A bicycle odometer (whic/ di6 ll,zmc9nh measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if youzl9/i lm6d c,n use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocitzu.0nwcbt 97q78 pno6l-vr eq y. 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 magni t0vqco7.96 lzrw8nenb qu7p-tude of either component of linear acceleration change?

Could a nonrigid body be descre;r:z3a1bj k wibed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Exugloqd; p6v y+-xm,km:x1t f k07pnq 4plain.

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 hand b9ube18,,n mnjcds/a,nbs /vs behind your head than when your arms are stretched out in front of you? A diagram may h1bjb,s,8snu/ /n ,b9 ancvemdelp you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheeh mwdi.hu2v t8/kt/ey2(p 3 ial 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 sprotedii28/v kapu.23y/twm(hh cket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower le)aylt hy+96plgs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distrt9laylp) 6y h+ibution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bee*k emq9 a-l1uam?

If the net force on a system is ze:rfwgt(kx : :z-:9i k( jhvwfd;kwk0ero, is the net torque also zero? If the net torque on a system iskk: krj : wvw:i z:txfkg-9wf0d;e(h ( zero, is the net force zero?

Two inclines have the same height but make different anglee .y yx7y:(rsalt7qi :s with the horizontal. The same steel ball is roi:y: .re (yt7s7yxal qlled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultanv7pl(4 xldj0*fx.uafeously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom ofj4.f07 axp * lxduv(lf 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 blfy5,lblo3w l/ny-, same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has th l -/,y byn35l,fobllwe greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most mo )9w c3soutb ;ywhf7+jving or rotating 3 c)uyofst7j9w+ hw;b objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Ear*cjbqpqt7/ tu xy750gr z :k1uth’s equator, how would this affect the q7p 7juqgbkz 51x:*ru/tt y0 clength of the day?

Can the diver of Fig. 8–29 do a somersa7t6y7m 24h*msmgtq l hult without having any initial rotation when she leav*ym 7hmm s6hq2ltg4t 7es the board?

The moment of inertia of a rotating solid diskz 7 7 rrn6hyl:j(p)/5 saykqss about an axis through its center of mas: rsa(ph / ys75jy6s)krlnq7zs 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 stool holding a 2-kg mass in bw97ke3.to g9q qe+dpeach outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the sa7qd+3kowe q99pet.gbme? Explain.

Two spheres look identical and have the same mass. However, one is hoajw p1r8rn76 3f vc+jallow and the other is solid. Describe an experiment to determine which is wh 6w1a jnf p78rjcvr3+aich.

The angular velocity of a wheel rotating on a horizontal axle2)lw1 um o io5b6rkw(k 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 top of the wheel. Is the angula1 )526k u(mloorbiwkwr speed increasing or decreasing?

Suppose you are standing on mw3y3/0eyalwkf -d-sm ug u1 3the edge of a large freely rotating turntable. What happens if you walk toward the uswgd03ewy /f -1kmlm3y-ua3center?

A shortstop may leap into the air to catch a ball and throw tvx h;y0q ( g*e9z4lqgyg r5i2it quickly. As he throws the ball, the( ;hg9* g2y4 tqieyvz q05grlx 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 of conservation of angular momenzr 1i2gm 8v kpw4f-3kdtum, discuss why a helicopter must have more tha3p4v2rki1gz-wkm f d8 n one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following yqgi. )bkmbcw7-4p(o angles 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. Calculate, using thegy)*w pe8- ;q+nk racc information inside the Front Cover, the angular di yn +cg)rac;e-kp8w*qameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed amk-s3m /ei 0lz)vf2qp t the Moon, 380,000 km from Earth. The beam diverges at an angle3mzs qkev/lifp-2)0 m $\theta$ (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(wv jex(jpw v- da68o d4)8zpp a rate of 6500 rpm. When the motor is turned off d884j wxv pd)(w vp(-zepao6djuring operation, the blades 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 floor 3.5 m to another child. If the ball makhxf2l6- lpsy(7-4 tt68ahzuoy (hd yjes 15.0 revolutions, what is its diamel8a4ohyutzhp-sj67 h6ylf d( x( -t2yter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many reh qrko2yi vja(6t:12 mwz:*xevolutions do th tmr*vi wak(12qoz ::x ej2yh6e wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate hrddzys2 (q .,cth /4mits angular velocityq,dhdht.czyrs42m / ( 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). +g 6 3,u0nj-fzosvg1/eqwzmw (a) What is the linegv ms1+gj 36, wewzn/fz0u-qoar 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 Eartxp/0t0b taf 7sh (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point ba81r:wp ltic8 /1dff9 vge9a
(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 centrifug 2cj ti04n.reme rotate if a particle 7.0 cm from the axis of n2m4e0jc r it.rotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abo3q4;gso0u uhn ut its center from 130 rpm to 280 rpm iuq 4s3u0nho;g n 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius7c 5aegn 7nf8do)h+um $R_1$ 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 Mol bcw:7bu4) gq)kh 5qhon, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 :h)hl 5gb)bq7 uc4qkwrevolution 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 unift hmk*vw .k6q bu)h gm1qeu*j,1s w-r4ormly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this tuqk4rh6-ues.1mj*wt) 1b g k*qmw,vhime?    $rev$

