A bicycle odometer (which zs ;-f0yn.p fcqhp-dr p.( oj0measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicyc d hf0c-.yn;.jorfzsq0 ppp- (le with 24-inch wheels?

Suppose a disk rotates at constant xukmmid24 -3xangular velocity. Does a point on the rim have radial and/or tangential mm- xkx i4ud23acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describepf yn3w.u. m3pjy(vyy9-yqq7d by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exer- d1,ao i i)v ve31vg/e2fbm 0eamk,tpt a 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 hea .y .dmk2fdgj p5gw:mrk3v)7r6ukc ) sd than when your arms are stretched out in front of you? A diagram may help yovm3.5k7rks):gc2 ku ) d. wjrmp6dg fyu to answer this.

A 21-speed bicycle has seven sprockets (q, plc/xrg*h/o *q wwat the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocw/,cwpq /rohxl* gq (*ket? 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 legs with slcu46 in y04l6*baku/bi(p iflesh and muscle concentrated high, close to the body (Fig. 8–34). On *0b bnl(44auyi p6ui6 kls /icthe basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam?sz7qedn1ittqu)pj 434f 0x .b

If the net force on a system is zero, is the net torque also zero? If the net lxt6cb/f(/+m qcdptw*s x.a6 torque on a system is zero, is the net fm6cxt/dpxs/qaf lcwtb *+( .6orce zero?

Two inclines have the same height but make different angles with the ho;twm4z-ubnb ) rizontal. The same steel ball isn wu m4;tbbz-) rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (fdq7p+tu s+4 bzgn2t,rrom rest) down an incline. One sphere has twice the radius and4d+2 gqt7 b,ur+n ptsz twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start fraw5a6,s d7bxdsiq ,p.b6ehb - iys3.com ra. ,67h3bc-edidw sss,6paq 5i.by bxest 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 the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Y1wqrlhr 86ml) hf 8.lzet most moving or rotating object.lmqrl zhrhl81wf 68) s eventually slow down and stop. Explain.

If there were a great migrat*9:-5tcvbn8ir bmzflion of people toward the Earth’s equator, how would this afft5*8l- f vmribc9bz n:ect the length of the day?

Can the diver of Fig. 8–29 do a so9z3 g+qlx/sh xmersault without having any initial rotation when she leaves the boardl+ghxxq 9/sz3 ?

The moment of inertia of a rot (-ip 4uj9 bax.glpsq5ating solid disk about an axis through its center of mass is pbqp9a54- .jslg ( iux$\frac{1}{2}WR^2$ (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 mass in each outstret1*uw,5;jyc9eeffi n c ched hand. If you suddenly drop the ma,ecei u c5j9 fwn1;yf*sses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howevv t4+2x/k6kaug w:9/ hdy rml(,ikejier, one is hollow and the other 26h(d/i ewkkg jiy/+9 k,:vxalmu 4rtis solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontwh8 (b tq 1af2tzhc:5 osg.,ncal axle points west. In 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 acceleration of this point at the top of the wheel. Is the angular speed increasing obft,h zhqag8n(t: sc.1wo c25r decreasing?

Suppose you are standing onv*w5g t di4ljpxe+g4 .6)zmn f the edge of a large freely rotating turntable. What happens if you walk toward the centem4)pwg. v 6n+d*j5ztlxgi4ef r?

A shortstop may leap into the ai8snt l8 su47plr to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legusl p4l7t8n8 ss rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservatz)l3drip1ik9 0 oj so+ion of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operapdoz3 ski+09jlo 1 ir)te to keep the helicopter stable.

  Express the following angles inh-w 7q5v;*j zd*glp ym 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, using th f+ou a hq3djs8l/z+a(e information inside the Front Cover, the ao8+h+ j(zaq dlf us/3angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divergu;uf 9 ( eg(el9 mxeu9uzx7n)fes at auz9nue m u;u)xlf fe 99((gex7n 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. When the motor is turned o9khs58n n/ lbmff during operation, the blades slow to rest i /mkn5h9snl8bn 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If ter1 jd69isi6sve 17kgbp8nc/ he ball makes 15.0 revolutions, what is its diameter1ipv6nj 7b1g8kr/ee6csi 9 d s?    m

  A bicycle with tires 68 cm in diameter travels lo.wc 0oca 3i38.0 km. How many revolutions do the wheecw 0co .ao33ills make?    $rev$

