A bicycle odometer (which measures distance traveled)prls0aa90 k+5 ch zun3 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 0zukn+pca905a 3hsrlwheels?

Suppose a disk rotates at consta. dgx,g ,fajbc0a8.vndi9hst s//bc5nt angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component o. ba.s/ tdh8,x gb,g9iavc/dfc5nj 0sf linear acceleration change?

Could a nonrigid body be described by a single value of the angular ; 2nqgddvl*zpd9)ja 9velocity $\omega$ Explain.

Can a small force ever exert a grq8ds crjv3c2 .9sg3 gyeater torque than a larger force? Explain.

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

Why is it more difficult to do f6w ,i p4b):ta9iu1te 3xlooq a sit-up with your hands behind your head than when your arms are stretched outo )f1l6q4a,out: 9webi ip 3xt in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven jm6khyp /l)l 3z0w erg(i(2 aesprockets 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 rer6m/kalilh y p(2(zw0e j)e3 gar sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs wn2u/q a ekgu*r0: uc1atlvt8; ith flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamicsau 1k82q uc ul*/vtgte;:r an0, explain why this distribution of mass is advantageous.

Why do tightrope walkho 5dj pfj;8+cers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zer3 e44sh lokah h+aym:; 4 hcb0;g*vffuo, is the net torque also zero? If the net torque on a ouaa4;f v+m*4y0 lb: ch; 4hk f3gehhssystem is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontal.w9 iely.jwn.. The same steel ball is rolled down e l .9iewwn.yj.ach incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling,hh 9izrwz ;:1 zrv i;pvd9un5 (from rest) down an incline. One sphere has twice the radius and twice the massh;1zd5u9;p 9 rhwv i,zvr:nz i 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 nh8zl mdrq)o33 j +)qxand 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? Whichxrlq )jm)3o8n3d hqz+ has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentu ,gm18e ls: ggvt,s.ojm are conserved. Yet most moving or rotating objects eveme.lto, sg 8, sgvj1:gntually slow down and stop. Explain.

If there were a great migration of people toward the 8mns p c.(f xq q4ah6pv+j6gk+Earth’s equator, how would this affect the leng p4s jhcgaf+x(6qvkq 6n m+.p8th of the day?

Can the diver of Fig. 8–29 do a somersault without hk j0hq fj6iz4 4obo08r;tnkn0aving any initial rotation when hfb8 q6oj;n000n ot4 r4 kijzkshe leaves the board?

The moment of inertia of a rotating 6s(m iha7j feoke::dt9i +c+ hsolid disk about an axis through its center of hf7+sm:c6 tdij: 9h e k+a(ieomass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stoo/: bmw 5dnpz*:w e) ;l:ls*kgi;ciwfwl holding a 2-kg mass in each outstretched hand); :w;/wlwg:b:izp 5fwdlin* me*ck s. 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. However, one is holwbsv :zda2 4*nlow and the other is solid. Des4s*:bandz 2vwcribe an experiment to determine which is which.

The angular velocity of a wh y86du;rhg03car nhl:ude,u:q +x 7lieel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the 0xdu ch r8l;n :h6 ,aueig7:ludr+q3ytop of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing o f 2jvt:wvbfn m p)8y(gd2b0q4n the edge of a large freely rotating turntable. What happens if you walk tow v(j248tdm yg)bvwf02qnfp b: ard the center?

A shortstop may leap into the air to catch a ball and throw it quickly3qw7v;i8 o gbg. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fb7owg g iq83;vig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss whylot42 k;yx+ moi6g: xx a helicopter must have more than one rotor (or propeller). Discuiy kgl:x;+2 4omxx o6tss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anglegzbke5 m 5f1; sgm9v4ks in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calcula:w1b /s6vpvv tte, using the information inside the Front Cover, the anguwv/svpb6v1:t lar 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. Th.gol) jvv)2 e6cml.dpe beam diverges at anv ld)2.cgp.olm6 vj)e angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motorhruej,7h18 w nok4p+6 8cnwpu is turned off during operation, the 6 8hr7+o4jwn,1np hp ku8ue cwblades slow to rest 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 q*e*a tw ;d.5kza;ahi floor 3.5 m to another child. If the ball makes 15.0 revolutaa ;*wzi5;eh* qat kd.ions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do t6-(fep0zqr lphe wheels mezfl60 ( -pprqake?    $rev$

