A bicycle odometer (which measures distance traveled) is attach bw /d2k)xqxna55ikj,ed near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch whee /x5j,nk bw)2ia5q dxkls?

Suppose a disk rotates at constanx 7k krkpueh+tzyoh.)r4 .;2ut 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 compoxtup;k+4yrkk..z )ehhu ro27nent of linear acceleration change?

Could a nonrigid body be 2sb+85b1 zippk7jw rt a:3pcodescribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque,sr1 mka+wu1/q0yw ty 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 ac;6 hr q sty59c4ve+bp sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagqc sb6cptye5h;+ v9r 4ram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three (q)z vi26 cndwat the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In 2czvi6qnw)d( which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run904mgh /qu yutntf1 (v fast have slender lower legs with flesh and muscle concentrated higy1v/09t4gf qmuuhnt (h, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, 7t3jgi88t k wvnarrow beam?

If the net force on a system is zerf nav z.pau5+oxj:)y0o, is the net torque also zero? If the net torque on a system is zero, is the net force zero?: py. u5a nja0z+fox)v

Two inclines have the x7ma1iv * ;)pf5vwzsdsame height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the ss *pi xzwmv7;da1v)f5peed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollch51bh kqknz(j, xuc 7 0.wmu-ing (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed m(.hq ,x1j uc-n7kzwk50hc u bthere? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the s ;m9a(o rtkwg-ame radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kineticrtw(m;ko -g9a energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum arc2j1/0y9hhte ur h n*we conserved. Yet most moving or rotating objects eventually slo0hw 1cyhe t j9*2/nhurw down and stop. Explain.

If there were a great migrati,,tsqycpf/ xz79epvrh0k q3 j6 ch 5y*on of people toward the Earth’s equator, how would this affect the lengthhpq y9tr/jh ,cy*px60vqez3 kfs57,c of the day?

Can the diver of Fig.t+j -bqabbv*p3svc kh 1d/86 d 8–29 do a somersault without having any initial rotation when she leaves the board? +-dpq a v*btdb8h6j b/3k1csv

The moment of inertia of a rotating solid disk about an ax7d)yqw m rp*jmdln 5q6n;5 f3qis through its center of massqw5jy f36) n5m;qddpn 7 q*lmr 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 fi a9kf5h*hwbsva)c1qv*fiv;ej. :;on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity i f*wkhh; a *jbivfse 1)ci 9;av.5:fqvncrease, decrease, or stay the same? Explain.

Two spheres look identical and hpcu nh*io;a2 2ave the same mass. However, one is hollow and the other is solid. Describe an experiment to determine whio2pac2 unhi;* ch is which.

The angular velocity of a wheel rotating on a horizontal axle pg:lwp 61r2g4gae wp9 loints west. In what direction is the linear velocity of a point on the top of the wheel? If the angw9pg :ae6gw rpl241gl ular 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 freely rotating turntable lm8t*pscr/-z;2uwadbj;. p x. What happen.sbart*/w pz 8;l- 2jcdpxmu;s if you walk toward the center?

A shortstop may leap into the air to catch a balf7d ; qtf+wu/bl 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 legs rotate in the opposite directionqudf f7 t+w;b/ (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a hp(i) r57dt,b bdgzz u5elicopter must have more than one rotor (or propeller). Discuss one or more ways th55zi7tpd ,(z b )udbgre second propeller can operate to keep the helicopter stable.

