A bicycle odometer (which measures-mez;qfawy+f* e i7w; distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use if*w;me+i7;yawz q-ef t on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point dg5kc u 6ae8:zon 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 whu5 d68ezca :kgich cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described:49pck7so7w1kf;ccj rhn o 6 v by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force?p1axnz1wyy0q0ia n3my,w-73ee 0yaq 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 4iw 7f mewv)y2than when your arms are stretched out in front of i) efmwvw42 7yyou? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets ato yz,5eud -(av the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small 5eavz,d o -yu(front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs aj4q08 hrhyj.x7s8j7fe pjr:with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain yqeaj7jr . x:r hj840hs jf7p8why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carly;q. lt9b: wrjcfjp, i j;b-:ry a long, narrow beam?

If the net force on a syst6*e4 ikyjl0tvoydj j9i*s() vem is zero, is the net torque also zero? If the net torque on a systemyv60 ) (* yesii o*jdjk9t4vjl is zero, is the net force zero?

Two inclines have the same height but make differenieapf) mr*.spfea9)2x kco ,+t angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ba+pf)m eos)f.p 2e kix,ra*9c all at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incl;llca0;d7zrvcu0bt4a dsl7: ine. One sphere has twice the radiu004:a 7zslr7l;vutcd bcdla ;s and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have tp:r-pdxj*-ypry2s fti :l ) *the same 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 ap yt ydr:-rxp*:)j* sifptl-2t the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet mostg;9fk 1ghrm ; reao+0-wand6y6txt1p moving or rotating objects eventually slow down and stop. Explain 1nt91xteog+- g;;rmf6ahraw60kdpy .

If there were a great mi27o8x1c*el k9 xhw (3hwfk;(p atm m+wfmqn8 agration of people toward the Earth’s equator, how would thm hn(k2 m18 (tlhwkqa w ec*3x+8opaffm7w9;xis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without havinx2ju u- c*qa 0)(x3(ejuldbadg any initial rotation when she lxq* a c(abu( ux u0e-d2d3)jljeaves the board?

The moment of inertia of a rotating solid disk about an ,fbapq b -gu8pl93fm.axis through its center o-m qpu, lgp8bf39fab.f mass 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( 0soino: su:o ;zn;m; (nknvf a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? oizsn:;(m s;:vn; ofknnou 0(Explain.

Two spheres look identical and have the same mass. However, one is hollow (2a* h8qw042wq5 /iskekxpes h2lbmqand the other is solid. Describe an experiment to detebhs(ee2k *q/q0wpm hlqx2 ai5k2s84w rmine which is which.

The angular velocity of a wheel rotating):fn)5cbimkr 5htvf91 5xpmi on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceler xfctbm1n mhiv5 )9p fikr55:)ation 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 rotat jc5(7*pycbs aing turntable. What happens if youpj5ca*(ycs b 7 walk toward the center?

A shortstop may leap into the air to catch a ball and thr-t bdu ga1.i,ksdb:f ,ow 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 direction (Fig. 8–36). Explai gu.tb,1dk:i-,bd af sn.

On the basis of the law of conse5 ;d iolky-d4ervation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second plkd-4id 5yoe;ropeller can operate to keep the helicopter stable.

  Express the following angles in radians: f7u/./ ei nr2/*3atjigrw hpv -ywa4l(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 amccy p;k+t 4 kzudvjd: 6r7(0p7gd yz+lazing coincidence. Calculate, using the information inside the Front Cover, the angular u:0zdyk+dytg+zpcj7 c6v7 drl(k4; pdiameters (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 div*lm h:ml en8w6erges at an angwn86 : elml*mhle $\theta$ (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 tuwbd f 7w7p*utngew.pd6,r7u7 rned off during operation, the blades slow to rest in 3.0 s. What is the angular accelw 6bp7 77 ddt, w7.wf*unurpegeration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anixk es9vf5/ zz4)z 3eqother child. If the ball makes 15.0 revolu)ikxz/sfvqz 3 5e4ze9tions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter tra,4;sv6rjpx. h -htgdj vels 8.0 km. How many revolutions do the wheels ma h 4;xjg6rthvdps.j,-ke?    $rev$

