A bicycle odometer (which measures distance traveled) is attached near t1j3 g ,c )fjvu xqkn-)/s;5 ltk+p /6jkpxjulohe wheel hub and is designed for 27-inch wheels. What happens if you use it on a biclv;pqjn 5 6) -,/kgokjkuj/txp1c+slx )f uj3ycle with 24-inch wheels?

Suppose a disk rotates at conp z- 7lac5vx ge4/ckw;stant angular velocity. Does a point on the rim have 7xpla z/54gc-;vcew kradial 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 acceleration change?

Could a nonrigid body be describedw3,24lvhwuk;vks o x 1 by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explb: )vic. h-pqnain.

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 than wh3aupzzua.7a*(m lrer+l 94 sben your arms are stretched out in u9zual 7* r.rmas+ lpb3a4z(efront of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three udt6nlu1l 3 yi9;r;21d hcemlww :j i4at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a largy 1dri6 ;hi2lmn1d43:uc w jt lulw;9ee 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 beinofc :qz3)b7o,e+co ccg able to run fast have slender lower legs with flesh and muscle concentratedf3,bc:)e co7qz +oco c high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam-c7srm 1 0ahop?

If the net force on a system is zero, ic /a ze843r+vw+olciy- l1 juis the net torque also zero? If the net torque on a system is zero, is the net 3lyr +8/eucazviicwj o+-1 l4force zero?

Two inclines have the same height but make different angles with the horizobqrj3 w+tm6y )ntal. The same steel ball is rolled down each incline. On which incline will the speed ofw j ytqrb)+m36 the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incl(xj18pqrx v l)*s i4fcine. One sphere has twice the radius and twice the mass ofpl(1xxs)4c if* rj8vq 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 theny5 0mabjbdk;8 hg7.b same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energyk8ha7ydj5 ;b0gmb. bn at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most mozhr nus*:8 p) 9:pgeajpm( 02e9*,eglvbryfvving or rotating objmbp9g 9v e:av n j,pu2pe0hyserg**rlf():8z ects eventually slow down and stop. Explain.

If there were a great migration of people toward9nco 2f yg1qdtbh-(* e the Earth’s equator, how would this affyt *2(qgo91he cnf-d bect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initialda1*s o7 dq+3l7u5dci y14bi qlyck w. rotation when she leaves 1 qdc l4q.iyw1 a5ucd+*7kbsdiy 3lo7 the board?

The moment of inertia of a re,ock 4m/ ie8tk: 8ghtotating solid disk about an axis through its center of mas/ k,4ot: tk ceegh8im8s 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 sts x 389qbcq0ms7chuo +ool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay tcbh 9xs7 8 qomq+u0c3she same? Explain.

Two spheres look identical and have the same mass. However, one is hollow anzcev6 iwlqq(f; /50iwd the other is solid. Describe an experiment to determine which is whicz0c/wwf leq6 ;q5ivi( h.

The angular velocity of a wheeldvypn :aif;83hoxh. *g1bfb4 rotating on a horizontal axle points west. In what direction is the linear velocity of a point on 1. hfvai 3 b:d*o4hgfybp nx;8the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edbw vc eev/.a8r.4kby4 ge of a large freely rotating turntable. What happens ibb4 8 vvke.4.cy/rwae f you walk toward the center?