  (a) A grinding wheel 0.35 m in diametewenl:7q 1fxxj1o. 4hr 2q6lch r rotates at 2500 rpm. Calculate its angular 2 : 7qloqlncrw61efh. xhxj 41velocity 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 su( 9c3j gge 1otigvbr7tq53)revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m b(o1e tj ri53cgv3 9g)sq7utg 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 arounda;jixxbj; bx0a )7 89rgxqi 7d the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speedrg:u y,r, t+zd 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 particle d1j ,z,:4f+i ragi5 v,c7s (o/s;nqhqhetikr7.0 cm from the axis of rotation is to expes(,in,r h v,1iqogjd4; rh f5e kt/ c:a7zq+isrience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accn agwefqa 5h 67a7u.t5-et.stelerates uniformly about its center from 130 rpm to 280 rpm f asttq7et6a .ghe5a wn .-5u7in 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 radiusr*x s;o5 wcsb2 $R_1$ 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, astronau2f+yci+pzj/ q nm *6zmts 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 q 6c+mmf*pj yn2+ziz/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 15,00/n0q)6rbpi kx0 rpm in 220 s. Through how many revolutions did it turn in this x kprq)/0inb6time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculatax7zb c-28r*4 9 .vlp6m mcnsfecr,uqe
(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 osbi)y8mv ct5 tf7b3 ,for the stresses of flying highspeed jets in a whirling “human centt 7ctvbify5 3m),bs8 orifuge,” 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 240l8 1x3qz/;nywu:y qv/dw rj 6v rpm to 360 rpm in 6.5 s. How far will a point on the edge of tx8q/ rlu3w:v;vyj6w1 nzqy/d he wheel have traveled in this time?    m

  A cooling fan is turned off when it is running) 4x;m5u,bzsbpf,a o5-dnnga at 850rev/min It turns 1500 revolutions before it comes to a stopu5an f,pd bmz)ng5a-so;x, b4.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the cafknzy2p7yt1 5 *.vrbrr reduces its speed uniformly from 95km/hzb1f.yk tpv 72nr*r5y 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 cz-ihz w*8us06gz+as+9qcsc speed uniformly from 95km/h9++qc-6cgs 0u ch zssw*azzi8 to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on eacphxq5 *i4oav 1h pedal when climbing a hill. The pedals rotat51oph * x4ivqae 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 ofs/bg w-id .zv82g t/gl 55 N on the end of a door 74 cm wide. What is the magnitude of the torque ifb .gsdvw-t8 //g zilg2 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 axljgusz fds0 l7 c2kv v,/225fage of the wheel shown in Fig. 8–39. Assume that a2 s ,gdz7ksgalvjc5f02f/u 2 v friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the endseq52v3 epn6o46j uk-lb3sc jy of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torqu35jpso cbq ekl- 2u jvn64y63ee on this system.