  Express the following angles 3ca 6x r078z+bvsywac3.zj mj lj* t5min radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate,,comm :yv;ry7y4yk na;.n t s+ using the information inside the Front Cover, the angular diameters 4styo7+,a; cmy m.yky nvr n;:(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. xf97ecz qr+:hzaq :(oThe beam diverges at an afa :q:qz+ (hor 7cxe9zngle $\theta$ (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 ratysjoj5-/ yf, he of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.fys5/oh jjy -,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 chilp,e im 894 8+ls jrbljuj1w8..uens ogd. If the ball makes 15.0 revolutions, what is its diameterplj.n 8.j1uemew4 b uorsgl8 8j9 s,i+?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How mf(n9jj: b,aa1t /mnkrrl ns-+ any revolutions do the wheels make+tbf 1l- mn/,n rj:kra(n9saj?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2o x(dy tp m5eawz38g7)500 rpm. Calculate its angular vx)g( odtpy8wm ez5a7 3elocity 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 s (Fig. 8–38zwl 3s-whtnd9 2aza .g2y 93fc). (a) What islwa g9 y2z2tdcf-. a3 nh3w9sz 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 velocity of the Earth (a) in its orbit around the 0m, t.gnsyrlg l70xjz 8 hh-ed,7s84 qoib j2vSun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed oigrr2ud s (b;v6( i6akf 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 p. q3k*c vredwn945ka centrifuge rotate if a particle 7.0 cm from the axis of rotation is to expew.en d*cvp k9rk34qa 5rience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm t7 7b-yjwyhp*py : er;ro 280 rpm in 4.p eyy7r: wr;7yh -b*jp0 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 :rc:p iw1m/adsfv y 69hcxl4*$R_1$ 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 Moo6d8izlitju 2f5;sz c)qme./ nn, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecrai68 f/cj)teun qim. s zl2z;5dft 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 cewh u*yp)g)h11hty3./lhq o in 220 s. Through how many revolutions dq.pt*eh/h)o1l31y)uhcw gyhid it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 12cal+fm1 i1so)00 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whilstyw59 . +yu e( ++crn2qhwavrling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its +r ncq+(+vs2luye t5wh9yw.a 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 rpmq3:kzrks og8 2jvmjc2d7.v 8t in 6.5 s. How f:7.kjo 8tzgvdk3qr2 s8 c jmv2ar will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turnmq jgu a/nbay1n9k5:*ed off when it is running at 850rev/min It turns 1500 revolutions before it comes to a stop. juq9 n1ambyagkn: *5/
(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 asivj2r k-silbk *92ydplu.h gat;)6 + o the car reduces its speed uniformly from 95km/h to 45km/h The tires have a li6*l-)k. + ajr2i;uh9 tg2dsopy vkbdiameter 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 reduce00wbwlhc ef-m;wg9;ppor 2m 1h1e fp2s its speed uniformly from 95km/h t;wwb0eo mc1hrp;el1-22p9h p ffm gw0o 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 bikd gyrv.0w 1xl7e puts all her weight on each pedal when climbing a hill. The pedals rotatw 0rygl1x v7.de 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 (y 0xofl-p5x- pw.i;gsf8eu d the end of a door 74 cm wide. What is the magnitude of the torque if the forcyx w dgpx;(ef.ui-5p8fs l0o- e 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 whe(2 igkp6pq+47s qiinh- t0yyv :a.r wrel shown in Fig. 8–39. Assume that a fr0y4kiph.2:(6 iyi-v r+trq g wqp7ansiction 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 a91rw/b g8ld tairy( 9a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positi byi(/ldwar1t a98 g9ron and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening 3laqpsu ay9ys.3t.4 ito a torque of 389t u iaqapy.3s4 .yls3 $m \cdot N$ 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 sphemb.t cia:i.(6/mtm ucre of radius 0.648 m when the axis of rotation/m. itcb.i: m6 ua(mtc is through its center.    $kg \cdot m^2$

  Calculate the moment of iner7;dpz31 jm 8)m ue,qz zqawbos z.d4/jtia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ig)z1aduo3b 7sjz4wzm / .em;j qpq8,d znored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the0 4uhz5ui. van end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Cal a0h iuz.u45vnculate
(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 constbut wgw6n+6*o ant angular speed (Fig. 8–42). The friction forc6nou wwt+6g*b e 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 array1gq z j9s*jvq 9;ng/ez of point objects shown in Fig. 8–43 about jv9zg/9gn* q1 zjq ;se
(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 oxygenl8jee (hqu r2z9x2b9 ui+xt 2v 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 sf,4fh w ,xg(wup- u;okpinning at the correct rate, engineers fire four tangentiahfuu4;k og,(,w- xpfw l rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder ;bvf*4dqr gea 3ah 9i(with a radius of 8.50 cm and a mass of 0.580 kg. Calculgr;4f ea3v( 9bdi aq*hate
(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, acceleratingtjg7+,t/*3x fzwang5fp v/ uj 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 tang 1ob(7l(n 65osi,hq oz(kf jouentially 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 torque required to produce the accelelo ofo1n56 , 7(iuk(hbosjzq(ration, 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 even3-4 w bukc+zo-s5fes 2t,4a q braa-aptually brought unw3,orfc p4aa+ktb54 e-s-uba zqas-2 iformly 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 accel6o/,j/+qrd /wbk7n/ ycfjwh berates 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 gu1dna.h wp,:smp)-r (:d ydt thrown solely by the action of the forearm, which rotates about the elbow joint under the a-) :rdda.wpd,h mpt (1uys:gn ction 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 consi-rd/ o3f6fuif fic d)n2m) .rxdered a long thin rod, as shown in Fig. 8–46.d n6i))/ fu.c2mo frd f3ixf-r
(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 twoh:w,2ukcjzwjix 9y c : w:3;lvh1- vga 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 iw stp iz+2 xi1api3-4lf0i.cthe hammer from rest within four full turns (revolutions) p2 wc-xl03 i.+iiafzi1itp4sand 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 mo x 16p9tis/zy bwq3s(nwc5 o2ument 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 torque of 280 . 8py l algzx5;y*wnr;$m \cdot N$ 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 rol c ..a(fuevxc0c a (dkv,mn4r)ls without slipping down a lane atcumx ear.,fnvk)0( d(v.c4a c 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun a;uir llm,mhxk orf3k i4d.400s the sum of t4x 0 lmk r;r0i od3,muki4fhl.wo 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 radi): 9cxjjmq6nwn1x el1us of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of)6jxwle1cx j:m1nq9 n 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and c /h2yo )5q;dvc oiu2urolls without slipping down a 3cvuq;iucyodh25/ o 2)0.0 $^{\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 fall and vv;n1/w/-qj f-hl)yhmj 3rvw )n )xfl 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 mvlyqh-r ;)fjvj-w/xn wf/h v)n1 3l)conservation of energy.]    $m/s$

