3 kjt4fzqdb; hout slivbf+ ;9iq93jk t4dzkppping 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 ver+ pha0g.kmmp.)k vks;tically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before im k p;m)0 .kvg.hk+past hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating w,a+ b s/)rxah:f;qns on the end of a thin string in a circle of radius 1.10 w,xa)ss;fa qr/ bhn+:m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindricalp1 nyekh(b-)asmg6)bq *cykm ./ 1koj grinding wheel of radius 18 cm when r.h61)( m so a-ygk*qb)pcejbny k /mk1otating 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 platfv w2c/, *ua7xvtjpw.w f)0czo orm that is rotating at a rate of 1.3rev/s If he raises his arms to a ho2u7 jcw0 ). xt*a,pzfvcovw/wrizontal 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 momekv4a. 8z2vfbjp/b 2zo nt of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is herokbv2./ab4 pj8zz2f v angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can incs hwo,y8058ce.-tg 6thyme-, gmm k eprease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s thtg8gm,mw - t8yyp6mso-ee 05kc, eh .o a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating g ylx 4 b(pywaw+qrfnqianq0.83v93 5around 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-kg chunk of clay, approximatelyl8wn.3yf93g40v + qb(5qniqawpx ra y 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 khuhban07nseg 512hix x 5,k4.cbyn7a 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 angularg( bld+ j.9zfd .n)tcs 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 *d7 bi xfj w-rp q/j;3uai 3j;2r*splkan identical disk rotating at angp*u3wpjj;rx 3 ibd-q/ r* j2; alsfik7ular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at1xb14v 5(yoa 8py o* ndxt9clf 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 stocr91 0rmx,he jx*ro1ands at the center of a rotating merry-go-round platform of radius 3.0 m and momento 0,re1o jrrx1*cm 9hx 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-goguhaa-942mlkdia-5mn r7acr4 *k j m;-round is rotating freely with an angular velocity of 0.85ha*m2r kra;-u9ak4mdg mnl 4cj7ai- $rad/s$ 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 ink4npxzh4a4 k. u.-ton to a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation ratn.u.p h4o4k zxak4-tn e 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 int cbcmcb.b6796ufg v7 excess 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 gxhk 52eu6ma4$ 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 +f8g +ik dpp-inka6 w.can rotate freely without friction. The moment of inertia of the persf+p8ka pgkw6.+id-nion 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 edge of a 6.5-m diameter qxf lm8wg3p ld2-/.vb merry-go-round turntable that is mounted on fmg.w8vb 3dxlq-/2 fpl rictionless 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 gr).r5r/v3ur yb;u l.lj oph4rcound with 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 rr.bo4 vjllu5.hyprru /cr ) 3;ope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Er. *k(zuma ghe +rl:.harth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentuh rz .*rg:.+hlk aeu(mm. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from re/o :ku7n )iyoh+j *ubvst 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 o(2qt;xlx dfa6*xl yu8f a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest ove2ax(l d8x6yl fqut x*;r 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 solid cylindricalqfk4 +te j5/gae( hz,q 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-longetq/+a e 4qkj(,gf5zh string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, hon-g(azd4 295y eia x6t4h bdzqw is the 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 Sud ygk-sb4iea / bdl7gx+d26 r4n, 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 kmdka di x4g2 y4sge/7b6b+rl-d, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a lo -mk(bxor7m:qw-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able7omxm:bqk (-r 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 illustrates3eqif+7:8 :gu yieb*bqn,::f c erly 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 on a horizontal+u auzfp5 j0zujj s:.a6( xsgs53zp/a 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 caw4cw + /knz)ein pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration w4+) wzek/nic 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*h8o u*u mjx;8(po gmb on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which *;* mbojp(xhumguo88 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 rt .dvh6lif*e*9 ycg lb+b(nzk,x+v *;qwb)tis making a turn with a radius The forces actin(l*nz dr* q;96w +vtb c efg*,t.iy vlbkxb)+hg 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 roevu s42 m6fnu4ck into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achu2f6 sevum 44nieve 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,eu aj.sbuu-jsx1k(t 25 /2h/-w yksep making reasonable estimates for the dimensys u up2-2k5ts-w e exs1bhj/au.( kj/ions. 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 cylindricalna x)s7x/v ;4zplcv;r plates, of mass ;pz )xrv4n7 av; s/xcl$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 r(*ci,fl (m gyoadius r rolls along the looped rough track of Fig. 8–58. What is the minimum valuy f( o,lm(icg*e 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 dhyh te0u ll8fl171f j)o not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolaz z,9w/orj9n -/t shsutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accelehsnjzs/ -rt9, 9/awz oration 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