A bicycle odometer (which measures distance trcxl6 y,5wxin zcs2u jc m(,9i5aveled) is attached near the wheel hub and is dely5ns m9,(,i icw xxcuz5 26jcsigned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular vxjl z8kz4-akdrni/lfr( b r:(js: k4* elocity. Does a point on the rim have radial and/or tangentia: ni(k*ra 4fj rkj-/:bkr4 (zlzdlxs8l acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be desos+l 7,dq ht2be/4oti cribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exejejw2z /m)g 2srt a greater 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 a sit-up with your hands behind your head tha43ud+gqm- uxg+.o ep cn when your arms are stretched out in front of you? A diagram may helpc-x3uq.+pod +4gmeu g you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel a8a+lx6 px(kr;;;2io, hiztv1y u ml imnd three at the pedal cranks. In which gear is i ,p(u;mllr1aimo;+xy 6ih8 tzk2x v;it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower 0mtmznkpb3;g q *4qc:legs with flesh and muscle concentrated high, close to the boqc;: b*tpmmnq 4 gzk03dy (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig)4lwh8 zpsruxqi a7 ,+. 8–35) carry a long, narrow beam?

If the net force on a systel(yvmce1q f:+w+gf9 hm is zero, is the net torque also zero? If the net torque on a system is zero, is the gyvfqhl w+e:91f+(m cnet force zero?

Two inclines have the same heigdka v,cku99 gn:g)f4u ht but make different angles with the horizontal. The same steel ball is rolled down each incline. On which acg,vdg)9n uuk49kf :incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simusw p1+z9z06n pchk5 nrltaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bot p h5 cz+zkrn6p10n9swtom 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 mzxu81l2*mfkq2u .y amass. 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 mm 8 x2u.l1fyqzkua*2 energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. 7 /ksnx sru/rdhzi +/2Yet most moving or rotating objects eventuad7 x kzir2rn/s su+//hlly slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, howo-)tc /a m9hhhzb8:j rf1iyv 1 would tzmihth oj-/a8v rbch y1:91 f)his affect the length of the day?

Can the diver of Fig. 8–29 do a some)-o8::up5 f; bqxvr8bi dgbdqe ,k *nwrsault without having any initial rotation when she leaves the board? q qr8dne -o,i5g;bvx u) :8*fd:wbkb p

The moment of inertia of a rotating solid disk about an axis through itz:;y;:+zo kjzmh rl4ts center of mas; lz;: :+ ztkmyzjo4hrs 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 rotati oi5 x9*ojx-obx:xag+ 9xnco,ng stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the sa-axoc+*nb xijx9:x ox, g59oome? Explain.

Two spheres look identical and have the same maskse :6 e3+4; jfuobyjgs. However, one is hollow and the oeoe; sjb4fjgu3 6: y+kther is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points wye.d1o njho,63cavm6eo: e5 aest. 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 t3ooo65c dene6ea v1:.yhmj,a his point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standi7leky ,;fl1 (r4i evokng on the edge of a large freely rotating turntable. What happens if you walk tow1y felk;4v oker( ,7liard the center?

A shortstop may leap in2dmt9h e irngg.7 kj+-to the air to catch a ball and throw it quickly. As he thrdg-gkenj 72h.i9mtr+ows 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 (Fig. 8–36). Explain.

On the basis of the law of4:4 ujtce:h m*w ;q)dvxfato2 conservation of angular momentum, discuss why a helicopter must have more than one rotor (or v ;*4h t2: )qm:cjexdfowua4t propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in )s v5w bj/dxnpqd-lr/2h (4 xsradians: (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, using ,sc 9dg tu,/wf3bj9g fthe information inside tg,9,utw3f/ c jgfs 9bdhe 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. The beam diverge fm-dx qel,:/cs at-fexm:,/ ldqc an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate or(vmrna7pw9 x7k4 tj-f 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 sw4mr9kr(ajn- p77xtv . What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chi z(d*wwopw3,w i vm2tep.hgf 29m 4j8zld. If the ball makes 15.0 r.f ipm48 v9jw22z*m w o( zd3wh,egwptevolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. H; u6((hezfubw ow many revolutions do the wheels mauz6;w( uh(efbke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates 680rgk sq*vaf0/db i.jl8g vjat 2500 rpm. Calculate its angular velo j0b0 qil8rk6dfv *asjgv.8/gcity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–38)sc.;nmqh5 0dt . (a) What is the l .5tn dhmq;0scinear 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 the Earth (a) in j dhdhmxdci -(3+5tk 12x3aqq its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pointv)d5;e gwi0lde i*3dy1e 5:vj(gemba
(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 iftaj-1+cp ,hlo a particle 7.0 cm from the axis of rotation is to experience an acceleration of 10-c1lj+phto ,a 0,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cent.sdmh +fwxsrp) 6:b- jer from 130 rpm to 280 rpm in 4.pbj: fwx)h- smd sr6+.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 radiuumr/0azo q82h 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, astronauts aboard the Apollo spacecraft put themsel,z q2 7 u0ffn/jn,zikwves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of j,u2iqnk/, fzz0wf 7n 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 uniforml+cnz5kp m 1xu1y from rest to 15,000 rpm in 220 s. Through how many revolutions did 1z 5+unk1xcpmit turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 5 a2b+1z, 5 j*y1 1a 8 gxep)hnysdmq4zhnatpws. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying 1 v)u: u/vse(4pnur5vuc- kw uhighspeed jets in a whirling “human centrifuge,” whu 5:uu 4-k/(ve1cvspnr )wuuv ich takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter a 5)wkgz2p*cep6p 5yv rccelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travelzc5wpr6*ep )kgyvp5 2 ed in this time?    m