A shortstop may leap into the air to catch a ball alaipqi5, qv8:wp-f1u nd 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 ai u85 lf-qapqvp,w 1i:nd legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservatio opg p0jdlyp+21sd m,9un,qa *n of angular momentum, discuss why a helicopter must have more than one dl0p*,jp+sao nd92u1 gp y,qm rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following an-rgmk j 6:::ntyz m-dmgles 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 Earth because of an amazd sl/pui0f*a9ing coincidence. Calculate, using the information inside the Front Cover, thu/*lai9 fd0 spe angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at ths14ar bdn,x3xj c 7e1ve Moon, 380,000 km from Earth. The beam diverges a74 bjcxev3s nrax1 ,d1t an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is turn6oq:i *qgzg1t8c-:ff eig6 vred off during operation, the blades slow to rest in 3.0 s. What is the an6-egcv:fir zq: 6g8t1 goq *figular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a, etwa g bkt5a-s55n)r level floor 3.5 m to another child. If the ball makes 15.0 revoks)ena b 55 trwa5-gt,lutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 kk mvrn- *7-o4 chghd8- dafnnzm (2u*zm. How many revolutions do the whee24fzo-uzmc(d8-hvn*an7 kd m* rnhg- ls make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2hg(qvw. td/ 9g500 rpm. Calculate its angular velocg wqh (vd.9/tgity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–38).pz6jus(zc ik xbjf.91 r8iu-pe+) ntl)s :bg9 (a) What is the linear speed of a child seated )z+ul pu:nt ce89)ri91(s -xk z6 spbjj.gbfi1.2 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 ip7mh t3i8.t vEarth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sul) z ncg;m5ptp 0*yd5peed 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 rljk9.m0kcy*jg icd50nkb8 i0f 9d-fa centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experienc yigckd0jikcn90km59bl8jf dr*f - .0e an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from r6y+ k(,u h; 8embkie tcc2r9w130 rpm to 280 rpm in 4.0 s. Determinwyh u6 r8km,;ir92 (+e ebcctke
(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 radium /pvn/ca;f tuoh4 2v;p*xb6js $R_1$ 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, astronauts aboard the Apollo spacecraft pu2i ;:(gws ek65fatk,wrkme ;tt 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 tho 2fr ;5t:e6kgwwk,( msitek ;aught 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 rps e32q( m6yjnjm in 220 s. Through how many revolutions did it turn i e2s (6jmqjyn3n this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.9uske8k5tjr8 cp0 f y9 Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a w. v8n mn+rcz79 pjxygl0a+hm, hirling “human centrifuge,” which takes vmj,0 pxgmn9 rzl.7h+ c8a+yn1.0 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:ig-bv. yn2 ip r4ri3 d1jg/uz 240 rpm to 360 rpm in 6.5 s. How far vn j p :di1gzri.i2yrg/ u4b3-will 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 850re1pf7gowpj8g 8qp0 yl(d: zr6pv/min It turns 1500 revoluti(w 6qz 87pylpg :dp0pgrf81ojons before 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 make d-xd(yb w0j(q.t da*r65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have t( b0dydr*a.dw( q-jx 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 yx/,u(8q y8d8wmwzl tas the car reduces its speed uniformly fr88/du m yy,tw8lxzq (wom 95km/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 her weight on each pedal when climbing a hrzj9 8b eff5c s*62mdgill. The pedals rotate in a circle of radius 17 cm.r26 5 fm*js98zecdfb g
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of .*wpp570 tv+/qdub hxsz ann755 N on the end of a door 74 cm wide. What is the magnitude of thexp7* pu 0nhtsab75vw/nz+d q . 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 Fig1pjfy.) nit+ mh.m.jdc8p j5 h. 8–39. Assume that a friction torque ofpji..+m).thp8f jhd5jn 1my c 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 mas pg.ygo9b)k45 ymdtf6sless rod which pivots as shown in Fig. 8–40. Initially the rod is held in thpdg fky9o gyt.)6 mb54e horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engin ys: y,4fy.gpne require tightening to a torque of 38 . ygys4:pfy,n$m \cdot N$ 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 radijja2cb4ryapu*i(c*(t1u5 f tus 0.648 m when the axisujab j p*ca4i1( fu5c*t2 (ytr of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 oijfl l8b*gp-2 iw*khl ---cqcm in diameter. The rim and tire have wc -g liflki-2 pqoh--*jl*8b a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a tpjdws 0d7jw4 7cs.m3u hin, light rod is rotated in a horizontal circle of radius 1.2 m. Calw7w d ju.7ms34d jcsp0culate
(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 pottelrm59tp5; xqc7dqum- r’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and thc t57mrd5l ; q-upq9mxe 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 array of point objects shown in Fig. 8–4rvr3b4jh y. e(3 abh 34b.jv rre(yout
(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 5x7csboc;uu9 $5.3 \times10^{ -26}$ 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 spivqo)8+1wr-.suc 8a p6dpp m ctnning at the correct rate, engineers fire four tangential rockets auv p88w6mqr d a1tcso.-p+pc )s 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 radi8 sg;c;kpqjworb/zx c d21 w4+us of 8.50 cm and a mass of 0.52cgd41jw zwrxo/+8qpsk; ;cb80 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelpgu, y7-a e*1sk-ys /zifn0h+a; ecoberating 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-rou,m bix vyrhlquvt0q)58y:;*x nd 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 a yxx qqml:, v5*)0u vi8yt;brhnd has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating atokyamo8( lz(0 10,300 rpm is shut off and is eventually brought unma(y o 8k0(lzoiformly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a /vg:i+r a9gpos8oqsu a3 -i rcw:;5bw3.6-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 theg 8wuh/c4) lqe action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is acceleruqlgec /h84)wated 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 thin rodap 5poe.:npvm/- kk*r, as shown in Fig. 8–4-mk v.5ro*pa: p/n pke6.