  (a) A grinding wheel 0.35 m in diamexu74 mgf ,;b pega))c2*xv yzster rotates at 2500 rpm. Calculate its angular velocixb v)gc;u4,7f zxygs2)a pm *ety in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complelma;g 1hmzlkg3, n;8 psa4gz;te revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m48nmkm laz ; pg;;sa3z,ghlg1 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 Eart/2w;x0 k6rms5f yz xknfr3io/h (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sp5 +y -0lcnjbq;j gv8hieed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centqi-5+ogam,1svg tzy 7rifuge rotate if a particle 7.0 cm from the axis of rotation is to experienv o zat m1yqgi+sg7,-5ce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm/prv*y 3 c ypb0l.u)mw to 280 rpm in 4.0 s. Dete.b30)mpvpy r c*l /wuyrmine
(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 o3dwnc d:v3v,$R_1$ 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, astronamhp4 dnybz0 v; 1*n2dtuts 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 1nphn1dyvbzt 0;*m 42d .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 i9r3ces k2c :vbn 220 s. Through how many revoluti ksvc9b:r3e2 cons did it turn in this time?    $rev$

  An automobile engine slowm9 npb95vvu(z s down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flym i4 oup2 9e-bm4ilda1ing highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolu1ub4 mpdaoe 2i-4ilm9tions 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 rpm to 360 r6i ( ,kdr hv*8xqptb-upm in 6.5 s. How*x-u,pq 6 vbt( d8krih far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revot pasny c)*6 //czfd6olutions b6/cdocps f 6*tzy)na/efore 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 as th 60cfa7lw dwgy,k- o7re car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter o76 kly7a rwgdc- wof,0f 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 69w xe4ogkgq,lh4j 7u nfmg9t8 fa(6i 85 revolutions as the car reduces its speed uniformly from 95km/hif u 848k9mgen(gqf9g 674ltxw hj, ao to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bibj mhtj 6liod/):*x 7+vn3uy7za2ndcj1dy1 nke puts all her weight on each pedal when climbing a hill. Thd7t3a yh ond/ :)1+m*6 7lndyjbji jvux21ncze pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What9w k(x awcvgyd85if(8k6g ig3 is the magnitude of the torque if the force is exertediw vcyxf dk8ag9wik6(3(gg 58
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in9 jzt)x2uv(yu2* ccsd Fig. 8–39. Assume that a friction torque of 0.4*2)x vu zdy2t(j9 cucs $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the end n1) zpabu hsxk2(y-0cs of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the hoxh ky uzas0cpb n)2-(1rizontal 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 to a torque 49bc otln4 8ulf 5tdr2of 38 o4f5u c49r28tltbdnl $m \cdot N$ 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 mv6q/vg(/8 yby6wc vwd when the axis of rotation is through itswvwygy6qc86( b/vv/d center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wn 48f1axoi6nf )+ njx7t*hhu oheel 66.7 cm in diameter. The rim and tire have a combined1hi+a86 u *)7ofjt4 fnonxxn h 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 rotated in a hori-/ewf x7+xhk n)81c hy+xwfmqzontal circle of-1y+khxn7qx/+ h8)mfx ewcf w 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’sy/axq *s+m4pj wheel rotating at constant angular speed (Fig. 8–42). The friction force between her h4axs/yj* qp+ mands 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 objects shown ichmn233b clsd0gxpp6; k:7 co+iy z+kn Fig. 8–43 about3+:p7;cgy3lhnidcom62x kks 0zb c +p
(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 oxa+oh 2m7 oo;x +wz6 yawcyy;(eygen 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 cylrj.uzy iv2 0:*acua3 qdc4 wh4indrical satellite spinning 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 m, what is the required steady force of each rocket if the satellite is .2h w0:cd 4ayc43av ri juzq*uto reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a ra;99j+g c* z gn z1;bukge:(m 0xbzluqxdius of 8.50 cm and a mass of 0.580 kg. Calculaubexx9* nzju bk; ; 1q9+ggzg0mzc(:lte
(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 to 3 p.cr6:apt2:o+dapq nw oq c;7 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merrym 6t*kn3n ci5/he/lwh-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 hnl/c*6 /ikwmn35 the radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off eaf23 f-p6hy) ujaaiol6 lznz)n(u( 3 and is eventually brought uniformly to rest by a frictional torqujnzlpl haineuy 2-) fa(6ao)3zu3 6f(e 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 ejy4 mmu+ )b/zwy: x4r7 $m/s^2$ 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 bad hh4 c,qpwq6)6da2hg 5 w-zfall is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest tohcpq)za f qw2-g4d w56 ,hhad6 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 inbii(o:t9, gld31qwdwrrf/ .v Fig. 8–46.i1b: 9/tw,g wlr d f(q.ivod3r
(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 mas0g,7k hzrem-jses, $m_1$ 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 wit koepi8 r hh5h934hf;ohin four full turns (revolutions) and releases it at9o 3fe hi;rph5hok48h 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 iwi lsyz dw 33l/ljj9tqf(d)l,u ,f ;,lnertia 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 ot e025v24d bag+ pewfnf 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slip+6diveg5su :/zhjc (v4 io5vsping down a lane se(i:6+dc5s4 o 5vjhivzg u/v at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic erl z7fa*rsr.+s ;/ht rnergy of the Earth with respect to the Sun as the sum of two terms,7+l. rzh r tar;fsrs/*
(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 masg5/:fbv + *tps(p wlvbs of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assu:p*/vf bw s 5lb(tpgv+me it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and roll81c s m6av5qras without slipping down ac1r8am5q sav6 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 st hn q.+ du x7+7yemnfyx1*wb(barts to fall and its lower end does +bnf7b * 1d7wyxhuqn+x.m(ey 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 rotating onn i24ze:aicb 24nnkd7 so/)t z the end of a thin string in a circle of radiusint o sni b42ckzd)4n2e:7z a/ 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrixm*)f(jmze ts4i j ,gicf48 , +r)anqycal grinding wheel of4gtf+z,fsi(ri ejm cj q 8)* xya,n4m) 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 platfor k4 r6w/,1sri3jssbcr m that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decr3r/6rsw1rs,cks4 jibeases 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 ofb cbst2(aoosrc:9sq-o) . ht/ inertia by a factor of about 3.5 when changing from the straight position to the tuck positions-qo t9 a:broc).ss(bc2o/th. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate3m( + 8dcvkqwl+ qmcr6 from an initial rate of 1.0 rev every 2.0 s to a final rat+qcl8dmmw6 v+ q3(r cke 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 vertica3m*6s,if4epi k nmz8k l 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 claeis8mk i6zkp4*, f3m ny, 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 a figure skater spinning l ;q.htlhn pp+qpd:(. 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 Earvd36v, qqf0bda-*jjhth
(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 mome7z2o96e telz urbm, 0/eqkub9 nt of inertia I is dropped onto an identical disk rotating at angular sp7qmlb k te o96buzu,z20e e/9reed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns +b1 g erk4(xs0q r. rjpoi,l 7f 3pi8zbar-g4bat 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round platno dt( 6.)p hdb2a(hzoform a(zd (h2dht.n o)op6bof radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an a v)vx fc1udu95ngular velocity of 0.5u u91xfcvv d)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 (8,uxsza ck7itxj z;l8 e f9742zsfzq collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular q ,xucfksei(z 9zf274t8;8slx j 7azzmomentum, 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 excess ofxbz8kv 2+pir- 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 u -sbh8.v q5c c )+fa0ee*capo$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotated:*y7 yvccns / freely without friction. The moment of inertia of the person plus the platform isy7/vy : dcscn* $I_P$ 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 dim6j1 +yhj nv ek1th8p/ameter merry-go-round turntable that is mojpjen+m/1k1 h h6tv8 yunted on frictionless 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 thb)wj ctpvgqh b8j(j4s.*+f + ge end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does c)bg+gq( fb j.h4jpv 8st*+w jthe spool’s center of mass move?