  A cooling fan is turned off when it is running at 850rev/min rnmmrwf0gkv*/+ p *9m It turns 1500 revolrm vf*r+p9w nmkg */0mutions before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car m+2z)do5 swklpake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/sk2z pdol+ 5)wh 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

  The tires of a car m j )o:apru8 *2lwunvoo/sxm;,0jx :xj ake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The xjw s:xp08/,ao 2 l) nxo; o*ruu:jvjmtires 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 bikeb 6 9nsgcr/q8x puts all her weight on each pedal when climbing a hrcb n8gx/q6s9 ill. The 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. What is the mag- 5v itqldswz)- 9g9ganitude of the wg)t5 g99isz vql- ad-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 t d; odn8 *p 6b4 uwmzhl48p))pqnxu+lkhe wheel shown in Fig. 8–39. Assume that a fri x; uulzql*opd4np +886 4k )bnhw)mpdction 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 th(6s ;3 +jmf5rw- nh;eip dnhhbe ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the n hmfrp+-h( h;is 3;ew5bd6jnnet torque on this system.

  The bolts on the cylinder head of an engine requirm x8c.)vacl9d59gi ube tightening to a torque of 3895 b).gvum8alcxi9c d $m \cdot N$ 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 nwg ee*gpm,9610.8-kg sphere of radius 0.648 m when the axis of rotation is through g 6pm,ewgn9e* its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in:dxheq /iz/ tdkh/9 d; diameter. The rim and tire have a combined mass of 1.25 kg. The masihq/d9/ d xd;ztk: eh/s 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 inwc54hs;v +pzq,pd-ve a horizontal circle ode,ws p5vz4+v-hp ;cqf radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at)0oiuxw: x uq2 s+ d:z;f3ba 4c)d6qntafnge; constant angular speed (Fig. 8–42). The frictioxnf:t)ns+da 6uqe2a i;f4x w0 bz3; q)cuo:d gn 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 inertiipr wa k8+g7u-a of the array of point objects shown in Fig. 8–43 about ri - g8kp7wa+u
(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 vmj(/eymmt1y nrjhif ,l03/f- i.lwa1 kjk50 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 cylinp /3 xqn2qvgv4drical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–443nqv42xq gp/v . If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder wt4qu3t b; oj;ov 5/to:s1u iogith a radius of 8.50 cm and a mass of 0.5t5v;ojooos3/; uu1bi :t g4qt80 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from res y+v,c9a7b qv u.i(hflt to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hak i2m wm+zn.+snd-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 the acceleration,nksi2wmz .+m+ neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 1yu ;1b0w* z(w .wxflxj0,300 rpm is shut off and is eventually brought uniformly to rest by a f0bjx lw f*1(wyu;xw.zrictional 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 smh7 zu(dehi;*9* kvo 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, which7)q-a*kj ub/ huj /b2i nbct:t rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45.:c)/kbnua h/ij2b *t7tqbj-u 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 considered a longo nfo,i.r. l*qz*1 ush thin rod, as shown in Fig. 8–46. ,o lu*nhisr1 q .*o.zf
(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 hxd0 lu6+p lej u0pk llp8c.; h)o.)tqof two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from res aom -u02biqco9nym 7+t within four full turns (revolutions) and releases it at a speed of 28 oqancbu m29mi7 y-0o+$m/s$ 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 iner k6jed 1tipu,8tia 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 dek(vxt-q(v ,oe velops a torque 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 an aq n7u61 *maf3:zldyzd radius 9.0 cm rolls without slipping down a lane at 3.3 *da yq61lfnz : uazm73$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic enjz io :v16n)k qkm; hmcmd-e31ergy of the Earth with respect to the Sun as the sum of two t nv :q1k-km;dj1z6m3)omceh i erms,
(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 ma0 r ,/ypclay9n3l 6kelht v5i.ss 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? Assume it is a l9 y/lv.ap5nr h6l t3 e,cik0ysolid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg startfrne4c x56c4 c. yati5s from rest and rolls without sl.iy56c5cr4cfex4n atipping 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 i 8*6js979uayv b-srla s7x qcu2xd8o on 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 y2xqca7j*r8vbs97iua 6os s98-xl ud just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum n; )o gsjc33:/ deczcmof a 0.210-kg ball rotating on the end of a thin string in a circldc3s:o/j )3z ecm;ng ce of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindricalr2d31 5ve4 ppr: fovi (.nshwj grinding wheel of radius 18 cm when rotatinr: (owsh.v4djn1 r25fpe i v3pg 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 rozx z-hbshms0r e2./)luxg, n +tating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotatio 2u-)r0,m n selxzbx/ghzs+. hn 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 Filv:si)t ct 52x8qqc o0g. 