A bicycle odometer (which measures distance tri q 5p;6/k5-cb1t +cskhgp hvyaveled) is attached near the wheel hub and is designed for 27-inc-cystk1g/pi ;k6 p+c 5hbq5hvh wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point a g; ump* 4 um90qfjw6e7+ngivon the rim haveu9pgn0 wg7;q6mvei4u m +j*af 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 of linear acceleration change?

Could a nonrigid bodiy(zowtb5)m)lg*7ti (z9 ahw y be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque thaw /svwx ofw+ng9zs84 ,n 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- l7j oqy+((vvvup with your hands behind your head than when your arms are stretched oyv( vl7v+ qj(out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has sevenev3 sk upt -l-b-i6fn) sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front spri-lkp6- 3 -tsnbe fv)uocket? Why?

Mammals that depend on being able to ru eencu y53g2d +e;hky,n fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, e 5y3cy,ugeen +2d khe;xplain why this distribution of mass is advantageous.

Why do tightrope walkers04 )fkb6sa8 esp6- 7qpou xbes (Fig. 8–35) carry a long, narrow beam?

If the net force on a systemgzsw7t z qy )k*kwd1*96y f-xs is zero, is the net torque also zero? If the net torque on a system is zero, is the net *k*6sq td xgw1f7) zw-y9kzysforce zero?

Two inclines have the same h s(d*(3g)tykl.4v f -;trdmfp5y aua eeight but make different angles with the horizontal. The same steel ball is rolled down each (;lkfpu adt3f )grte d( 5-4y*sa.vymincline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneousl1yq/tk8m :a hhy start rolling (from rest) down an incline. One sak h/ ymth8:1qphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the saaau5pbc x. w+njubb r3x+24htuu8/p)me 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 has the greatebjr c3 )ux . n+8u hx+pwtabaup4/ub25r rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving g:6,xnk-waq-ukjy mxxk95f w ,br+9zor rotating objects eventually slow doxbm ku,-r6a,5kwkx -jqgy w:9f zxn+9 wn and stop. Explain.

If there were a great migration of peoplt ; ;lg+h btm638(zq4lomp mjye toward the Earth’s equator, how would this affect the lentzt4lm(3ohbl;86y;m g j pm+q gth of the day?

Can the diver of Fig. 6zradhcw ,1k0c m h*avgg-34p8–29 do a somersault without having any initial rotation when 3zhhc ka6w cr *m,gagp 41dv0-she leaves the board?

The moment of inertiakfy2cmvv4sl9+ p5 u,m of a rotating solid disk about an axis through its center of mass ilfy9u, 4vm2c +kps5v ms $\frac{1}{2}WR^2$ (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 uz:bqk eucpyy1:, +)o stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, wiu p , q1)ke:zby+:ocyull your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howevet3-e.-pvsbi1ft ip.gjnn0a, r, one is hollow and the other is solid. Describe an experiment to de.geab--ifn ,.pv1itpj0 tns3 termine which is which.

The angular velocity of a wheel rotating on a horizontal axle points szyt ;l05mk uygb+ 3*(r bc1sawest. In what direction is the linear velocity of a point on the top of the wheel? If the angular accelerz kc1y3mstbrguy ( b05sl;a*+ation 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 tur6oe bj 5/k3xtcuf434 roqy2qbntable. What happens if you b4/c ye 3o fxt265bo3kr4qquj walk toward the center?

A shortstop may leap into the air to catch a ball and throw it qz, jyc/3:vj xhj46scgt r5d.auickly. 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 (Fig. 8–36). Explagj j,3achd5t .xyj:cr6s z/4vin.

On the basis of the law of conservation of angular mop5m1+ .v4 uirp8ygihumentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways hmyp u8r 1+ v.4ugi5pithe second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 3rbip*iph t 8kfe47q5bk:p/h ,0 $^{\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 ou )/wr26x6s 8edcldf5q y q-bff an amazing coincidence. Calculate, using the information insre5 wf )8q 6y qb-/cd6xudsf2lide 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. The bq: usp *3ui8fxeam diverges axsuf3uq p:*i 8t 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 a9wsc1d,r9cxqtnbf1 uh yv . e5uu25;rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration a1au; db5x ,f.e9cvqs9 huc t5ruw ny12s the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to 9-zko uidstf , itx*0w;i*o8ianother child. If the ball makes 15.0 revolu, 0tfu*i oi*- itow9 8;dzixkstions, what is its diameter?    m

