A bicycle odometer (zrh4r ip-t vs .wa05-s-e *vzuezf:-bwhich measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if 4r- z -.*: zuresvawv 0e--ts5hbzfp iyou use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point onkp/cu:t d09m n the rim have radial and/or tangential acceleration? If the disk’s angular veloci9mnkp/ 0utc: dty 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 described by a single value of the angukeske.c3p:l 1lar velocity $\omega$ Explain.

Can a small force ever exert a greater tzf8c-g1kkvn e m7o*.a/ugyt.orque 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 l1 3hzomav p8r9rs4neww.f4 h / r;-emwith your hands behind your head than when your arms are stretched out in front of you? A ;8-em hhe a/w3 z1rn.rwr9of l4s v4pmdiagram may help you to answer this.

A 21-speed bicycle has seven spr6,cb/toyo/ 3 nr cn,mkockets at 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 front sprocket or a ot/,o3/b crk,n cy6nm large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with pl laymr5bm9tye;*+) tcd-s+qa b8j7 flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distributio5ymb ems 9+btp l-*dq;tyr+ a7clj)8an of mass is advantageous.

Why do tightrope walkers (Fj be5y)6 (l2sly re,lyig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is tsgip/d5jm91e-k//3mi lbacaf e;w ,0og; dn qhe net torque also zero? If the net torque on a system d; 9b 5d/lfgmks1i g3/o /w eamaq;0ncpiej-,is zero, is the net force zero?

Two inclines have the same height but make different angles with the hor5m)w m+ ulizew 6 l8/nbs(1dxdgvn r69izontal. The same steel ball is rolled down each incline. On which incline will the speed of/ +5(nwm6d1g8s blx )wri9 nz ledv6um the ball at the bottom be greater? Explain.

Two solid spheres simultaneg/()r) k,ja c ucgs+pzt;y/kcously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline fi ;c+/) z cu/sa(),pg gjkrkcytrst? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylindjip*tv; u6h2 oer have the same radius and the same mass. They start from re;*u v 6j2itohpst at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. bjz7jnvi*vq8:, 0 vit Yet most moving or rotating objects eventuallyt jv nz80bv qiv7:j,*i slow down and stop. Explain.

If there were a great migration of people toward tpmi*c c:h)g.m8bbv w 3he Earth’s equator, how would this affect the length of themm 3cwhvpc bib:8)*.g day?

Can the diver of Fig. 8–29 do fw )zo3cg:,tuguou9 + a somersault without having any initial rotation when she leaves the boazu t+)u9u 3 gfcoo:gw,rd?

The moment of inertia of a rotating solid disk about an axis through its cenb9x +ht (g78g .phbyi-m7edkster of mass i-mgh+h8xtb s7yk97b.pdg( i es $\frac{1}{2}WR^2$ (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 rotatooa) r fn;gf5nxx7l 7.ing stool holding a 2-kg mass in each outstretched hand.n 7ng.rf a7;)oxolx5f If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howevn cvv 59 +a-sdi,uz5rxer, one is hollow and the - 9x u izvr+,dnc5s5vaother is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In.--s l nty2q1cfv5rzn 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 poi1ny l5 zrvcs.-q -2nftnt at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edg;r -7im rew5+rdg*ud4sr:erw e of a large freely rotating turntable. What happens if you walk towareire g5ww-r4+ d ud*m r7s;r:rd the center?

A shortstop may leap into the air toy c *g a;-c*kk( b,zvlly47 zwumb2xbkf1e.f( catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notic4bb2;ff y gcbk k*zwm(vl1(7.* aexl u,ck- zye that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, di2s5v/zzvunmmnw0z 9 7sv9oz 4scuss why a helicopter musnz7 o 4 zvv05znsv/2zwu9mms9t have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the followin:oda :4;da0 t vllrc pd8 7lcy(q9no1mg angles 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 Eart gx9+eovr ao9;upk /p6h because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the M/pegp u6 o9avok+r;x 9oon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The 9t/5w)*ecu3 ozh c3l) xtxkxgbeam diverges a*kx)t9luogxw)3z tcc/ e5 x3ht 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 rotat*9og1ib 9edld( yr +gle at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to resry(l9dg9i o +eb gl1*dt 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 flix*nynoiq :1 wn ::vqg3u;e f1oor 3.5 m to another child. If the ball makes 15.0 revoluiuyg:n3 inq:n vf11 xwq;oe: *tions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How m: f;gl 3cq/kn;*o dakad2l fq,zlv 4r;any revolutions do the wheels make?,al l42n g*cl/;3 : ;fo;afddvkqz qrk    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angul j t76zikp2j2bar velocity itb7k2 j6pjzi2n $rad/s$ $\omega$ =    $rad/sec$
(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 revoluti/855kgs:rf(o(h0v-yuwx hvkfy fkh. on in 4.0 s (Fig. 8–38). (a) What is the linear speed ov(ksy kuxr-.: o (yf/vwfkg505 8fhhhf a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earsav;-mab 4zzx c4x6yli;j4,4)qn9ghdm su0 g th (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a utbs0i hytn-cp57( kper4r 16 z6gf(ypoint
(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 aoxpk+/ +mh tbdiw.m 0e:q0: ik centrifuge rotate if a particle 7.0 cm from the axis of rotation is to expi:wibh mp xd/.kqt+km0e :o+0erience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelzs(wd2 gx1t;w erates uniformly about its center from 130 rpm to 280 rpm in;s dx(t21w zgw 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiusg3rfttpeo2 u) i92s* xz0n 2ytjqp98b $R_1$ 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 spacecrzk 5lnziwve5;k+( g-iaft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determi zlg5(zki-e ;5vnwk+i ne
(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 restnh7i k 6/9:l1qysedz2uweia* to 15,000 rpm in 220 s. Through how man iene/1u62dqkyal i:sw *h9 z7y revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 l,gcl.)fa) qo 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 9dfua 1lku1a3stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn througaduukf l3911a h 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 fro0uq;tgu+qb7 q zw/:-c n8usk mm 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? g/u7c0 zsb+nk8 qm :-ququwt;   m

