A bicycle odometer (which measures distance traveled) is attached near the yp3z e14 i:xzq0r.;qn-pw jtqwheel hub and is designed for 27-inch wheels. yr34x- tznpqwj; :i0epz .qq1 What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angul*b tnjkqk;0,jmv.h :v ar velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point havekkbn qjj vv0mh: ;*,t. radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velvt+0q w-zo2fww*w 5a3s.mc krocity $\omega$ Explain.

Can a small force ever exert agul nbwg,,38. )+hjgc5 wla nw greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head 4 4 z87e 6j.vizxrroqgthan when your arms are stretched out in front of you? A diagram may help you to answeiqjv 4e8zo4gz 6.r xr7r this.

A 21-speed bicycle has sevev8k c3joam1u bqy2*y(n sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, amuy1y3 qbo8ka (v*c2 j small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legsaxi q7 s3f)vvj0- vmu. with flesh and muscle concentra3v )q .7uivjfsm-v0axted 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. 8–35) carry a long, nae.s)5w lok*f4 s kuq,arrow beam?

If the net force on a system is zero, is the net torque also ze w-6 j /p,*vmgkdvma1cro? If the net torque on c,d wm 1kvv- apmj/g*6a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontal.j(btcnv .52; 3n* u5dnn fdimt The same steel ball is rolled 5 2( n5b *3ndtndtvnif j.cm;udown each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneouwoft-50v t4 (a0ma uipsly start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Whi50(p wti- uatoa04vfmch 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 radi6z6 00zmrxpmw68wp-f rw9nabus 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 kinetic energy at therr m6xpw8an-f609w w0zz6 bp m bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most+kc x4 , e jnc:,pdkjg.qmt1k5 moving or rotating objects eventd .kn ,5ejckjpq:cm t4 kg1x+,ually slow down and stop. Explain.

If there were a great migration of people toward the Earth)ch) v b0cqv+w 56+dkp bdls7q’s equator, how would this affect the length of thec+0 hlq7 vvqbs)d6wb5k)d + cp day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatix8x jxnffm.3 5on whe5.fxxf j8n 3mxn she leaves the board?

The moment of inertia of a rotating solid disk about an axis thro+gzdm 72wglj 0ugh its center of m27gdjwl+0g zmass 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 stool holding a 2-kg maih 0eg6 0 yeo:1-9gi/xo4/ubefe k rngss in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, - e gyrhkix10 o/nb9u6g/0if oegee4:decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Ho.9 q7oc 3sg5cf doyt/ywever, one is hollow and the other is solid. Describe an7oc9f otg5 /. qdcyys3 experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. Inb3t0b1 jvxz3 d 6dpj+s wh+0tx b bd3j63zdpvs1jat direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing vuebv)eml-h w8bp339+i yx6 w on the edge of a large freely rotating turntable. What happens if you walk toward thb 3h+3b6eip-v we 98lx)vmuy we center?

A shortstop may leap into the air to catch a ball and throw it quick-3p(s tg mnh, 2afv9bgly. As he throws the ball, h,-pnfv gsa 3m t9gb2(the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law tf0( p(oys;erxs 7e 1cg/b c)fp o4f.oof conservation of angular momentum, discuss why a helicopter must have more than one 1fpf;(tog)xeo0. ef bs rc7py4s(c/o rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians:,q qfm2/jl3 rr (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 ol y .hzped(faa,6r34t uf, l/mf an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters f,r, lhtly6/up( eza3.a4 fmd(in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at 1q*2 qx ;kkdhatq-kk6, oqy i8the Moon, 380,000 km from Earth. The beam diverges a26qqk*h dq 1 qko-ky ixtk;,8at 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 rate of 6500 rpm. W j17s acilom-xcyx :.;hen the motor is turned off during operation, the blades slow to rest in 3.0 yj:.cl;o 1xsc-ai xm 7s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the bhcaa. -8-; oy:2zhej/dsml6w k *eusxall makes 15.0 revolutions, what is its diae*2 o-z6. lm8 :-w/a;aches ks yujdhxmeter?    m

  A bicycle with tires 68 cm in diameter travels 8.o (*e3f8x*qowbm 3unu,)o 7q;fhpvk 7,dne wn0 km. How many revolutions do thvw o3nub)fqu7; em,khdo3* xqn ew8n ,7(of p*e wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates z r r366yrven; 2+y atdki2n4wat 2500 rpm. Calculate its angular velocityni 3vdw+;az nrk6tr2yy6r 2e4 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. /9 *btt 4s5(27dqidbq hcqnrv8–38). (a) What is the lineadsd( n4 hc r bbqt9t7qq*5i2/vr 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 aroundtio 5 cerk33f6o1a p5z the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ofm:hm g*h5cir8zt/ u*xrk o-q3 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 particle 7.0 cm from the axis ouuqy)zcn21ff* -b2*jrn,r rcf rotation is tfb2q rjrzcynu-2)*f*1 n, ucr o experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel ac1cvyl h lr/-,dcelerates uniformly about its center from 130 rpm to 280 rpmd,/cll 1-hv yr 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 mpac:* nlt -to6 0 6no3x.eseq$R_1$ 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, astronaz anzd83b:i y*uts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 mn8y*zdz bi3 :a. 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 s. Throd4mzsrrf2.3- bw 0tbcugh how many revolutions did it turn in thibs r0.-wd3bmzf 42trc s time?    $rev$

