A bicycle odometer (which m.l536fm0anzh z jjs jfl5(:eseasures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if ynsj3 6l:smz.a0(5ffz 5jhejl ou use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim hm2o3ves-uh 3qave radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? 2m oeshuv q33-For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be des)9hq9ttj :nxmv c57t ln2 o9c (ts)opbcribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than 1 ubn4m40n dh+bmc. fua larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behinf t;n8af1 ,kmed your head than when me,ka n;f1 8ftyour arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedal 1kseq)6z. 7lqm nk d/e6f cnr;er2qg8cranks. 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 kd 7n ;8re .1kf6mqz/ c)lgqq26n ersea large front sprocket? Why?

Mammals that depend on being able to run fast ha7x).,5onn tbz,8 :4loljbbx7s kotaj ve slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageo,8 s4jlxk b. ,757tzo:tlbo)n nbxaoj us.

Why do tightrope walkers (Fig. 8–35) carry a long lmixh jf0h*7hw3;(w d, narrow beam?

If the net force on a system is zero, is the net torque also z/a ud;pv -kwvzf9t88 sero? If the net torque on a sysuas-fz/8;8vpd t9wkv tem is zero, is the net force zero?

Two inclines have the sam*g/)xo ttsgrda0 s*8pe height but make different angles with the horizontal. The same og/* s0t gr*d8ax s)ptsteel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from re.*cu jb)eby t2st) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has th.e2tjbu)c *yb e greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have t cuu / tmvbo-q:-h+,vmhe same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which hv/ubq:vm+- o cm -h,tuas the greater rotational KE?

We claim that momentum and angular mobb4:tst 4 s;pg+asa;wa 1 r0domentum are conserved. Yet most moving or rotating objects eventually slow dssa;4:g sa+;0 1a 4tbdrw optbown and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how woulp;ul z.b*e i9br jl2n4d this affect the length of t2p*b. lr zejli ;b9n4uhe day?

Can the diver of Fig. 8–29 do a somersault without having anhomt37r2kb( p x;ug (ly initial rotation when she leaves r (7lbk 3;om2txhp(u gthe board?

The moment of inertia of a rotatingykmcr8 j4dc /u4-7qs i solid disk about an axis through its center of mass -i8cs44 jc ykd/ruq7mis $\frac{1}{2}WR^2$ (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 eh )8/yzmo9+rq7kbvy s5jq4x stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the massej mby+oe5 hqz/s49r8q xvk)7ys, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same*m6b 0q afx*cu42uuz8x (uo cn mass. However, one is hollow and the other is solid. Describe an experiment to determine which is whio2 q6uxx8nubu mcz*f u4c*( 0ach.

The angular velocity of a wheel rotating on a horizontal axle points wew1boo ms4d/ jrg:qyjvpwbs :7u;/+3e st. In what direction is the lbs +/qbd/ goj: 1swp3ryo:w7m eju4v;inear velocity 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 the edge of a large freely rotating turod qm d t9k.euqpm29g h3/tz+:ntable. What happens ife9t/o9 pg q :zh.k+dm2 3tmuqd you walk toward the center?

A shortstop may leap into the air to catch qfj2ggu2 qx 6+a ball and throw it quickly. As he throws the ball, the upper part of his body r2j 2qgg6uxqf +otates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law gk1xmj mw8( x 9rqf/)iof conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the )g fkir(q9/8x xwj1mmhelicopter stable.

  Express the following angles in radiansqiucni1:p); o: (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, usingb5ph/w/ yvb j: the informab:/ybv/p w 5hjtion inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. Thexqnrsk w(;c/qqy*15 xvz s0+w beam diverges at an angle kxw*/5r0nqcwz;+q1 qvys (sx$\theta$ (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 motow5obcnb0*ta b(:*rgqdf) qnky18j f4r is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bl*j 5wd a bon8qb c)0:qfg*r(b1nt4ykfades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the balq poo5je hr-/m2v)sc;l makes 15.0 revolutions, what is its diah2pj-v5e)csoo ; r m/qmeter?    m

