A bicycle odometer (which measures distance trd9 bo7we g4eh1aveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch whgw719 dbee4oheels?

Suppose a disk rotates at constant angular velocity. Does a point on the9 pb 84mp.ou0, u:admli1mob q 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 bl u14ouqmdp9p0mmi :o 8.b, aof either component of linear acceleration change?

Could a nonrigid body be described by a single value of nx rp-wdosm(z0 )n c+r f3m-:cthe angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force(p/)zrdkq/:ndl yr) a ? 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 than w5yxo :v b6,v5oofh mr+hen your arms are stretched out in frony 6fvbr5ovx:5mh ,oo+t of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sproc4x7-d- ptpg.o*t invckets 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 i v4pxt7 t -ndg.p*o-cis it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower xoxt0n;hnmsl.u2+kq xx q,93legs with flesh and muscle concentrated high, clohq,x29 3nx0 xmls .+k t;xqnuose 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 vbsv7/43,vnfi5zq9lme rom; ?

If the net force on a system is zero, is the nzd,2uwga hnt 27y /e:cet torque also zero? If the net torque oztd/eua2:,72hwg nc yn a system is zero, is the net force zero?

Two inclines have the same height but make different angles witk,* /ws sgk9dmh the horizontal. The same steel ball is rolled down each inc/,s 9swkdkm g*line. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneouslp u sc+m1he:fjuq w7l 4h)0y)py start rolling (from rest) down an incline. One sphere has twice the rhq41:ue+)fp0 7ch ) plwj symuadius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same m7yor om9s0/aj ass. They start from rest at the top of an incline. Which reaches the bottom 7mo0/9yjr aos 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 momentupgny)7m3./v p dn (6vh4pyrj em and angular momentum are conserved. Yet most moving or rotating objects eventually slow down j6v 3vgehp pd)74yy/ .rnpnm(and stop. Explain.

If there were a great migration of peoplerrrhpu s9):2t pcq b3.uu 6di2 toward the Earth’s equator, how would this.upi :c q2s9)r2u uhr3b prdt6 affect the length of the day?

Can the diver of Fig. 810oomxh/ alhm+0- p ff)h7l hi5 ,caby–29 do a somersault without having any initial rotation when she leo-,0p10ha75l afxi oclm /ybf hmhh)+aves the board?

The moment of inertia of a *mr v/w -e*2xgd 1lwbzrotating solid disk about an axis through its center of mass ismre/v1xl-g wz*2w * db $\frac{1}{2}WR^2$ (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 54v,h(okp: u/eie,alev y(wcrotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop thy4wh, ceiepv ,laok5((u:v e/ e masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass.d(h (-xuurxr5w3vvq/ ax :h6c However, one is hollow and the3x x5/q rvuawh (u cd-vx(6rh: other is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points we..) e hhh e5 *crf.sns4qlfty dmor973st. In what direction is the linear t97) . o5*h.yshe e rnh.dsfm4 lq3crfvelocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on ,4ddjvk(-9a x8 wxrmuthe edge of a large freely rotating turntable. What happens if you walk toward the centerwv 9xx ,dkuamd-j84 (r?

A shortstop may leap into the air to catch a bacmx/ne(mf: ( lf3kohv nu+:d:ll and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quff3:+:h vxd (eo/cn( km:n lumickly you will notice 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, discuss why a helici4 )0mcx3cknk (cir3lopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicir3c(ck k0)nx l4icm 3opter stable.

  Express the following angles in ryp g, /*y4vppcmucrz: wdyh,-fu 7(3q adians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, usin:b7 lknkhon06 +dq x0zg the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earthdk hqn kxn0:b6+oz7l0.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km faj hfv ot(y/1v3ja+7l rom Earth. The beam diverges at an angle yt1h/fj(v3oaaj 7l+v $\theta$ (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.qqw6*xd1r qna mk,(7u When the motor is turned off during operation, the blades slow to rest in 3.0 (1q mdw*kr6q7,nqua xs. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a levelhjf-c wbog70 4-xgb,ibf b 0.dty1s2q floor 3.5 m to another child. If the ball makes 15.0 rev bq7- f,it1 yoc. f04j0d-sbbgwbhg2 xolutions, what is its diameter?    m

  A bicycle with tires 68q 1evu4fqs.c8(gq,y49bg w xz cm in diameter travels 8.0 km. How many revolutions do the wheels make41,8zbgsq 9cqq(yuw. v4e x gf?    $rev$