  The bolts on the cylinder hv-u 0 xh p02eijh)i:sc57qasiead of an engine require tightening to a torque of 38pah-u)2 h0xi7 s0qvi j5: cesi $m \cdot N$ 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 6y7qkv,. snt i q8fv.cfh a(d,a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its cft,.c 8v6y fq(h7 ,daiq.nskventer.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The r75 r)4stepnp:jddk z/ im and tire have a combined mass of 1.25 kg. The mass of the hub can be: tndeszdp k)r/ 75p4j ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rhio8x-2- m; ncm 1zbaiod is rotated in a horizontal circle of radius 1n8- 1;mimzc xaoi2-h b.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheelrby- q2ixwbm: h say25) sr- k9/,gpam rotating at constant angular speed (Fig. 8–42). The frisq)sma9 -w,m r:/xy-b iha5ygb2p kr2ction 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 wp8* ls7e i3e p54/nqyktskos, .a5qaof the array of point objects shown in Fig. 8–43 a q pqe8*k. w/7aa5kopnti,3e45lysssbout
(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 mass is l 2+ 3k, /vozos8/8y51p jomqvg4kyvyk 2 lblp$5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct ratedmfm fhos,d5g73ft( cb) :25;wfiab m, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the sa,m :f( mfmfd st)5ibh wo7da23bg;cf5 tellite 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 of 8.50 cm pg1h( w 9r8wk:/ellmt and a mass of 0.580 kg. Calc:9rl1wep8lg kht m (w/ulate
(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, accelehu ;ro(sybx)oo 7j 4827zdmz mrating 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-driven merry-go-round and is ambo+qo9n+0 v sble 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. Calcumon+q09os b v+late 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/4cjv /efwpk.-g6u jb is shut off and is eventually brought uniformly to rest by a frictional torque of 4j-/gp6k/euc .f bvjw1.2 $m \cdot N$ 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 at 7z wlo/1jj6qg6t wzz17 $m/s^2$ 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-kgg1ri(zv)vb + p dmlbd8 -p6hq. ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball im zq)-dvb8lidp1 pb.r 6+(gvhs 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 bladesoe ,kjw6v6e rc;an; :62za oh can be considered a long thin rod, as shown in Fig. 8–46: s;zecoe6r6n6; o, 2vaawj kh.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses,3as9o/w0z7uqasn8b1x1 0xe, fwh typ $m_1$ 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 acceleraaaxrm-z .x13jbe 8-xt tes the hammer from rest within four full turns (revolution13xjmb-z8 aax.-te xrs) 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 moment of inertia of k-d4.ynuz 3a e kn8jy3$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops84s hsb3fz1m+cp 7xhh a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of massqa sfgncls(4)g;5zsd iq 2b.) 7.3 kg and radius 9.0 cm rolls without slipping down a las; qb2g)c 4z.5qslasgd n)fi( ne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sajw8b8 e o.idg+* s1clum of two ter d+b.c*es8liagoj8 w1ms,
(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 +p p3,pxkzql )z56fsr of 1640 kg and a 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? Assume it is a sqskx p6+pz5p 3rf,z)lolid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls witjmkdsz j(30o9 hout slipping down a (zm0d3o9skj j 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on (i ,auxqdm5osx7 *y,uits 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 d,omuqyx(u ,ia*s57x before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating og) .j lvfaz35.6gfa unksh *-mn the end of a thin string in a circle of radius 1.10 m at an angular spee*gf63 kzh.)vn5-. a jmgauslfd of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindu l*go72do) lgrical grinding wheel of radius 18 cm )l7o g*udgol2 when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate ofew nfu 7bh4- lu:c5r)u;e8hj w 1.3rev/s If he raises his arms to aj:f8;wn w4l- ehb5u7uuh cer) horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of08wbq8uk8wv 0hjbfjvy-.2m3 u ;uast inertia by a factor of about 3.w8;-skb3j 8wu 0ufhqmy0 v.2utb8ja v5 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 her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can inpc k*s) wi0.edcrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate o.c eiwd*sk)p0f 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 thrpw5htv 2e-s8/o tomk,ough 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, approximately shaped as a flat disk of radius 8.0 cm, onto the centewkom5tp-, /t8o2evs hr 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 spiq;5n*tzhreo-w t.r4anning 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 rsy .q8omnk,8 +s 3 .avld(tfqmomentum 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 ofd4uj 7v6q7fr fp mp:o: inertia I is dropped onto an identicaldrp fm 7qvj4u:o7p: f6 disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 29p2+ 9nyye 8uh-fs*at hpmj r).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 1,1 hbd;+kep 7 qpmvtmthe center of a rotating merry-go-round platform of pd, eqb7m1p k;t+h1vmradius 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 angular velocity ok d .3h wipk)+naiw-7qf 0.8w)wikdpq7+in-a . 3hk $rad/s$ 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, losing about half vfxwg1i+ee 1d5v 4mj 4its mass in the proce 14v54dvgim1ef wjxe+ss, 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 integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120 hse)0gp5.b(nz o7nhvbk/t rcq;i h- /$km/h$ 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 rpy wi 2 l.no-i+t c60 s :/1rs5lac*5cbaiwrw$ 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 platfo qwpeq,20ldh*f* qujz6+x:xmrm, initially at rest, that can rotate freely without friction. The moment of inejqe d, 0xqwf:p 2q6*+mz xhu*lrtia 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 wp(8s rr0nyk8diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of i(0 rp88rk wnsynertia 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 end of the ro*f5n)qwy5 e zj 7efrx7pe lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding ont*jzffqeew 5 57n) rx7yo 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. w m:gvs8tn5z i36,yyjj1s81 ks jch2cDetermine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (2 8s1tz1v:jsc6 cjyg8nk5 ,yjimh w3sIn the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from 3rzwi.c, l+n,mhu,:iebm;lwt 5r z2aasu *5 w rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a /so. .wcsw(5wor v-cy3kv( s puniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at c( ssc/oop3w r.c(5kw -y.vswvonstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cytfae/08(kc lh) *qzywlindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cyhta 8f ez (0ky*q/)clwlindrical 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 reay-un7y fo(n)v+ yv,zcr 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 as .eua5)k i9qgdo07fu ggreat, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what woua) ieg uu5.q0fdo 7g9kld 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 fntru-dd, 4 kcf- jgp48or it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheu4d fjt ,nk8 g4drc--pel “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 ans e-:b gcqhj rc-p,r ez0:mu98 $H_2O$ 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 g/w ; zdg glvecd5/g77wl vrgt392 c8ron a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length 9h u65bikwx,1wq mxo7L can 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 of the tip of the rod. Assume that the force of gravity acts at thex5 x w,71 o9bq6wukimh 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 ola ,lsj- *xu*o9 vkh5/fho)c dn the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which is- olch*x, *95l)ohva kudj/ft 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 makinp1up(1.n oo uj xpsj2/g a turn with a radius The forces acting on the cyclist and cycle are t/sjp ou2uox1 (npjp1.he 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:uz fzr-u wq8d.a /vw*.50-kg rock 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 rauraz :qu 8*wf-v.wd/ zte of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder9kuun6jg mlxxcp k*0+ cil5)ht2 50 sf and her arms as thin rods, making reasonable estimates for the dimensions. Theiplkhf 0c0su )nj+x9x5lu*kg6 5 ct2mn 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 tr8rp;io395xk*s b tjxwo cylindrical plates, of marxj *b9ir p8;3skxto5ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 track of Fig. 8–58.r0 -htr17b.fwmiosk 1 What is the minimum value of the vertical height h that the marble must drop if it is to reach the highesbm.- 1tw1orhk 7s0 irft point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dozq cyz+cjwf2tts18 . * not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spy *0lfz(4 r ecb-co3oheed uniformly from 90km/h to 60k z 30oro*(l4bf-eychcm/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s