  A bicycle with tires 68 cm in :qo/r oe;ll( kdiameter travels 8.0 km. How many revolutions do the wheels make? ; ork :(lo/lqe   $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpmnhc/ m *4w1pcdul, .yr. Calculate its angular velocitywch*p4u, .lrm yn1 /cd 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 make m,tam/ ;bi4tys one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 mma4,/t ti;by 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(nmph6yh7:8 xcttm6x) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of h vuq-*c b)y1za 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) muso18qo(bj)(h o3t/ s bba*q butt a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to expert((sb 3aboq81)/ qbjobt*ohu ience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformlyr x/c;uga s7*r about its center from 130 rpm to 280 rpm in 4.0 s. Dete/xugar sc *7r;rmine
(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 radiu d5;ukm:z6kgc.-ka wss $R_1$ 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 spacecraf pmb ai/9yw6 k/s(e*cpt put themselves into a slow rotation to distribute the Sun’s energy evenly. At the eyc(bps / wikp6am*9 /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/ fve 7zc zrrfiwe:b5nf6,-d - 15,000 rpm in 220 s. Through how many r ,6c7dnfr: /ebw5fizfrz v-e -evolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 r ztp rsa*1hy67pm 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 flying highspeed jets in a whir;c tkwgv ec0/.ling “human centrifuge,” which . w 0k/tecgv;ctakes 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 a6t(fp5 wy umh +ryvf :-so zd-j::*uelccelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have vuff tlr:5py-u+we6 -d: (*:jm yhs oztraveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 150wv+io /2sv4vk0 revolutions before it comes to ov k+ svv/i24wa 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 cbbw/ tu8kv oo :*n-)zrar reduces its speed uniformly from 95km/h to 45km/h The tires have akro 8 bz *uo)/b:w-ntv diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolu k70+qcs8rz vctions as the car reduces its speed uniformly from 95km/h to 45kmzq0ckrcs v+7 8/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when cl1zm 08n;, v0ttehhgjgyn*3qkimbing a hill. The;0en*h n3zjq0ym 8v,g1 gh ktt 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 forc md1:1hnea-bg e of 55 N on the end of a door 74 cm wide. What is the magnitude of thbd-h:gam 1ne1e 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 2xu:s,qs(dmew 7y49 ozw8l zlof the wheel shown in Fig. 8–39. Assume that a friction to 9(2qzws7 4d:lm yue,x8oszl wrque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of maspwurzv l*lqx 4dg5-bg6b50h : s m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal p0g5zdblx h*4 6gw- vqu:pl5rbosition and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine f))hg *vuw*+wv ort4v1*uk,8xtqwev require tightening to a torque of 38 wq*wv* )x)wevt+4gu hvk,*frvu ot81$m \cdot N$ 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-k f 82 0(7q*yh exogbc5rwkpq a 10.8-kg sphere of radius 0.648 m when the axis ofw*x087 qbgqe5-prfck ok( 2hy rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 6p 2+z2p v5ysha6.7 cm in diameter. The rim and tire have a combinedyp2ph5s 2zv+a 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 horizonj5 bd*0c5l zn;vrwuj.o ;jvp8 tal circle of radius 1.2 m. Calcn8j5v lp.ub0v;djo *w5r ; cjzulate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular spee 4tkg60d;xkrad (F4xdg k 6ta0r;kig. 8–42). The friction 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 in8u mvd(5qow ,w *.epobertia of the array of point objects shown in Fig. 8–43 aboue(wv,qb8dmpo o*uw. 5t
(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 whose total a o7o9e2uy mer vs)-u/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 correct rate,v(vv wft o;4k7 engineers fire four tangential rockets as sh7v wtfkvv 4;o(own 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 to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and abj,yhl3 v-ndw(q; dlsyb.( x+ mass of 0.580 kg. Cq(yh. ys + nv3bx-;llb,dd(jw alculate
(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 swingnd1fs e*tv1 9bs a bat, accelerating 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 tan9hr ofa;ordae-+1 e4khbt- e 9gentially 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 opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torb kr1e-t49; fheroe -aoa+h9 dque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventt/o. hi)(9 2cz iauqldually brought uniformly to rc9h (oz.i2 alu/tiqd )est 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 accelerates+ etx- 0x1i31f3mvm 7 qshb mn*sn+ktq 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, whicxhq6usv*la 2 i0 xccj*3/ea7 wh rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelxqa le 7sva /w 62ic30*xh*jucerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 8–5l de7ez:w/h 1sgtr a246g 15 hzreas/ dlt72:ew.
(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 obf qjie)(sug 9lpxn75l5u+ 0x xarn:- f 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 s 9hn54pt5pe.bora)fo /-) g4zazqc v from rest within four full turns (revolution) 4r/hgqpsp acbvtz zoaf9.4)n e5o 5-s) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a momene q3-6cg;mnbbucwf j4.m(s2db/ u: g dt 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 torh. c pjzk**oa)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 k7o 0gq6vga1lajlx.f;+eec z- be6i3 g g and radius 9.0 cm rolls without slipping down a lane a3lz+o6e7ee1 g ilcaa-q6;b. 0f jgxgvt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of +v ;mhzz5 q-m*wejl9zrmb+ ;mtwo te em+zzz;mm;v*+5rw b qj- h9mlrms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How md,8sh l,9 s ch gnv ou9021+hbhzqp3bkuch net work is required to ak,hqhub+o8s 39pvzgnhhl 9d 0c2s ,1bccelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg) fo0tc/lf ; i0rfl4kv starts from rest and rolls without slippin/ l;rfl0tf fo i)cv0k4g down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fu nf (dur2at4+i( b.2ao)i0iihvz2c zall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use consecbd 4za f)i(naiozri0(+h t .2i2 uuv2rvation of energy.]    $m/s$