  (a) A grinding wheel 0.35 m in diameternub8v msb/fl (h5.5cz etyo0 ) rotates at 2500 rpm. Calculate its angular velocitym se(fhno vb8 tb.0z55/ c)uly 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-tk44x5vs/xq7v8d bo )fj nm.s round makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is t4 v b45)m7ofssjd v8q.nxx tk/he linear speed of 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 ofc* *mr-tw1m cayxru5. the Earth (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 point-9j xzj4; zzqby.vqn7w w p:s(
(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 rot(n i1lwbwfu: +jq))state if a particle 7.0 cm from the axis of rotation is to experience an acceleratio1)l(qi+u swj n wt):bfn of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceler 9y+gq/z p/dxkm (6l)wvd d8eyates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determinedelv g+/xd( qywm6d9 )y pz/k8
(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 radiuo-b5*otqn.af+)(okzkokipg ; 23hdu s $R_1$ 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, v gubb. s09 4hu7zi.yx:tq8klastronauts 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 revoluul quts7k 9.4.:zg h8i0ybbxvtion every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,*538az bojlu,( f/ia j4 zwfk+l jb:iv000 rpm in 220 s. Through how many revolutions did it turn in this time? 4j:zf /kzwjbji5ob, i vlalua*f+(83    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 ss.lu 66 r;be x9qb ja9jg *fh*3lnlal). 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 flyine1 -bpscmp8 n-ay yx6.g highspeed jets in a whirling “human centrifuge,” which takes 1.0 mymp-yxc 6. nabe -18spin 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 accelerat6c 8 n; d(*yv6*om bob;lkxaanes uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have trc6(bn *m olk;xo nyv da;a86*baveled in this time?    m

  A cooling fan is turned off when it ;g i j0me+d(dq:sw1nh7q4yivis running at 850rev/min It turns 1500 revolutions before it comes to:e+(v s7y nq;d ighidj4 m0qw1 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 the ck.q xqed9-m3 uar reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 mqq u.93- xmedk.
(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 carxsp22+zaszg j-i*hm/vs* c5 t kz l*9m reduces its speed uniformly from 95km/h tczklp2mm*2xzsi/+h9jza -s *5 *gstvo 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 climbcbm 8s kd)1bh (er8n/eing a hill. The pedals rotath ecr1)m8/sdbne bk8(e 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 plr+ m c4dl:nd*7gn9g door 74 cm wide. What is the magnitude of lg mcg9rd+nd7 n p*4l: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 theskj k/ h0d2bbhd 02cl4 wheel shown in Fig. 8–39. Assume that a friction torque of0c/d0s24jb2bldh k hk 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are ar:d3u*8b wk rfttached to the ends of a massless rod which pivots as show:rfdu* w rbk83n in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylin(wa .e1p6(wq 6 kwmziuder head of an engine require tightening to a torque of 38q( uwmk .(1ez6wp wa6i $m \cdot N$ 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 w.x0 sab*vx1(x n hy0kyhen the axis of rotation is through ity(y nkhx*.xxb0av10ss center.    $kg \cdot m^2$

  Calculate the moment of ine4l:rny5 *5jnu huq16 r;d fqcxrtia of a bicycle wheel 66.7 cm in diameter. The rim and tire have5r5 fjhnylq1xn4 u ;6:dr*quc 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 thin, light rod is u 1w3wk5s8+ m gej5(xoyan.dr rotated in a horizontal cirwa kn8+r jd.m1w oug(55x3e sycle of 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 w byu9n0u2ohw3d;a;opw w;7o xheel rotating at constant angular speed (Fig. 8–42). The fria yu;;w 9wboxp nw;dooh7 23u0ction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array ofnu 4*h+0 jhidz point objects shown in Fig. 8–43+ni04 dhj* zhu about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists49jg jv 2dr.zn 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 v ;;p9 ma/7e/b; s b/odariclyspinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 msba///lv ro p79 iedmyc;;b a;, 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 uniforde( eqg)vd)e0x z3 z7+ mu1ap:bdv8pw m cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calcul8empzvp:zv)dwd7)(x1 d0u e3qe b+agate
(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 rest tq/lgcy1enza3 ;qjw* *cc 3xj9o 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 smalgb .hek xv 6z14c,.+e hsskn-sl 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 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 se g.shch,b k14xzks6e.+ vn-the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 r(hi9/ 6tou:/q it d+,hddybvvpm is shut off and is eventually brought uniformly to rest by a frictional dto/dt96 vdiyh/h (+iv qb,:u 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 3.6-kg ball at 7 jw73 ( - ymi/0uhihqab$m/s^2$ 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 action of the forearm, whichikf:.66 m-egr itcdqjhgx114d 7 rbhl 8p.6cq rotates about the elbow joint under the action of the triceps mr6k4bi:fq7q ed c ptgmhr ..8c1x6i-lg jh 16duscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be cxu6p1)fp 5q+wfy 3 ztdonsidered a long thin rod, as shown in Fig. 8–466)tzfqwpx3 1+y duf5p .
(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 mo92dqp5kpmbp. x4 d+qasses, $m_1$ 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 the8fxunisc ml18r , ;pb0 hammer from rest within four full turns (revolutions) and releases it at a splc8x;p, snubrmf i81 0eed 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 rc /rzb zae r59c4f+*8mzpb/ga moment 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 of 280 5r g9 gkbstx -+:ky1w:nf8hwp96plto $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius g m9f6sj4nsn7 9.0 cm rolls without slipping down a lane ajn7g4s9m s6nft 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic twn2jn8 0r+lkenergy of the Earth with respect to the Sun as the sum of trknlj2nt 80 w+wo terms,
(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 masz2kt p .5vea b7yv0o8cs of 1640 kg and a radius of 7.50 m. How much net work is required to accelp58kbtv ya2z7.o ev 0cerate 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 starts from rest and ro. w7, ,vnckzntlls without slipping down a 30.v tz.,kwnn7,c0 $^{\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 ofe4zbsjlpaw7da/ k aw :4f60(n its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation o4w64 pajz/l bw df7a(s afe0:kf energy.]    $m/s$

