A bicycle odometer (which mearq8 gk.x d+fd:sures distance traveled) is attached near the wheel hub and is designed for 27-inch whkfq+.dr: dgx 8eels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at con+zu0.;r9t(mt o ys fmzstant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleratzmo0 .y ;sz rt(u+mtf9ion change?

Could a nonrigid body be described n1 dy9vb-ubd*5 vf0on gh-*knby a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a gw:2g fc 9.mrc1moljf,reater 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 thantb 1l *7 ;y1fxk zwoxg,8jzd2c when your arms are stretched out in front of you17,*zl 21j gxd8o w;tzcxfykb ? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and threk14z ylq6k) ike at the pedal cranks. In which gear is it harder to pedal, a small rear sprk61lzk4q k)yiocket 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 hav:o bajstsm83e .+et-p38f kbte slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageps3e-8af.t3bje:+ kbtms8ot ous.

Why do tightrope walkers (Fig. 8–35) carry ho1z)r+mde (iix z:h 8a long, narrow beam?

If the net force on a system is zero, is the net torque also zero?/z4ckaxl397z as d 4xa If the net torque on a system is zero, is the49 zc4/xdak3xs7lz aa net force zero?

Two inclines have the same height but make different angles with th0f+ (g emra-u)auh-gzh j5vf1e horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain- 5 gz+g)hej1 r-huf0(af uavm.

Two solid spheres simultaneously start rolling (from rest) down anw9 i8c8cu r* algo8kk8 incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Whick8ac rgwk889* cui 8olh has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start - glagc.z49clfrom rest at the top of an incline. lgcal -z.c9g 4Which 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. Yet most moving orulprttd1ug n7q )1.,:wwo6zm rotating objects eventually slow down and stop. Explaimtt 6,d:nq17zru.)wup o lg1wn.

If there were a great migratidspu)d;+(hh3eg3 5 ; kxnhlbuon of people toward the Earth’s equator, how would this affect the len )3hdl; p hsx5g(nhube +ku3;dgth of the day?

Can the diver of Fig. 8–29 do a somersault without;q ng:gsx 3yj8 having any initial rotation when she leaves th3gns j:g qx;y8e board?

The moment of inertia of a rotating solid disk about an fr+e:v4c xe k,dnns7:axis through its center of maedrscn:kex7:n 4 ,v+f ss 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 /e:2h9gof 6 fet mo2yka 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocym: /o 6tefho gef922kity increase, decrease, or stay the same? Explain.

Two spheres look identical and have t .49fsy xt9qajlf .hcn70 fayb0:j 1bbhe same mass. However, one is hollow and the xfby4.ba:l9bafj 7ns1 f .cyq090 j thother is solid. Describe an experiment to determine which is which.

The angular velocity of utm)abir k 7 i8;mr4v3a wheel rotating 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 acceleration points east, describe the tangential linear acceleration of this point87i;i bm34rm u arkv)t at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the e6h0czb fcdnn d/ :4;vjdge of a large freely rotating turntable. What happens if you walk toward zvfc;b 6j0/d nn:4 chdthe center?

A shortstop may leap into the air to catch a ball and throw 5+a.9 t(s .8o idjgqj x m3)uhltnaya/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 rot.m h.yijj8tda)alq+xn5 s/oug 3t(a9ate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of cm8v: 3;plcq9keg +wtwlzz, v:onservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or morzl8lp 3e+ w:;k,cvgvt wq:9mz e ways the second propeller can operate to keep the helicopter stable.

  Express the following a r*(tqxutoj0(i6y l4i ngles in 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 E 3j)zy1murwl10d)qm jarth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen z 1)mul1 )jmrqw0djy3on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth.1cu 1y 58u uzcv5sb0rw The beam diverges at an anglw1vz0sc 8r bucyu155ue $\theta$ (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 t/y,,q+ovntzppo z 9qq)1+hss urned off during operation, the blades slow to r/+n9 ,sz pqoz,otp1 )s+yhq vqest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ;czkaii*uy1gb)np2a7i j,e v28zlm l:d.8bp ball makes 15.0 relk8lvg*e pb,i:27azc p8)yni mb.i2j1;audzvolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 kxml age.d0(0t7/ l pec:xn n v8iz75odm. How many revolutions do the whe:vtn l.e8z057mx x7ndca i0lgpod(e/ els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpmvl)j1o.st jlukmm )76. Calculate its angular vel ))s.olm7jt v6l1ku mjocity 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.el4m5 t84lpn-jj/ i;tst azgnx4cn 9 3 8–38). (a) What is the linear speed of a child seated 1.2 m from the center?8 e-39 n4tpljc lngjnizm4stx;4t a5 /    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of th 3/ dz.:ls tylndk8;r9iy6sele Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sz8ae/okab j :0peed 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 *xh5k5ibom3l .0 cm from the axis of rotation is to experience an accelem5 bxkloih *53ration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter whey0869 nyukf4un: w cyi1h(rtcel accelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determnyi(4 hyfy10uk9c:w r 68tuncine
(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 radiu6g;ekc / ulz vgd11 kjfjtx y; (bbd8j1j(.0ues $R_1$ 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,ugy4 jm n90j79u 0fxzbnv, q1a astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-minfz g uxn b79m9yj40nuj0 v1,qa time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm5(yto0kny7 cw in 220 s. Through how many revolutions did it turn in thi yc wy7on05kt(s time?    $rev$