  An automobile engine slows dowe oqo2 e 9rfcp8fb741ajp,u/an from 4500 rpm to 1200 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 whirl3h6hz94wr vciing “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachi6hzcv3i9 wr4 hng 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;p3bvv w;f wv7 rpm in 6.5 s. How far will a point on the edge of the wheel have t;;w7vw3 vbf vpraveled in this time?    m

  A cooling fan is turned off when it is running at/yhtt7h)4kv;xzh4 sn( wrlj6 850rev/min It turns 1500 revolutions beforxj )t v l;(/6h4 rhwkt74zhsnye 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 mak :qmo) xn-xl*ue 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diame *-qmux:ln)x oter 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 6*g-o rc2ai i:x5 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires havoxa-:* grcii 2e 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 g9tgtzkuf0u t)ej 0 *4a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a c)9 kf4uz ge0tjtg* tu0ircle 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.gaflrll 8bj d,1q8-w , What is the magnitude of the torque if the force j8lbqgd-l8fw r a1 l,,is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. fef5ww7qn 5u, 8–39. Assume that a friction torque of 0n ,ww5qe7 f5uf.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 massless rodcb -g 6z6x ojw0mky,0e which pivots as shown in Fig. 8–40. Initially the rod is held in the horizone0kcyo-mz066 bxw j, gtal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an eny33bdsw+aqp)p)jt.gxc0 a: ebc9 f p9gine require tightening to a torque of 38 y bp qa3+bfce.9wst3)da px9 g)0 jcp:$m \cdot N$ 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 sphere of radi a qo*x6au2-ffoeq2bmflh a++ 9df1kn+ -z.nyus 0.648 m when the axis of rotation is through its-au fxeqomn2f + fa. z2 d+1oy+q69bfla*-hnk center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bi*ax i xgw03ri6e0q5gk cycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of* 0x gie5qagrki6x w30 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 a tri/mi w*/mh8 whin, light rod is rotated in a horizontal circle of radius 1.2 m. Calcula iwwm//rh*8mite
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular spig **n)hdodn (pz:5 .z,zr 9ymqpsg3reed (Fig. 8–42). The friction force between her hands and the clay is 1.5qp:d(i.p3n*gdm,9zn zr z y)5gros *h 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. 8 sksh,e:eo/-py6*q en –43 abo*6:/q s-neey ,phske out
(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 total n9z*y20lo ;wwyteln6 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 tws /i4,kje5uqw4c+mi he correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has k4/u+5ec isj4 ,m wiqwa mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius ye )my1p o gan7k2r+s9jf: o;rof 8.50 cm and a mass of 0.5802r1;ro oamj 7)y+gs e9ky:fn p kg. 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, )abfo cxi7g 4csm)xh; na6) 6eaccelerating 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 tangentially on a small hand-driv am4 3wafkqt28wr:;laoj ye(r:v/ gax8/ i+vren merry-go-round and is able ;vr2j: itkwx+afrg q:em a8/y 8 vr wl/aa3o4(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 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 p9q )yz1e p5cri.un22xtusu7tly 68k off and is eventually brought 1nry6czipp5 82qe uk7s yut2lu9) t .xuniformly 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 ballpu v.tl4fz3v4 7r 7j8al5dmvjr kda14 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 p/f.d z67.sf+al 9napz1k uazball is thrown solely by the action of the forearm, which rotates about tzfa.1p6fuznz7 l 9.p daask+/he elbow joint under the action 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 consideredb a2nyyg2;y4b zik- j8 a long thin rod, as shown in Fig. 8–46ygzyb2k 2i;yj84 -anb.
(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 consisv wf s),dcf.9jts 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 restbt;hif,4k/ ;uxak kf8a,j(aa nz-v:v within four full turns (revolutions) and releases it at inkv8 ,za4/ajbf uh, fa:vk( a xt-;k;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 ofgh vf(iubu8/c(x6zn- $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a tio4 kkai(n- e:orque 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 g .v3c8+xpnekpcy 47qwithout slipping down a lap+4vgyn7 8 p3.cxk qcene at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun jd.hy+p(y:2; iwtl sias the sum of two tew lt is:y;dyjph+ 2.(irms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much u devy ;i.w)z8mje 1o7net work is required to accelerate it from rest to au)v.7 e8 mo;1idzwjye rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm ar1fwbg0a 1 u0phj1i6( xv*d jond mass 1.80 kg starts from rest and rolls without slipping do1 0ah 11xg0pdo*(iu vw6jrfjbwn 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 bala dh py) at,*b/hvy0au(nced vertically 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 it hits the ground? [Hint: Usv()y* /0uhyhtp a bad,e conservation of energy.]    $m/s$