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 maqcsq5 vx c to:)i80t2lkes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an pzt 8rkb 3qlts,0r, 9qinitial rate of 1.0 rev every 2.0 s to a ql3 tz 9pb0 sr,kqt,r8final 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 ve gpx1wyin 5 pggb4/+7wrtical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel+71w4 i5bw gpxng g/yp. 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 spinnr*k k8rs4 xf3oing 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 momere /-wx n4vyp ,chre66ka4pn+ntum of 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 inertia I is dropped ontoqg*l62 z yf eig-,8gdh an identical disk rotl- ygq,z6feghd 8 *i2gating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a,q m:9gqdd8y(+i:l zx bzv-wat 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 , prf*t 7zroh k4,9bqqof a rotating merry-go-round platform of radiu9fr* o,4k7 r zt,qbqphs 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 angular velv9 6pwbum 14zvocity of 0.6 vvw94u bmz1p8 $rad/s$ 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 about htz5z q.4n(bj l *.jlhcalf 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 n54 *zj(.hlczq tlj.bmomentum, 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 exces nzfvpfy- -9xupx;)x ;s 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 l3p;s85 gf s ,-t:cha:gmhnt p$ 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 redq; ,pb k 4s4cdlo2j5ust, that can rotate freely without friction. The momenqd ;obl,45u4 k2dpsjct 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 stands at the edge ow b 3ai wyf(m)wmip+x9cg2cior+ -x7z p0dj5(f a 6.5-m diameter merry-go-round turntable t9a+gmx(- 5x2ypzi c fwidij prb) mww(3c+0o 7hat is mounted 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 thesk e dajn7672k ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does j6e kskd27an7the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always facetoiha-:ld8h/is l5 m5 s the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) tl/m d8hi -tisoh55 :lao 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 atv -jn7uy,/fzo. eyi2h7 ja0r 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 i8yaxuw52d/s e n the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque de/ dyw52e8u asxlivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cyl5 lu4f(r;6r.xrz puz iindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cyliu(z4 r.; f pir6l5ruxzndrical 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.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear w zzye85r* pa4iheel ($\omega_R$) 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 8jto9* l, py*kafct0l0 .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? potcfyj t *0*llka,90 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 for it to use en ei7(.nz6yr cpergy stored in a heavy ro.epni6 7czy r(tating 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 illustrates5a x e)iushg8idji;t; 421oo s an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizom1kvm;hs5w w ;mw4z( hntal 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 (i0q +dtz n7 5ea8mezm4f.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the fmz d0fn74 t+5 zq8aeemorce 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 standix6(rds0df91/ no owetng 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 it rests (Fig. 8–55). The step has height h, wf9w n0/r os1tdoxed (6here h

  A bicyclist traveling with speed v=2s vv9cka 68ud4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are t kcuvva2d68s9 he 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 lea ptl8fva5)u. ngth 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 torque come from apf .)tluva85?    $m \cdot N$

  Model a figure skater’s body agit zl:9r1- nywg5h/ zs a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the an1 5/: wglhziztr9g-nygular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutcpu8+ku68 b0ofifsjvl 4v+7gw h assembly which consists of two cylindrical plates, of0 kvg88 7fvj +p bfsuio6ul+w4 mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radmo.ne wxz)id7,z3bp1ius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble muse i7.w3 1,o)nmpdxz zbt drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but..orggz6-yl wgxjh05 do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as thezouz8.y0 :vl q0utvf)0em6ud car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0d. 8zu)t6lym00 0evuo:qzvu f.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