  An automobile engine slows dorb+.e r:9dmcq8 mv9 zyk3a6 djwn 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 sq8 nbof78vghxth*2h:m u t)k:tresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachi otq:8gn kbh)x7:mvh8u*f 2htng 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 uniformlu*a9nwwpp kn;.- l t.by from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this 9p nwpn.bt a;kuwl-*. time?    m

  A cooling fan is turned off when it is running at 850rev/min It turn35 ;6mvxa1twir47 nj8 lbzd yss 1500 revolutions before it cotx81mnsbvly5d ;6 w z 7r4i3ajmes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as t--wq5f,akb h7sssgy bj -u .c0he car reduces its speed uniformly from 95km/h to 45km/h Th-7 fg .jss0sachb5w q,-ub-yke 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 r;w.dxc*1grho f;rsc (r, ma4 oevolutions as the car reduces its speed uniformly from 95kgrxo (m .adf hw,*1ocrc; s4;rm/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all he g0zxzbpz hp4hnc0:02r weight on each pedal when climbing a hill. Thp0pz0nzhc2g4 0: zx bhe pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wibvs cr7q 2p, 9l k+racjuzb0+(q o)qf:de. What is the magnitudep 2rsba+ l:orfc(0qbq)+q kc7j,uz9 v of the torque if 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 axle of the wheel shown in Figxhurcu6c sg7m *sby77,sn -7d. 8–39. Assume that a friction torque os6hx7-m* gcsysunrc7 7d7,bu f 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless0 bl5u6srrg*(svgw, p 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 d *spgv56 0urw (sr,glbirection of the net torque on this system.

  The bolts on the cylinder hjpqhx686o sct q ))s:cead of an engine require tightening to a torque of 38j8qhqc)ts o): 6xp cs6 $m \cdot N$ 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 0.648 h-s g:+mp;zq qm when the axis of rotation is throughzq spgm-+q:;h its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whee wwzl(vrvi/. 8l 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg.wvwi lr8/ (vz. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rott d7gd1 ,a z:6i6mxleuated in a horizontal circle om7utd :aex,i1dg 6l6 zf radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a box2*ecselyqp3jp i.vn d0- qwx6q21 8uwl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The l1u68pd2sqv-q ex*xw n0cp e. yj2 iq3friction 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 inerh jq; l)ay7s;ptia of the array of point objects shown in Fig. 8–43 abo )h;yq asjp;l7ut
(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 consistit -;repeh; h3s of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning a;z*u:zn5ijtwa 5t/ ogr skj(uiff18 :t the correct rate, engineers fire fourz j*(swtui f1 z;g ikuon:tf5:8r/5aj 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 /ekta0 ,6t -, hezyfztme5b 7 6rjytw.with a radius of 8.50 cm and a mass of 0.580 kg. Cale5ayttey/6,,0b t - fe7m.zkh rtwzj6culate
(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, acceleratindbmrog, f:t;r9zov a1f6ol : .g 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-drive oym3niq-wp7*3 b/w ( yp(qmypn merry-go-round and is ablemibwop( -mqy3(/ y7w p 3p*qyn 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 rotat5nlwm/wsj c) +ing at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional c n5ww)+js m/ltorque 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 acceleratv0j25 smov/bj v+ 9oljes 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 t s)py/z*am5 u vlh*b/jhe action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is acczm// h) sbav5jyu p**lelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long txudz8b-vvb 2/+g6h fthin rod, as shown in Fig. 8–46z+v6 - hbf2/utbgxvd8 .
(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 cons2pkk.m+ glp 2ynlt-tqi, w9w*ists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hs3m / 8 g,vul/vp 4thobpyls5)ammer from rest within four full turns (revolutions) and releases it at a speed/)yl4 bspsohvtp l m3guv ,/58 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 ofxq;u l7n07l3/kecay+3ly t6aumgs,z,+ ubg f $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops u*a m3yud*6 qg/c6ia xa torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping d gvsf v7pn1g *1e7ex2y dbgye iv;59i-own a lan yixygpevn7 -gdv1 g5v se;i29 1f*7bee at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as trii,fb*y; 9e6ilsvi -he sum of two tf y,iibv*i ;eil6 s-9rerms,
(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 a1xnl)x)f dduf/ oyu.s q u+*8a radius of 7.50 m. How much net work is required to accelerate fuxof ).)adxnsy*/u u +8qd1l 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 starts0gpy5f4o x dqar)(*ys from rest and rolls without slipping down axdy)af ogpr 05q4(*ys 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. It sta(.gxj m ovo9mny3)+bfrts 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? [Hm.jx+)fv3 g(boo m y9nint: Use conservation of energy.]    $m/s$