  An automobile engine slows down from 457j.jec:b -u 2q s3 xlmszq,lf )2nh:od00 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 flying highspeed jets in al vdx.4uag 9e;yz1:no whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachin:.4uy9 doz xgan;v1e lg 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 360fiw4tz;b8 j. aqhy oa bxx4 ,-:r-ybv2 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? 2ax b-b xibt r w:v4yyo;84qhz ,-f.aj    m

  A cooling fan is turned off when it is runnihuri u3x o.mn.z39ac/2e .mu qng at 850rev/min It turns 1500 revolutions before it comes t3 m2xu..ca9hr 3.iuzuem/onqo 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 revolutl(y xpl: oykl*;rjjdu 9y 4*x+ions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 moy;:j 94yx*rlx+y( * lud lpjk.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uni: d9 ; d1e*iciif g/c/5bkmliiformly from 95km/h to 45km/h The tires have a diameter of 0.8lifc /bi c9emdk* g5i:i;1i /d0 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 all28gv;dqq a/bk her weight on each pedal when climbing a hill. The pedals rotateg / 2;8vqkqabd 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 magxt(s h*+v- u xdnp.ev)nitude of the torque if the force is exerteduend v+()th vxx.s-p *
(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 sh*c: nw0tlk*cub wc.tp , 1b(jnown in Fig. 8–39. Assume that a frictio.c(w jntkul,: * 0 p*n1tcwcbbn torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rodzfvis5p, r3p9x y3z a, which pivots as shown in Fig. iz x9rf,,zyvaps353p 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of ixchr oim b5 12giw(sc4o-2 /ian engine require tightening to a torque of 38 (i2ci h5- r4cm1ox/ibios2gw $m \cdot N$ 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 ,fqoexb l3- hy31a-buof a 10.8-kg sphere of radius 0.648 m when the a x lf3yb3,b-a1qh-eo uxis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of in)oljke 9uvr*(s si7 9zertia of a bicycle wheel 66.7 cm in diameter. The rim and tirvu*jsikz eo (l99r)7s e have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is qpu. 0l3um 2lvrotated in a horizontal circle of rapq3l02l.u um vdius 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 co hzia (v)-6 si0v)tgrpnstant angular speed )zgi apv )tis6(v h0-r(Fig. 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 inertia of th+pwwto ,(g4h 9mu 7enke array of point objects shown in Fig. 8–43 abou nk+ w,gmoh479w ep(tut
(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 tota /l12-zi.vu x2zx m.vrp1pybz l 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 correctk6d 0ucn+r o,s rate, engineers fire four tangential rock 6scour+d,0k nets 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 to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder6njgvwxz o (qj+a*5x2+dwt:pg ok (q- with a radius of 8.50 cm and a mass of 0.580 k+*n (:2a tpz5owkgjg-x+jqw6qd(xvog. 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 rest to 3 *ma9;ow)b/ nq erwvn5 $rev/s$ 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 g5 ;hhrd( wa,eon 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 acceleratiha(h;rwd e5g,on, 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 and is eventually berhch8 qkx :47 uvdc2/rought uniformly to rest by a fricq :/cruvd2hce 7h 4x8ktional 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(yr 5z s3(x/e* njural4m cbr/1c 7wys accelerates 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 thee 54q sb,4/nr)yjz-tra 9zxhx forearm, which rotates about the elbow joint under the action4 asqre r-xz/ 5x4nzb9jt)y,h of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin2i glv xuuhi((6n68sowo0 m m0 rod, as shown in Fig. 8–46.mgi( o6 s6(w2 unlx0h 8i0vmou
(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 massu*e h *hv-iu.nes, $m_1$ 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 withmg13+ -pcnxnr9mmyau * dtw978b ety2in four full turns (revolutions) and releu8yrtyw2etp+9d7 *m- n cx1mbgm 3an9ases 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 m uble0m+fj3o ; ;6moggoment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque 6sfwqqun j 6zpx3y,.- of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rqf1v e(pvm( c,olls without slipping down a lane at 3e v(( pq,fmv1c.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with resczp4(ht p m*w3pect to the Sun as the sum of two ter3p (tp4zm*chwms,