  What is the angular mo5r tb8f,.q *qopt ,dxymentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radxp.d of*ty ,rbqq,58 tius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentu /ni 9pu+gbb (bhpvjzs wy,427m of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 15,b (9 zu gswp72ybn/bh+ jipv400 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 platfvhp)k ,,n.xcg orm that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, )x,,ghpck .v nFig. 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 he qxsxhys.vu:p*m x .j y:a3j;eesw739r moment 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, wh.jpxj9xesywhs uvm3* e .q:7:x a3ys;at is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin oy 2m)7bvx sd.rotation rate from an initial rate of 1.0 rev every 2.0 y2bvxds .mo)7 s to 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 around a vertical axfe1o on+dxsx,6:7zu3z m:ojs:z a+ wtis through its center at a frequency of 1.5rev/s The wheel can bz s:x1fwstxz3an6:oe,oj m+ 7 :zu +ode considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a fid htw2 d0 d6fqs7eoa3 r+h;bv,rq7z 5tgure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Ea+ z q4b ,ftt:ohjm0a;l450 erp sgoky9rth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an i t)xnz 7/vib7w2 vn jy q*-07j-tepwfidentical dise7 w2jj/ x) y7infvtznibq0 pt7w-v -*k rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ic)/8ypgvnh4fs7u-qat 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 a rotating merry-z6+hbdjal1kh y 34,u kgo-round platform of radius 3.0 m and mh, d3jzu1lkay4k+hb 6 oment 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-go9l om+p apzz,ivsr 0 m.67-hnd-round is rotating freely with an angular velocity of 0.8 d mpsomzhip 0 l6a,z+v7 -rn9.$rad/s$ 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, losing280i 1cehoudz a8dwl1 -bug9id-gd/ z 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 rotatioe8zd ald2-zg0ugh-b1 od/ 1uiwic d9 8n 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 -ipdkb be;6a8 jwyb(ef. nb9 7in 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 4vvt:wx yvrf rg2(nie ;m,/ n($ 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, tiach-;h k81 3cktb6d yhat can rotate freely without friction. T1k;a ck6tbic hh83-ydhe 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 stands ax 27y)8t swjkwt the edge of a 6.5-m diameter merry-go-round turntable that is mounted2)xt8s7wwj ky on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the,w2,udn )wafk end of the rope lying on the top edge of the spool. A person grabs the end )wufn ,kw,d2aof 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 always3 5 *moyfhon6/f11pqnr)qluf 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, tou 1r m/53yhol)nf*p 6nqfqf1 reat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest ahg,,ifs ;squpg b16/xt 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 shapejfp847egqs; 9n wx ;lxpom q8ju;;z m* of a uniform cylinder of radius 0.20 m acquires a rotational rate of from res87 x 4 n x em9o;sw*u;fmjlp;qqz;gp8jt over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each auf:al(( 6ims of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of massu:iaa l6sm(f ( 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 angular speed o.xu(9e vz67qc rve 83kuk1oaif 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 times as6sm69gg6sg ez+ ;t t11 qxg/nrxsx 4qc great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neuq1 gg4nx9/sqg6 ;xe6gmrx1c+ s 6 sztttron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a 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 uafywbr 61lv 5/;ajd/ase 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 without needin 61a/jadr/; bwylfa v5g a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an cz:cd2/klmbf;e 5q 0m$H_2O$ 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 surtlgusiskf w9n z;n+ 8m7,:a)y*tem z9face 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 fz; b4r)m l,j;n gg;jikreely (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 of the tip of thegzj r);kmijg n l;b,;4 rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and wennlev2 4ad. en7 7io6v want to exert a horizond67.4alvo in7nn ev2etal force F at its 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 wi1-due .opba4;7wiv vam oyh ogi+, /+cth speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal pm4+ b1 yaw.ov+g ,iuodav ch;7 -o/ieforce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 sling of length 1.5 m and beginv , q7qfg0cu3gs 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 af7 cvg g,3u0qqchieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater- pdr/ (olak7w-.s3+vn lckua’s body as a solid cylinder and her arms as thin rods, making reasona3n u7-s/rc(vwo. la+ lkadkp -ble estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylikq;-owpf)12-wk crfwit r ,j ,ndrical plates, of mr-f),wkkj-if1 pct;wo wr2q ,ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough t 0siyd8 pp:t1track of Fig. 8–58. What is the minimt d0p:t1ipy8sum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do+l:8p)m 7jj8gi v im8(e0paeiwqoz )s not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces 8p-hd )l;j;m bg .osxmits speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the8 xpb.d)- l;;mhsjg om 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