  A bicycle with tires 68 cm in di+q:v9/ ehn;k* fo ftkeameter travels 8.0 km. How many revolutions do the whq9/eeovh : n;ffkkt*+ eels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotatesqx;u une3/ an1 at 2500 rpm. Calculate its angular velocity inex1/; nqa3uun $rad/s$ $\omega$ =    $rad/sec$
(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 makf;k5pak b1j5o es one complete revolution in 4.0 s (Fig. 8–38). (a) What is the ;5jak1 b5 fpoklinear 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 of th7y hwa lh5q:0e 95vamze 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 po iug8.sh+,b cyint
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 c/2n4cpo9hln6 q c :mhwm from the axis of rotation ishc4cwh9m p/n o6 :l2qn to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly aoue4ingi73e( bout its center from 130 rpm to 280n 3o4ie(ugie7 rpm in 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 radius w-z(z a pn4qkc+4zvilq3uf/) $R_1$ 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 put tt6rqdqhwydbcg,)b 01:nk4 /x hemselves into a slow rc,wbx16knh/d gtr :0bq )d y4qotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 2w + i3lng7boh420 s. Through how many revolutions did it turn in this tim7o+ihgn 3lb4we?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcnwe* kkk 6)9 a7plosd5ulate
(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 flyin,z++oglpd8bm wefa9, g highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revmwo9g8,apef+, + ldbz olutions 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 240 r qfhe ,pr:to 6n9r-zbbl;;g 3rpm to 360 rpm in 6.5 s. How far will a ;:q3lnrgope9z b6,rrf-bt; h point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is 7n q.sc:6nxoxrunning at 850rev/min It turns 1500 revolutions before it comes to a ns 7nx :c6xqo.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 car reduces yu c(q7qrd/arbuo. .(its speed uniformly from 95km/h to 45km/h The tires have a diamc.u ./ r qayduq(r(bo7eter 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 revolut( f9hj lfn;b*lions as the car reduces its speed uniformly from 95km/h to 45km/h The tirh*9n(fljb;f l es 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 hzvm13isdt 4ow)faf61er weight on each pedal when climbing a hill. The 1f mowd3tzv 6s)1 fia4pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of +wbwpqw )vcye8 h nv v8:58gu)a door 74 cm wide. What is the magnitude of the torque ihep+bwg))8:8vuww 8y5 vcnqvf 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 tor2 n: zibi87aoyque about the axle of the wheel shown in Fig. 8–39. Assume that a frictio8 zo:bia2y7in n 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 massless rod w- giny k-tdd8-hich pivots as sho ny--i 8-tdkgdwn 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 cylinder head of an engine require tightening tocpt.wyqp (.m4ejx n;7z5 f/fk a torque of 38 jmt(.p.nxq/5ky;f 7p4 zewfc $m \cdot N$ 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 q.4qf(ny -cj eho;krc(nu *9jinertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its center.ne* j9q.cjr;ky o(n-c qf uh(4    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in9: ji wofmf +6,k,sz;t 6ywqyv diameter. The rim and tire have a combined mass of 1.25m+6 yo wj9t,vswi;fz 6,yqf:k 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 rodf(zv + cc8tqr+sv48ivhw +1r5kz2 awo is rotated in a horizontal circle of radius 1.2 rcqwr k8izv4w1v2(f+ av5z+ co+st8h 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 constcr2;hk-fz.y1-l jktrant angular speed (Fig. 8–42). The ft-yz;-lrhf jr2 k.ck 1riction 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 of point objep/* fzpyhp cbk *fl,0o( 5cwa3cts shown in Fig. 8–43 a5o*w( h,zcfplpc 30kf/y *abpbout
(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 whek b a7scm++0pqpgnx6) -p,weose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the co0:cb)kty1sc9*a4z c 2 txcqyerrect 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 m, what is the required steady force of each rocket if the satellite iszt42)* cx9s:kecy byac qt1c0 to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder 09(55ce 4 esu41fksen oqdje hwith a radius of 8.50 cm and a mass of 0.580 kg. Calculasc uf05ns ke44d 5ee9(jq h1eote
(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, accenmhc1n,7 x.uz3nd d0m lerating 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 tangential6 fh4-l geuzh-6y rk5zly 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 mass of 760 kg, and two children (each with a mass of 25 kg) sit opposi-zzr-5 lg6eyk ufhh64te 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 rotaedp;vb6zbk)ph (..th di2 ;guting at 10,300 rpm is shut off and is eventually brought uniforml kbi );dehp; .phd2g u(6vz.tby 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 accelerat5 ihyj1.in, ajes 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 action of the forearm, wh l5da/; dq x:ycn.mp(wich rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated un;y px5 wc(/dda.mqn :liformly 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.9/ostp3,rdy 5nop8 )rg7mtl u 8–46. ogty,8p3prnr5/um 9tosd7l)
(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 co1o m+ovxh)ochx p:h1f(b1h0 lnsists 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 0esme,25srq7q 0tneo om8y fu 4,bjh;hammer from rest within four full turns (revolutions) and releases it at a speed of m7,rqo;y2n4ojtme bss8e0u f5, 0qeh28 $m/s$ 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 mociufvdfn pwb2-5 vb)3h-dg; h-1 jjc- ment 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 tor f: nx2x*kwpro8 iteb;):-kzw que of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radid;j+oz5jurg .z*k0 wpus 9.0 cm rolls without slipping down a lane at 3.3*5r. dzzk ;g0+ujpo wj $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sult: + g*3( ecmnwbic3fly(n; vn as the sum of two terms;emgft3 (:b ni(v cnll+cyw 3*,