  What is the angular m.6ntc pcydwyo;e2f-* omentum of a 0.210-kg ball rotating on the end of a thin string in a circle oeny.tc6pywc* d o; f-2f 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 cylindrical grinding 81 8k yf/decw;t8 fx+bo o(6v:t s*bw pkjpqy9wheel of radius 18 cm when r fydwky;/se f b(op +86xbtjt8*k:o 9c1vw8pqotating 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 m e6 mil7pat/b n*;spowj./-tat a rate of 1.3rev/s If he raises his ar*7mp;lsnoi b-p//t 6mw eja .tms to a horizontal 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 one s.x.ov +q(qt1qv vjme:sgol +: hown 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 positioqoq(..v + vm:xjseq1: oglv +tn. 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 rate from an initial rate ofxbevkcm7) x gq1na 2j.(a7/dp 1.0 rev a(x.)/jm7qdc2ev p b7 n1kgxaevery 2.0 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 aroundtm sgw6sf,fo/ 7t19np a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency wfm,/961pf7 gtto ss nof the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum ofdar/ 1k9wi;tlkey txwft .. *)plv9a5 a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular rlq7dqbqru3r- )q gju 33 o,.wmomentum 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 onto an idena9dr:7,+y(oz u vt knctical disk rotating rc9v:u7+dykt, ozan (at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns3mkan xpntq7 p-t( p70 at 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 stvsc cjg23q24od-0f8ce3nqycxm h;q +ands at the center of a rotating merry-go-round platform of radius 3.0 m and momenc+m2fnqj8qcox2d3;c -yqh v30 g 4ecst 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 xjgl(0*sihn a6c9*v u an angular velocity of 0.8 jh l6(x9u na 0cv*gsi*$rad/s$ 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 eventu ws2r:+( 49lkwy,hsj7 de,pdfsdb vw(ally 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 angula9vsywpk: f4sj,w ded(bw2l7 hds (r+,r momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve;gj ue 1;fsdn(g.z5 jh winds 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 7pofxm:dw.208gbm2n yyg7x w $ 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 rotate freely withoutx.v4-7 ) u0 vy :vtftoj4czqpb friction. The moment of inertia of the person plus the q :zv)u- 40tfy4vjcvt7bxo. pplatform 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 sz27r+pzc im3sx5w c(6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1swz+spcm r (2i37c 5zx700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope 8 6notxrwic is.bd70pw85 v e)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 the spool88roniv7w6tib )p .x c0ed5sw’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Eartydve6i+2 md b6h. Determine the ratio of the Moon’s spin angular moi+b yd2dm 6v6ementum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates ccn (j,w 1 hmot1 .2hcdyif(;rfrom 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 inszgsz.h* + 2re the shape of a uniform cylinder of radius 0.20 m acquires a rotatioh.s*r+z2sgze nal rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made o9jx4 m 93mdf eaa:6sqif two solid 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 calculate the linear speed of the yo-yo whej9amsqde3a4ix f:m 6 9n 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 whee ip7s7,sp r3ebm)s ar8l ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0:a d qs+7 tfjb7j/uu,o 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, and that the lost mass carries off no angular mo jqdu/f+:u, as77jtbomentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is f9iys-*ce18 ;x2 wugk :z,) uk panbuewor it to use energy stored in a heavy rotatinns)uzekcx p9wa;u8-eg* wu: ky b12, ig 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 illustra 3*r+dbfw3kmt/p5vsptes 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 qpre w7cwe5 ;euf3 :9i-a slv.rolling 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 free 1l gae9s4o:up j8ekjv0 i*bf1ly (i.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 force of grav9e0jekbl14:8g vpji u 1sfoa*ity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radi -7*iw.izmav hw.b. teus R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will htm .i7eaivw-. .zb w*climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling w 1ac-rs xq9)lji8t i6ifu h.x2ith speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cycxucs82 6iqf)- hlai9.x1 ji trlist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m a- y8 e.v7 n)g(s3yeqhx+ctjnp nd begins whirling the rock in a nearly horizontal circle above his head, acceys.nhxn)-jqc+p e8t7yv3g( e lerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skaterg(kti fu. aj5r2eo 2d,pgd d5,’s body as a solid cylinder and her arms as thin rods, making reasonable estimates for the di kdjpr,ug2t 5god,fa(.de2i5mensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists (-k;w.dz2d5ny 8k(tr yfmqpn(;n dgqof two cylindrical plates, of mass-;wmtqy qfn((gkdn pn (2.8 zky;drd5 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 an m8pi g hcr0+* tp0t5iz4pd1mcd radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point ofp4m*+ 0p5r cp0tcighm itd1 z8 the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do noth+;cm7lc twt qe9+2g d assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniforml ehw r2p6x,8otl0ajt4 y from 90km/h to 60km/h The tires have a diamete0jxr42,e8 pwthl to 6ar 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