  (a) A grinding wheel 0.35 m in diamq v77( ic4fpsb6ezyzpjd r 1yadjf4;a29 73hxeter rotates at 2500 rpm. Calculate its angular velo j1 2f6 9 cdpq4hbi37fv z47z(yrxds aaye;7pjcity 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 onh2)fm c2ypp crj+/.xi4w+w wspfg4o8e complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seate2h2wsig cj8.)pp4 yrom+4wp c +x f/wfd 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 th+w8,kc1ulta* e6c cbse Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speedrl6*pldl;8 4u ua0+raor qey/ 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 7.0 c9syzf*5b+wq fq e s0c.m from the axis of rotation is to experience an ebs9 z c.0qq5 w*yf+sfacceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly x2 3x5c6tmkbaabout its center from 130 rpm to 280 rpm in 4.0 s5x6 ktc ab3x2m. 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 pl(,0p k9f4zkmx kmw5 $R_1$ 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, astronaf:3,kaiqi 3zwz q, :7i uizhf5uts aboard the Apollo spacecraft put themselves into a slo 3zif,qiz,5az:q:3wi uh f7 ikw 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 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 unifojin*qw1/96w q) dla)xgkw 9vdrmly from rest to 15,000 rpm in 220 s. Through how many revolutions d *a /9wdidnwx))v6qj1gkl9qw id it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate1 24lke0ro 7jk)qkqp i
(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 strytx2pa* 7 ,yqk 23wkolm)zc1wesses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final spee,x3z1p)wy7cw2q* k ta2k oym ld.
(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 diameterm:. ,.tq.tpn+zjmi* 1lhjbhx accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far wij q p :tzjlih.bt.1nm+mx.* ,hll a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/mi:q nrcv6h 71zcn It turns 1500 revolutions bzr :c7 nvq61hcefore 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,*7p.+a4 ukcx ydl xohe 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.74h yxx+ p,lkc*d.a uo
(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 th 9jcq/unhbc+ b 6kv+i5e car reduces its speed uniformly from 95km/h to 45km/h The tires have a ch5/bivq+cknju6b + 9diameter 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 ey (p333x uwyvg59e zgwach pedal when climbing a hill. The pedals rotate in a circle of radius 9v3 35yg3(xwu zewpgy17 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 enk ,no7s cvw/r6d of a door 74 cm wide. What is the magnitude of the torque if the force is exertkcr/n7s6, owved
(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 thzewvyp*m 4dt90-ovu* 6/rh mw e wheel shown in Fig. 8–39. Assume that a friction torqh/ ywuo09derm6tw-vvpz m* 4*ue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are atv 1ui m3ru7ni yzf,f2.2brl(umle 0*atached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Cmb y(u.lifi,0 71lmrua*3nz 22 e ufvralculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require ti(s+vxlxow. (jghtening to a torque of 38 v. woxslj+( (x$m \cdot N$ 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 radius 0.60;bm vdk/cca648 m when the axis of rotatid ck/ cb;0mv6aon is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wgn(:w 4eoahg; b.w/nlheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignoredg4ahg n;o .l/w(enbw: (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of f)08:g jmwpdwblw1 )v a thin, light rod is rotated in a horizontal circle of radius ) pgwj)0mvb8 1w wl:fd1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotat )unq u4x:7d,nns+neming at constant angular speed (Fig. 8–42). The frictio u) d :+u,q7xn4snnenmn force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the arravr 2. usqlqo.,y of point objects shown in Fig. 8–43 .sqvrlq ,o u2.about
(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 tot) ousc:3ju wt6a0y (thal 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 spinninaxwor )3z jc nd95m-0dg at the correct rate, engineers fire fourrd 5zc)jaw9om-nx0 3d 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 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 radihr (l-h)xia-g2nyt 2: -illtuqrr p0.us of 8.50 cm and a mass of 0.580 kg. Calculateanr:uh 0rl-lhi)gi2tp-ql y(2xr.t -
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from mn /md 7v9 f* cb qork-zk(ytuy**n*.nrest 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 merryat(ngpk 1e.l-xp- ryz) sc*4p-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 o4sg( yexpp- *)k- lar .ctzn1pf 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 off and is eventuald8ve9xtm5ie*qu3: m j, psn)ply brought uniformly to rest by a frictional torque ofs euqxpd e3nt*i,8m5:m9j p )v 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 hn:zb 8d/j7lb- 9vihc 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 thrown solely by th s92vsv( yj6jstwh)r1e action of the forearm, which rotates about the elbow joint under the action of the triceps muscle( j2w6s1jv h9sry t)sv, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered 4: :8tnm;s dq+4l:sp vewm ngza long thin rod, as shown in Fig. 8–46.:mmgtsesn : zl8d4;4v+pwq: n
(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 mas7/p jen )ujx*m wah,g,)tkz o:ses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within foure-bjygyrow:w hp*97/ta -f/ . wpubr( full turns (revolutions) and release/ :/.( wf9ot jpypae-rw-h7 gbuw r*bys 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 inertiiqov no4aqnq9*5 4 6uha 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 e)x*lv mf+ ;,z)wvkaxof 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without sli4.uin tf/gygxo.w,i 3 pping down a lane at 3.3o4fgix,/y .3n i tgw.u $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the s n02 z q-gkk rpp.lngie6;e62Sun as the sum of two termsn 26-k0pes2lngkzi pq.ge;6 r,