(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 much net6 w/2zaaxz zp;*o-c h0td.rw d work is required to accelerate it from rest to a rotation rate of 1.z0zh6*dx pa2aotwc; dzw- r/.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls withos 9+yk ysh4(kqg(l-v jut slipq4ksysyl+gk(- hj (9 vping 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 sk *d v96xsk7hw0p/3mdf p kzfa4b 2jz7tarts to fall and its lowxa7*ms62w7d fd43kb/zkp 9fjhv pkz0 er end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum 7rpxozzcqlgk*fz)* vkcj2qb ; 23s*5 of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an as2czl5bpgr q)zk*z;ojq3 2*7*xk fvcngular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding whvj44haj.u v. ieel o.4 j a4ujvi.vhf radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that isjx:s*5o zrd6 ub1kob5 rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fi15jbso:u b* dxrk5z 6og. 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 on si z;tr0rj3m:e shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from thi:03rz tmj r;se straight position to the tuck position. 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 anz5a wo+7,- lcje0f zl lwv:jj; initial rate of 1.0 rev every 2.0 s to a finalo5+lv,ze;0lfw l aj -wjcjz7 : rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its c6un3sa2z,h wliia 6+qenter at a frequency of 1.5rev/s The wheeiwh an+q a,z 3i6s26ull can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momenturd)jw - fpesj7,e 0b*um of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angulafh9ea /8lja em8 e1;(dq ,srehr momentum 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 ontoc ,jbq n.al*)n an identical disk rotatn.,cbaljqn *)ing at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns r/s. ui*(i5 gfz5f xlzat 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 t b6;s7aapd3pdce)u z*he center of a rotating merry-go-round platform of radius ad sz6c3p7udep;a*)b 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 velocity o8e x nk73ue7 5y:yohkepngfvxw5 n)v+8 yqh;/f 0.kyex:n)+3n7pwh5xo8yq yv g7e58efv nku ; h/8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses int9wcchz9k tz u 3tf31(go 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 momentum, what would the Sun’s new r9g cc(3 ttu1 fh9zz3kwotation 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 involvfp;x,)4kahdu e;b*hre 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 s9/f/ck eklcvye nsf -:*r w*4$ 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 rotahjs 9c)rlv 04ute freely without friction. The momrj0l)h v9u4scent 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 of a 6.5-m diameter merry-go- -/gkbmg(.h 0hyjv ewbq 5(um,round turntable that is mounted on frictionless bearings and has a moment of inertia of (g bkh m0.u /,q-hbemg(yjw5v1700 $kg \cdot m^2$ 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 oyvqr w .925*/l)gnje*mmtmc bf 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 qy9r/mvecmjtnmw2b 5*)l .g*without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side alv hnpm.7(q5 fievd owiyt 6ofpgm3 )-h:w(+. lways 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 orbh ve.(qfnf:7tl-(.dmog56ivowy 3 iphw+) pmiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ratpir4c4x juha*y 3)sq1e of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m ac/udy+q r +oc kyb5p 10ng1qr8jquires a rot g/pk1 c+qorb0yr qyd +jn81u5ational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricalm yu3a4puouy.bd(3tq7wslh 8 9gn2 m. disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin w 8ms9pqtu.32n.lgd(4uu abmyo hy37solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheel (h,ocq:z qncng-bym2 n6c 78)z $\omega_R$) 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 wi(5-) boushta9o rsy,oth mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to untu)oy-,95h(bra o ssodergo 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 lo( 5z1u cgoe.slw-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywhee1e.clu gz s(5ol 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 illustrat)ddrx eo;g)*qb88geres 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 (hoopd rt;8 3qqxg7m9es1vp) is 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 freww5s1r eg o 3ufu)o5f** (yeebely (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 thef b o15 u)u5ew *yeg*or(swe3f 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 hasb-zyuwbf(f + pbj9b,7 radius R. It is standing vertically on the floor, and we want u+ybb(jf, w -p9b7zbf 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 is making a turn1yd anyd)m-n : with a radius The forces acting on the)mn -yyda1 n:d cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into azc ;*z0skffq o74c s(p8pc)it.iv c.p 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 kit vpp(o cqi7f8ps.c cz;0sc4z*. )fthe torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater bv(0a+ i5i/hutxn;el/ klyw; ’s body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms; xb 0 +th5aun /ki(;ewvil/yl held tightly against her body.   

  You are designing a cluti+h 1lv .e)9mpy 0hlutch assembly which consists of two cylindrical plates, of masm. 1+hlyp0 9ieut )lhvs $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fig(z;waj 1acl0 q. 8–58. What is the minimum value of the va j0w1l qac;(zertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, bpf esmx-l5* ,jut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly frg , m*b7/irzmpom 90km/h to 60km/h The tires have a diameter of 0.90 m. (zgp/ r i7m,mb*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