  What is the angular mo *qro0pu s*hj,g.lo.qmentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at ** lgroqqshojpu0. .,an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grind0i.n gt q,1adxing wheel of radius 18 cm when rotatx , gnq0.a1tdiing 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 rotatin y2- mysu7a1kg )0mq;v0b pkpeg at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed 0u m0apvem )s7pk1g- qyy2;kb 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 shov:ck2m1yh+lx -tdyc 2 wn in Fig. 8–29) can reduce her 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 tuc2lhy1xmk-t 2ycv d+c:k position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate is xsxc w4g4 f9f7zx )a.5sej)mkxy/; from an initial rate of 1.0 .wx4xz45xss ) m 9a )eskyj 7/;igxffcrev every 2.0 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 axis through its center at a fre,y jt1xtlm+f+. s+ rlkquency 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 t.s t yflkjrl+++m,x1 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 figure skater spinning at 3.l9ny00/rksy pqp*2 o t5 $rev/s$ 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 momenb 3zi0e f/2hwbtum 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 mom rt o./0daq efh6wx6 +t7hot8ceok+j*ent of inertia I is dropped onto an identical disk rotating at angular speehtajeok8o t+/6r et c.+ow*7h0fq6d xd $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns fgk ljbd;v431at 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 standsg9v hla(b;ex7bo1v h , at the center of a rotating merry-go-round platforevl b h o,(9hvagxb;17m of radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angulgwpjo /9 z,1qzma -ws4ar velocity of 0mgp q,swozj91 z-a w/4.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a whitea/z 4 pz7:ckde km+y/n 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 rate be?(round to the nearest i d :/nkmekzp7z/ay+c4nteger)$\approx$    $rad/s$ (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 win:pxtn/v4i( -o-avsj gds in 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 gv77yrq ow n0o:n(lykf o75f1$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate fr3 c/ c fpw1uad/e( +l4saja,sgeely without friction. The/l cgaw,s 1c3/ asufpe4 d+j(a 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 at the edge of a 6.5-m diameter merry-go-oau qv2e 6*t8 78rcodk lv,k5fo-f-nmround turntable that is mounted onka-7 2t8mcf okvor5 fn6* d8luqe- ,ov 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 gfr-1(b icn6xmround with the end of the rope lying on the top edge of the spoob-fr n6m(1x cil. 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 mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. n rn5qpu)o4, ii/:jtz4i z8y4+okmh hDetermine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latt4t 8o ji5ri) /y+,4huo 4 znzpkmi:qnher case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from res.7cdyg1t hk4tt 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 ofsz.yo ebo,pp,ux9o; * radius 0.20 m acquires a rotational rate ofpszxoo,p ,;bo uye9 .* from rest 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 tw76v r; z r4zmj/sfotw;o solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrijoms z fz;w;74rr6t /vcal hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear w hn,iqz* 91syuwbbgkc r6/1q7heel ($\omega_R$) 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 mas v x29lv6ay4)j6/(szrd /u wh-ohjvqr s 8.0 times as great, were rotating at a speed of 1.0 roh9/hv/j (64lj r qs)dw v2rx uay6vz-evolution every 12 days. If it were to undergo gravitational collapse to a neutron 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 usen0 , skbla /l+pzi6ks/ 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 need+ kpk6/nlia zs,0ls b/ing 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 ceuf+vlj 2. ;6jfnd,c$H_2O$ 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 surfar/p; pk6zc(u/aqw .awce 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 8g3 /mdxgv9lpcan pivot freely (i.e., we ignore friction) about a hinge attached to a 3pggvm/xld8 9wall, 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 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 standin)s 5 uhj0newe)g vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against whins5 e)heu0 )wjch it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn 5/+so7nyzbv j with a radius The forces acting on thnyzb/vs75oj+ e 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 sling of length 1.5 m and beginrjk gi49vc t8.jg/ux / 0az5vbs whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5. ztj 5igv jurk/ba9v4xg 8c.0/0 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 rod *u7nl kyj 1(.k+kyxy1ww e1cns, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning ska y1 yjk(1uwk7kewncxy1n.l * +ter with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical ,bakofa:3h hhuu.(,pt 2 lr -uplates, of mass up. a( 2,:rfho,albtu3h-hku $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alogw0k6 6id vk3tng 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 the highe k idt6wv0g6k3st point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but jc n*vk4;9pz iuq.c+l,a9 hvr:ik 3o xdo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed x1* khu haf) q9ivy*0r;dog/wuniformly from 90km/h to 60km/vw h0 9r) x*gfqidok/u1y;a*hh The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s