  The Moon orbits the Earth such that the 0tob8e hn e66gsame side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the te8o6gn eh60b Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest wmbdwni1cll 2 a2r490 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 cyliixh3anc9kz/ 5nder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angu3zhka 9x/5cnilar acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two sola3 c; epyoe;,u d4+hhxid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to c +cu yee,p43h;d;ahx oalculate 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 ij(q*gc8 z *y3rjsuy,4 mm6* bx2(q dq rugqf6hs the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but wiyu ed 671mi0cvth mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 1 7icemy1vd0 6u2 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, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is forkhvtn8-x;ehhk)8)p d 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 o e8;)x d8-kn hvhhtkp)f 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 t1 e f5i9,vkehyy6i;;g9 d bxg$H_2O$ 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 horbrl-t 996,n1-1quitn d n n2uea:tbrhys0,uhizontal 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 frik de9qang m h0sye-qmw (txc56 r/+5d(ction) about a hr(q5q(m06cte mdw/y - exn+5sgk9a dhinge 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 rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floo aw4k p r6zxu(3h+37axaxlge )r, and we want g ax6x) zekwa+r3p(3u4lxa7h to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road fu2c7u4b9xy1 gl. ynd is making a turn with a radius .ux y yuc2b971ndfl 4g 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.q 6gx8l yzbf(/50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating 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 /(yz g x6fl8bqtorque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder andl )2vxf zwra*- her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angulaf x)z*v-wl2rar speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindri83pfl;x bsm/cezf w5izf90y+0zy bx5cal plates, of mass 3f+0x;iec 0m lfyzx/pw5s zz9fbb5 y8$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 r2ba:,l8-ierqc3wo yzadius 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 i-eo w2q,c rblyz:38adrop 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, butd v /lc9q;:1vn(okhts do not assume $r\ll R$ h =    (R-r)

  The tires of a car makew/ewzg+ cn ox10lp; 5e 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a di ozp0;x+ een1/l5gw wcameter 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