(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 rsp6 ,iveg y6qa5 lk28nadius of 7.50 m. How much net work is required to accelerate it from rest to a rov6852a ys6ni glekqp, tation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm anr4ii-s8e sx k:d mass 1.80 kg starts from rest and rolls without slippinerk-: issxi48g 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 star5.u6 omvzk8r s; e,g/selxqq8ts to fall and its lower end does not slip. What will be the speed of the upper end of the pole jus, e6r. zse/8goxkm8vs q;5lu qt before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball r3j cbodwk774ca-qe v( + 9:r uo5vjoctotating on the end of a thin string in a circle of radius 1.10 m at an angular speed o5 u oovrbtj:k7oae79d-4w v+j3cq( ccf 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindi5f,vw,cuj n +hng wheel of radius 18 cm whe n+wvc,j h5uf,n 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 is rotating a8lfscyj;):al hwt3*a 6juw3 xo de*,it a rate of 1.3rev/s If he raises his arms to a horizo8aaw6lj,s* h x3)e co3t:dj fyl uiw;*ntal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the e2w* wgfzd/g/one shown in 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 rotations in 1.5 s when in the tf/ 2/dgz*ewgw uck 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 itsmng3kqyb ;kth:(n/xnact +5 2bs0 sd69(ra nitial rate of 1.0 rev every 2.0(;byts:53dsan6kqr/ t+2hg0 tbnnck (x ms9 a s to 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 brk: cp5bo9) qat a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diametekqb9pb: 5)cror 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 momentum of ahfl.8rr9 (pd-1* popwm4n lx j 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 ofzso dv m8r - ,cp9:rl+gabqdf3)rt3s( the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of iner yhycz.5)5lfx/x rhvt: ktl8,tia I is dropped onto an identical disk rotating at angulhz.y t:tfr /h55,llv8 ky) xcxar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2ut -gifc1 c(7x.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 oj2s-s)9 ( u haunhali/f a rotating merry-go-round platform of radisu9aahj -)h ls2/(i nuus 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 wmb3 u1ys j)cw)ith an angular velocity of 0. jb1)ym3ws)c u8 $rad/s$ 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 aykmnkybxv;m 5 a:a,k-0q 5eo; 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 carries away no angular momentum, what would the Sun’s new rotation rate be5k y mvmabk;-q 5nyxo ;:,kea0?(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 pmn ( g ms/y5n 6r6oadmv:bl:0winds 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 n rpxiby. 6(0sdfx :0v$ 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*5kg7opgz etz8c r3hbk8ac9*, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platformkzcbhp 8g3ke9oz*a7g*rt58 c is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter bc5*g9b b0qy b xz3k/ e 7,jot/eb/udjmerry-go-round turntable that is mounted on fricbu3 z7/bk d /,jb ety/ cejxb0*95bgoqtionless 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 oqr3n rj va+cp(p )r6uouf8pf 3m0-t-vf the rope lying on the top edge of the spool. A person grabs the end of the rope anpa-p c+m3(u8rf3 pjvoq0r -fruv )t6nd walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Deteroclf.y x7hho. t5iy6,mine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular mch fl.iyh5o7 6yx ,t.oomentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerate1 r, dzxbee(6zi2tg q7s from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m oy/gwq ) u7iiycu, *h+yh9cejqo6.8i acquires a rotational rate of fr)i78guec q+ wh6h u,* i/oociyjqy9.yom 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 med7 bam 5n8zvo*c*/czy-a ;f) x(m( mcj:qbodisks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservacjfocyvnm )m:b o*qzmb; 8/7-xe*ad((az m5 ction 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 thc fkjiirixkr6.5r hzl 3p/ 9-2e 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,yi3w 3pq lw df:0cj-k: 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 uniform sphere at all times, jp3 k0:yi- :dwqc3lfwand that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low ak-i51vlq) aq62cooj -pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be -q61c)oalki a25 vjqo 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 an4tlva 2 iw928mqsl to*.ti)ab $H_2O$ 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 rol,lii) f6mn49fk* cbi kling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore 2-z i72 :lmgxd9wq8dfhk:an x 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 releasegdx7w dmqa 9hzx:-k 2n8il: 2f, 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 verfr 8;hrt 0.skliuhjj lal,+86tically on the floor, and we want to exert a horizontal force F at its axle so that it wilu. a6lrsht;l8rihj l, +8kf0 jl climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2 edrm14 e:q oi:jiqh 1z3bo.9dm/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle a qi:ebe3jomdq 9 .i1d hz1o4r:re 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 slinm l o6jab62*oqg of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of a* q6booj2lm6 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 he+ qgx4xhs(p0w7 l3 glor 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 hl4x x(lop+qh7 3gws0g er body.   

  You are designing a clutch assembly w-36y aogddxm .hich consists of two cylindrical plates, of mass -ag6d d.xmyo3$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rvyxv;qhhjzb-d xh 8z+k0/,7j; t wt+ wough track of Fig. 8–58. What is the minimum value of the vertical heig+-hzt7tk bh0y+jzd ;w ,;8wxvqx jh/ vht 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, b-m5(gv1p6 adx8phm-3enlhh hut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions adhm:vt: .t5 ifs the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (aitfvdm5t.:: h ) 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