  What is the angular momentumqn+sg-gaud8jp4,cra f3 g.u 6 of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at a gn-d4g.cua8q ,f 6gaps3ur+ jn angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentu6+s u yvnen942bb c:jbm of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpnej+u6vb 9y4: bnb sc2m?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his sidesiw0;.4lru6 iktknv m. q25r x, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal.mvsrl40. t nix;2i qrk56wuk 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 r+g2, ,ucdv6 wnq6 elaqeduce her moment of inertia by a factor of about q,6v 6qd+,cw an ul2eg3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotationqbz22nrc, m-:nej; hm0mm cbsw ,-t,o rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3b0;rqczh,ocmne,n2b-sw 2: m, mt-jm $rev/s$ 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 vertadijxxp0)0-: fzbggb;4c db: ical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter xj0i:0f; bp bx:c d-)zgadbg40.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momev)jl :h*xk i.tntum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of qlre, )j .qtn9the 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 ine0bwpe8wvo.0z3oz.g bhvcugi 3f9h9ht .d2 i2 rtia I is dropped onto an identical disk rt0 fu.. 3ihio 2hb. vwez9wdg0 3h2vb89gzopcotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2. .+mv(i)rlv zd4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-roundhd.) dvlvi 30i 8)gxgt platform of radius 3.0 m and moment of inevtdg3hx gi.)0id8 vl )rtia 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 6;9qdkbqe7h b of 0.qb6dek9b7; q h8 $rad/s$ 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 halfnu ()z/ai;bcy yx),xp 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 yc z(u,y ;xi)npa/x )bnearest 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 exc) 9uzlko upzbjn9/6d5 ess 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 o5nnl86cf;l,seb r4l$ 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 fr2jqyiy/ : tq(lfpp- :ut1m4ha eely without p:j4yfu (qhp-yqtitm 1 a /:l2friction. The 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 ed(pr9pkr9xs:- yw8a 0swr oxk *ge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of rkrxos 9 :py*-xww 9rkpsa08 ( 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 lyi9msy:7sk z55c1yra5uxqn yqd g)zv6oij ( 07nng on the top edge ofqm7kuo9y :xnrdy ( gn5y 5i0qv5sjzza)c671s the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of 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. De7/)vbiy 1gxq-r s3j;a m lbb)rtermine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)v)xjil ;yb)7r/1q mb- sbgr3a    $\times10^{ -6}$

  A cyclist accelerates from rest atf)yvnqw/8gjmqp+ed;/cm t e7/k. w 0f 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 m acrjxt3nw3v6o*has azri2n5 :+ quires a rotational rate wx356rt *snnahjv z+irao2:3of 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 two solid cylindrical disks, each of mass 0.050 kg t9oyhxg v ju; :btm*24i;nt .yand diameter 0.075 m, joined by a (concentric) thix ov th;.9 mtb;u*jng y2tiy4:n solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how it:qrfoo 53lld gj.x6 5s the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mask c-h, gms5rq/s 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 thrrghkmc ,s/5q -ee-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 r;zx/z 0iz* pp ;*luag)dky3lfor 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 flyl*0d3/xzyap grpz;; )* ulzki wheel “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 an09zr2vh py;.59yvcgmjzq5 s e $H_2O$ 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 surface at speed v=3.o(* 3d ed(ikyh2r6fll3 $m/s$ 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 lenggf (i*ns1nm -t.jcai*th L 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 j(c *inmtanif -1s.*gacceleration 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 cxsdpri/- wgc7uu/yq 478:1vg b7z i awe want to exert a horizontal force F at its axle so that it will climb a step agai4 b aczr1/p77:/ucuy-xiqdi87vwsggnst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.20hgu2laqhb tfin:-u :o,r5g; m/s on a flat road is making a turn with a radius The forces acting on the cyclio5 ,2b-nu ;rl::itgh u0 afghqst 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 begins whirly /k6q+v6zxgying the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come frogq+ 6y6ky vxz/m?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rocibr 7 km38, c06+u-qbmlaj wnds, making reasonable estimates for the dimensions. Then cal80 imcw crqb-+ b6ma3kl7 ujn,culate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrick3h/-f luv9mt6q rp( dvm6 zf7al plates, of mass 7v uvm- zlht/3dkp(f6rf 69qm$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loopeub 2y2 zwza4c2jbn *3ed rough track of Fig. 8–58. Whatj2zz y* ucneba2432wb is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assugsdr:(:dtg a-me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces it ,4xndvrp0cy;qqx2 u0yv9aa 3s speed uniformly from 90km/h to 90cyx,3r;qdvv pxa20qa uy 4n60km/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