  A cooling fan is turned off when it is running at 850rev/min It tus3h( 4*e(w x)fq jwhkurns 1500 revolutions beforeekh(j4fh )3q ( *swxwu 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 65 revolutions ashd4;v1r j*bdr gf xjk-f0:: zh the car reduces its speed uniformly from 95km/h to 45km/h The4bd:hdgj0rz :f f1jhrv*;-kx tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the ee v*mjp::j(ocar reduces its speed uniformly from 95km/h to 45km/h The tires have aovpe(jj e::m * 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 alwy8k7+t2 g 5;e-:vpj sgmi3:pkwtb v tl her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm g2yvg:m8:5;3bte twkp wvj+kpi -st7.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. vne* jolv*m)*;qz*yogdu1. l What is the magnitude of the torque if the force is eev* j.dmlovyolz gu*q)*;n*1 xerted
(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 onkiagq+icj t1 u 0u449 jal0/the axle of the wheel shown in Fig. 8–39. Assume tqt40jja1 0n ulckio+igu 9/a4hat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a mac * lx pnz26gh/awhf zg4-qv;5ssless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the nf/5*xp6- ;qw vhlz c 2hz4gagnet torque on this system.

  The bolts on the cylinder0 u-mmq hu1.ve head of an engine require tightening to a torque of 38 uh.-1 uve mmq0$m \cdot N$ 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 m wtj7t2:l s5 ajbhen the axis of rotation il25j tbsat7: js through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in 1/o+xus+ nuggb 9is +fdiameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignorenb +xus/19 siou+fg+gd (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a 8lq0to:t i iuvn 0iw k3i2w*rp+2 p-sfthin, light rod is rotated in a horizontal circle oqi2vsw+t 8f-0ipnpl*o ki wu3ti02 r:f 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 bowl on a potter’s wheel rotating at constant angular spee z jy(h.gre)x (sg53hbd (Fig. 8–42). The friction force between hbrzeg.3( y 5gxh()sj 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 array of point o;.inbk0m0v tsc-b- idbjects shown in Fig. 8–43 abos nki;c 0btb-im .-0vdut
(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 who(44rux(g tdk57zji 4ye*b ok k 6vc;ysse 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 cyrianv)ex 8np1el)ctgx6yw e r(315-klindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 15e8ey 3iawx ()xvl -tcpn n1rr6e)k g8–44. 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 radius w2bx; un65ccj of 8.50 cm and a mass of 0.6w uncc5; xbj2580 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, accelerating it from re + v0gd*1f4cezte dt(q6oql d,st 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 tangentiallyn ba;q-3j qc9 c6fzv3x on a small hand-driven merry-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 ;v6q-ac9j xb3zf3qcnmass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,;xpy aew1dg 5wk- q1n p87cgc2300 rpm is shut off and is eventually brought uniform g78xkd;pp cw -c1na1gw 2qy5ely 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 accxr.mq t*83(a- q ky.cwi mm;xaelerates 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 the 5-3 ikn *-kz ja/6i/u-xaniy (wqb vrjaction of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is i (/-j5nabin3rukazq/-vw-xi*j yk 6accelerated 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 rod, as shown in Fig. 83 94c wy d6aqle)bv-jc–46.6w -b cvd)al493je cqy
(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 consj;1qayi/j 08yhg- agdists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four f8laawzfqe9m/ va9 5ip-8)kca ull turns (revolutions) and v9 p 5z9ca/e)8qikam8fw-aal releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of in*:c02a xcdk f2s3qfol ertia 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 torquylmmmo 7- 5o eco)3/idvkn1 -re 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 dz9y(8qt d l9wkg and radius 9.0 cm rolls without slipping down a lane at 3. (ddz99wt8q ly3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energ 0ndb.g5u36n hros7 psf5v,bc y of the Earth with respect to the Sun as the sum of two tev,bf5cdohbrn5pu.gns3 s67 0 rms,
(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 w1sr..y0fd grx pt/0x04uz bdj )t.ljn ork is required to accelfzn.0j0t).40rgrd x1y/ bpj s.tldxu erate 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 sknf* v:7 ypj:itarts from rest and rolls without slipp:p j 7k:vf*yining 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. It starts to fall and ms ax7g(-1 vlyits lower end doe la(x1 -mgv7sys not slip. 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 rotbns hs2yngt3n 1b. )6fating on the end of a thin string y)bfn .hg2n1sts6 bn3in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angulauhe xb )4ey,d flqk7/m8zz/d3r momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotatingy/hzkdx q3f/ l7 ze4edm8u ,)b 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 az kd0un wsr8j +l7;js: platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal powk+l 0j78;nzus jd rs:sition, 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 ik 3f1tpu,pn :gbw/z 7cn Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotg tu :b3/,kzpc7wnp1fations 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 rotati6i; t4do( f5z u;*efd rkmj,tfaez/ n(on rate from an initial rate of 1.0 rev every 2.0 s to a fu ta5fjk6fre( e; d,;i4zz/*tf dom(n inal 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 aroun+gxq+kbazct *u0o /1(ac, qg fd a vertical 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 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is tcc z,ag k x+*bu0oaqf(1g +qt/he frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentu7 s pj3frkj56jm 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 the c65 zd e+fnr h5cmo((bEarth