  What is the angular momentum of a 0.218 cajlo7zdlc1w/o*)y/ n ;nro0-kg ball rotating on the end of a thin string in a circle of radius 1.10 wc*r1doc yn7/ 8;o n)zoljal/ m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindiq5 4obs.v,h ving wheel ofviosh,5 qv 4.b radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that i hezyhp446z o0-h*a rjs rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotato0h 4r- *epya4z zhj6hion decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of ine;1/ hrkvz2uj vrtia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck positivu1; zkhvj2/r on, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of)/uc )ztx*uqiw * t.le 1.0 rev every 2.0 s to a final rate of tuu q*zie tx)*.wc/l) 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 centerk-1qc 5sgtqj0 at a frequencyc1stgq -50jq k 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 the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momeq yprzps/ k 3:f65om; ape2r*bntum 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 6twz*)tn5s6bv 6j lokof 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 momejgf uu. 1anu,/nt of inertia I is dropped onto an identical disk rotating at angular speef uu/g .u,jan1d $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 ,rl7e+l9s8-ge o(y/jsr3a y tzkjo (l $rev/s$ 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 w1et(y p l dzcx*j9gg22g( pk4merry-go-round platform of radius 3.0 m a24z(d pktcjge(pg l*wy9 gx 21nd moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocib1c2wij*o, iqb 8ohz;ty of 0bio,;ih*wcj1 o2qbz8.8 $rad/s$ 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 abrn //zevw3g 9yw-j2uv/tta2 kout half its mass in the process, and winding up with a radius 1.0% of its existiv/ tgwt- /9rzkn3 2w vu2je/ayng 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 excek9cd 0sy.v w* ae:o,ybss 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 : lj 5ktc1q +j.y6d))lx :pj.vjaojyv$ 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, thbu ;o fez06xb6v)ofn6y/lha9at can rotate freely without frn y6b/;lfah 0z9o fvux 6eo6b)iction. 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 sta 9i( kcxa ogn:jaa0gt(gd(w ( :myl/1xnds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a xg:gcadg /w( mlt x9i:o(y1 a naj(0(kmoment 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 grougue6j s 6s(xqx-ga:nfg -sn8:nd 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 dista8u-e :xx:jgqsf6n-g g ns sa6(nce 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 suvmuk4(32)e l2kn ;cdhdf5 5qryqi i0pch that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) tok4 u2;h q5qi0y3mcpfvi2ln k(dr)e5d its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate o(4a jr:0gkitl f 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 ig/yue ) i, gofpx:x(hkxx * q/bhs;4+zn the shape of a uniform cylinder of radius 0.20 m acquires a rotati(uxx,x)hi:; yoh gxk /*fq4s bz /+geponal rate of 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 0.05d:peqbu )0h3r0 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest rd3:e0bup)hq.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is d nd95jetl v13the 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 mass 8.0 times as great, fv.2yxtkde3m hfhf53 i6lqp1;p y-s 5 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 uniform sphere at ad15;hq 5miesxtf 26 ph3-fp3 klf. yvyll 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 to use rc1wljgp5o07 9 j3gcpenergy stored in a heavy rotatgjcgpo031 5c9 7jl pwring 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 illustrates an ,ft,taogo( g( vjo9n v mhzd:6 .0yh*d$H_2O$ 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 ojpq u+j*p+ 0cqn a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., wefqw(p8dm yb63 08cjms xxe/n) 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 s/6 mq x3w d) nbxyfm0j(e8c8prod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. ags ; vekzmy9 d8ykz85:;yw)o It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which 8m)zs 8:yk yzev;59waokg;ydit rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with spec3hzr 7 qu.jj*ed v=4.2m/s on a flat road is making a turn with a radqc.7*h ujzr 3jius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of lengtmo+e4yac7lzt,z *x -g q nn66fh 1.5 m and begins whirling 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 whey7az g , nc4ztxn66-l+*fqeomre does the torque come from?    $m \cdot N$

  Model a figure skater’s body as /o/htb: q0akiuz yu .1a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outst0tqz :u/hikaouyb .1/retched arms, and with arms held tightly against her body.   

  You are designing a clutckav39vvuy. 7 th assembly which consists of two cylindrical plates, of masu9v vy t3k7va.s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ratw3(of967fypjk)i d adius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if i dkf)7(jotw6p ifya93 t 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 assum 0sv-h+, chpwbjo*9m le $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car r3e)4cvo*lwp ybtp06c+p 3n hueduces its speed uniformly from 90km/h to 60km/h The tires have a nclceb *0t +3y6up p4hp3) vwodiameter 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