(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 masy8m ;rjiu3rkqehx.33/xi5 x sses, $m_1$ 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 fromscj8daot;t n z+h4z30 rest within four full turns (revolutions) 0sncj 3o+t84a; zhtzdand 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 momentnctdu7 nl0nx)2j .3ko . c,1vm n4ektw of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque omd 9i s8jxgxl7+(0 utxf 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 r,vry ;2ea m5jyguha3 9olls without slipping down a lany5 uaeym g,; ahrjv932e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth wcy w0p*qx4a9 ifz sx:4ith respect to the Sun as the sum of two caz4y ip0x x*ws:f49qterms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net wo5vtm12tphj z 0rk is required to accelerate it f zv p51ht2jm0trom 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 starts from rh 732xaj77c f.af dbf mq*mn;lest and rolls without slipping down a3f.hbf7jam l qa27dm;nf 7 *xc 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 tiprg40.vzt )gf4r6o, tv+zqcs t. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the gr+t,oz.f)qgt t z6rvcv0r44 gsound? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of ah.b8v,u+uej e2+ap 2waplu*k 0.210-kg ball rotating on the end of a thin string in a circlpa hp+ +ub 8 2*wu2.vj,eekalue of radius 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.p+h/ *z g36kaf xgli ist:pqh+6ezu0 qxd 9o0*8-kg uniform cylindrical grinding wheel of radius 18 cm when rotatind/ + a3*ghepoiilt*h+p g 69uxs 6qxzz: qf00kg 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 r qkz z9jr+gl)os))d8 sotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed o9j zdsz r))8lko)gq+sf 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 ms9bybb26b 8wzoment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position 6 z8bb2sbwy9b. 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 rotation rate from an in(1vf44r kd4nbg scs+bm e p;5nitial rate of 1.0 rev every 2.0 s rc54e;np v(m f14k bd+b4ns gsto a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a :fjzkxj law1nd 3638h)pz 6hjfrequency 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 :k w3 6)18hd3azlfxjjznj6hpa flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at r+cndu.k8 ,3 u5inzlz 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 p+-x)jem1hu0sowh ; bof 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 xly ;t6x0c/0igj *r/sxcr4u yof inertia I is dropped onto an identical disk rotating at angular spl6y*xu g c0jy//r cstx;xi04reed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns u ,w(ou6y 28ltkqsw/eat 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round platforimm, -k6gh rbl,)-)iofvzez/, xfvp / m of radius h-o6p,g/k i/)mibr fze,v vm,lzxf -) 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 angudv 9vksk7aq +d4jy(, hlar velocity of 0.8dkd , +h4v9qyvkjas7 ( $rad/s$ 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 cmzh*g.o0o q):w5iwl collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass ca om)5*w0qw lgiz:o. chrries 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 windss yhdry9 wtzwd 1ix1:f0;t0k,a u0zh ( 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 ti bvgm2uttqa8:dw t 82;h t tl+nt96+$ 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 pl6.;uxqluf y2 eg+ nbp2atform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform is lq +egn6xu 22.f;uby p$I_P$ 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 diail+j 3tytw b9ofh1/ u;k,k8uosqg*8 n meter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia ofkuigs t/fou;klb wo38h9+81ytn*j q, 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 r j*/j-wc un3ifsr9z/on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What lnzj sj fcr9u/r3i*- w/ength 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 face2 r fz9sb o/dnr9is*l/s the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting 2z ob9dsif/r*s /rnl9the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate 1bl7;ma rzfvg 58h.zh 1qu9arqw;m. rof 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 ofrdaakoj tyd*; n26dd )4 2go8p radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calcj *6ddprkda; ontog42 8yad2)ulate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of twosj9a/e-0hfos ip fxn8 ux:1qb/x z m+1 solid cylindrical 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 ax 0ajspx fx -q/i9f ez/+bosnum8:1 h1nd 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 angulae5vhxr9 0 ,e 2 wcxcgl1,sgn z/9zdzb0r 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 S7g** wq0u5h+wvkz rg aun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to g*qw gura+wv7*z h5 k0undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile hgm*/s aa8v a-tejy4/ is for it to use energy stored in a heaa j /ahvg-y4aste* 8/mvy 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 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 illustrate .ertobe7z2w. t,j 2,ovq djp38cpk7t s 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 (hoop)sjcy0r op3/x 5 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 lengtb c* *ooz;n3. bhar)1 /kdbvnhh 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 acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rodbvorhn* 3)1z/n o;khab* b. cd, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vert ,qhugo nyi7y o)ia;14ically on the floor, and we want to exert a horizontal force F at its axle soo; nqaoyi), h 7iug14y 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 flajd8jv .2z;*p 9vfmerg(bj 8d+ll *dlgt road is making a turn with a radius The forces acting on the cyclfdl*8 8p9j l+ . g2dvezjmdb(rjg;vl* ist 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 gzn bd+v7s. 19cy4ffr0.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it9yv1.f r czn4+d f7gsb 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 solid cylinder and kf e,.ftu0ey /5w( jqy+;z3foyzen;: dn w qr/her arms as thin rods, making reasonable estimates for the d;(w qyff0fykw ;jnteueye/noq/:rd,5+z .3zimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, ofo3th:c jrr1 ct-j5*dc mass5-3 hjrcd ctjt *c1ro: $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roug:,mf ,oc,hm ecs 1nwu;8aa bq1h track of Fig. 8–58. What is the minimum value of the vertical h aoaqu eb, s,c11nf w:8hcm;m,eight 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 asq.v5 n ckywm2 bsv*5j1sume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the ca kv+c:n:whx /*d:vec.td*i fjr reduces its speed uniformly frodhn kv*tiw:fed: c:*v/ .jx+cm 90km/h to 60km/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