(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 I is dropped onto an idene-/mh)u lgzy m1/oey 5tical disk rotating aomyh)l /meugy15e /z -t angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 (yl0;rsdloe g3 x* zyk8o.igg1 cbp,5$rev/s$ 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 . a++u2 n u+iwmbpe3xi35kjmdthe center of a rotating merry-go-round platform of radius 3.0 m and momei+ jdi3kmu5un+2me+ 3 px .bawnt 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 ixeqn6 :x x9) 4yzl4-5ydmidyrs rotating freely with an angular velocity of 0.8qixn4:dly d) y eyxxrzm5 96-4 $rad/s$ 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 abot*m.47lzo7qdju qwo: ut half its mass in the process, and wi.q77q w4t:jodlmo* uznding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in ect ;9 fjr3(8ymacqku) xcess 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 1fh2u,g mt q(fvqj*j- $ 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 c3; h jsqrd4aqnvw3pw i8ci2gm ti) 38-an rotate freely without friction. The moment of inertia of the person plus the platform ira8jp;qiw v42hti-)dqmsn8g 3ic3 w 3s $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-rpy 8g5gd0l +k rua73 2t0*gmmmwmfp2jh18jhzound turntable that is mounted on frictionlessd* 3tmpjm zwyfu 25lgg0pg8h 0m7j1akh+m2 r8 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 ro;aqr;t-vb ww4z/ m7wtpe 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 length of bwwwtvmtz4a7-/;q; r 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. Deter f,6d7*cc5 8eokcx qggmine the ratio of the Moon’s spin angular momentum (about its own axis*k8e76dqg 5cc,f xgo c) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates frogmh gx3* ::))fnfg1sp,gu g3amgoi2gm 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 thegi5 j+i ,kyl.l shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torquei.5yk, j il+lg delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solidvr* n ovb5q;eb/t. rl8v as2m/ cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of masvs8 */brvt. 5vq onmlae;b2r /s 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular - ecrjqzm zp7(0o1 (wcspeed 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 xz3b. qp:9qh.pqp-7.+jowz q ts1l3bv pnq6 qour 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, what would its rotation speed be? Assume that the star is a unifob3zjq q.3h.9 q nq7q+.1vpx boqstlz pp:w -p6rm sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it toux-r d exfh;k8k*n (4n use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrican*k4 ux ;e kf-8hrnxd(l 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 illustrates anzrr-3 byov( w19 8x h+zxd8evj $H_2O$ 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 )o(:kep ip;xda76 mnyhorizontal 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 pii +kbkd; 7ug0q3*qs4p5+pkpjp3 hqaqvot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held hori5pk kga;qu pq+h7q*3j+qb sk430 pdipzontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floo1c vs.x.f8wia r, and we want to exert a horizontal force F at its axle so that it will climb a step againwx f.iv c18.asst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on :tidk,k pe t45a flat road is making a turn with a radius The forces acting on thep ik4te,d: tk5 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 sj bis w)zs0a7 07g*4pe+uetpuling of length 1.5 m and begins whirling the rock in a g 7pist4*)jw ezs+e07up b0aunearly 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 from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinderi l6hraxvi2i (. q;ok *7date6 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 outstretched arms, and with arms held tightly against her body.aia; *qh6dk2xrvit io76 (le.   

  You are designing a clutch assembly which consists of two cylindric6+(z iddmbyanc72y z 9al plates, of massnd2zi6 dmy9 z+ba 7(yc $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 l3yd(;0z/ ej9fmqc,hb xnb- nradius 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 cdz,me0qn/y3 x;h9 blbjn-f( 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, bypl7i6iu7d2f el* :cxut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car re4,hd g.rj3 ekzduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the r3kdhj ,z.ge 4angular 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