(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 ac pz/ou6*o -ux mass of 1640 kg and a radius of 7.50 m. How much net work is requo uc6/zx*-op uired to accelerate it from rest to a rotation rate of 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 star 5(1rr jlfs 7x-r..o2x8nqz-zszo(,zucqn wwts from rest and rolls without slippi5r z .-luxnrj o zx- z12rcq ,.wnqs(owzf7s(8ng down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It2v34-sb0g rw;pmrh58t l ych u starts to fall and its lower end does not buc 4;0 ys hh23 tlpvr-58mrwgslip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotx ivv)e0+vb.19f/b*ffl 3ue 5 ztolrmating on the end of a thin string in a circle of r+. rl5zimfv )/e t*9l13ffuvbv eb 0xoadius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cyliq uqft0wv( ycidrqg0.od r56- 9vi.6 xndrical grinding wheel of radius 18 cm when rotatinr9v ( y0i .t5x.6qqrowu-d dfc60v giqg 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 platf5yhzlv7e a(g(us(b ( dorm that is rotating at a rate of 1.3rev/s If he raises his arms to a gh7dsu(le5a b (y((zv 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. 90.y8vg )zk,bci5c u y7wpzwvb4t-w i 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..wy9wzib07c,zbyuv kcv 4t i5-8) wgp5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of 1.0(u+wa.kf3d9b bo d qa* rev every 2.0 s to a final rate oaafu3dwbko( * 9d .+bqf 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 axiswhz *x5 ivam12 through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kgvw251z* axi mh 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 skaqgowo+9pe5g7 d 8dv u.ter 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 angula byiwmyn .; ni-tsskm 77t04)ar momentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia n 2eeq9l fo2uu +k/.blI is dropped onto an identical e9b fuq2/ l+2 ueko.nldisk 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 ;7tdt(gd 93ak+n im: krf9ecr +r,mdb2.4 $rev/s$ 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 rotaq1e9n7wt,+hl.ay :ywzk x ,tjting merry-go-round platform of radius 3.0 m and moment ofat9ywlke wnj.7 ,qt,z1:xhy+ 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 row+1j1 grzvg ;xtating freely with an angular velocity of 0.8 11+jw z gx;rgv$rad/s$ 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 i yk*)2p2mnfp8qq i0vvts 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 in)0vq82k n mp2ivqfp* yteger)$\approx$    $rad/s$ (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 involvi.v6+ogx moed5;x1kf e winds 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 *przq hq9m)c ; y9c2bhal0w.i$ 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, bp( rkpcpj,vq 3*(,ct46 bs quinitially at rest, that can rotate freely without friction. The moment of inertia of the person plus the pla3j6,bb vs*tqu,k4c cr(p(p qptform 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 merko+n/(* ym bzkry-go-round turntablezm/(nbykk*+ o that is mounted 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 end of the rope g22gqwrgq06 as 5z 5qulying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–uqas gz 565 02wgqrqg250. 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 facesbsmz mqw)56, i the Earth. Determine the ratio of the Moon’s spin angular momewq m, 5ib)zm6sntum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates f m aqxwa+ rt39arra/c 1)(v/zsrom rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 v03 imhtv3bdufz y0f0tq/2rhou 72e.m acquires a rotational rate of from rest over a 6.0-s interval at constant angularq0y2v 00z33 v utfuh.fito/7 b2edmrh acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricakf3k3+ 3g oroj :sdfv:l disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of sgf33j+ k dv:k3:ofor 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 thzdfutoahd ++ow0f7lfgy/e 59i ( i47d e 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 z8 .h ph y(pj qsp*89aa4a0lpu3w:kw rof our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, whakha8y:ljp4ap 3p0hsq (r*w pw 8.u 9zat 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-pol-: 9*c)rqdxqmjuo o2.sdnjpaz:s:; x lution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a totaqas-*rmqon:cj.:x :d;duo 2xp)9zs jl 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 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 illustratesbg(0+f g iu9kh 04qpxh49 4w lkiq-bvn an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoon- 9vim, ;av3(/ kes*qrgpst/f nbb;gp) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely siptrz7 hq *f( d(m8,m(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 oftdhs(iq z(r,*f8 m7pm release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and we y rldff/*v g:;wf3e4jwx82zs want to exert a horizontal force F at itj vf4g;3/:y*d efs82 lwfwxrz s axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flcz ou)+c.; qesc f.)nqat road is making a turn with a r).cnfquo +czcq se.); adius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sml impfs9qn2/ i/r3.i f;fxw( ling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above hi r9m/qif i/m2f 3x;lpwfn .s(is head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a so-d-yu8wd ,loog xfg-:lid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with o df-d,- xluo gywg-8:outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly 06cm1 ;npf nrqwhich consists of two cylindrical plates, of masr0fpn qm1c;n6s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radb9bn qyqq ,z60ius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is 0 ,nzq9qqy bb6to 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 zxz +ezjamlon3m ,xh,i4 t:ppi 1(y,*not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduce 2vviw7 5x,-g/hikxl cs its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire?2xhix7wvl,cik g- 5 /v $\approx$    $rad/s^2$(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