A bicycle odometer (which ,z(ys5q . m42usyepenzmjy3( measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use is psen23e4( 5zmq,.(muy yyzjt on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a pob ;0x,q3:kbbj(u lpcgint on the rim havl:(ux pj q3bk,cgbb0;e 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 body be described by a s)g5 ls;g.uxs ningle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Epv03 qkalex-7 xplain.

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 y3r,d r l0 cf:(1tfc (xtttd2aiour head than when your arms are stret(:(atc r1,dcdx 3 tltir2f0tfched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at thhmx (7ed.2g l(qqtxr 2e 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 7qtgrmd2l.e(2 (hq x xfront sprocket? Why?

Mammals that depend on being able to run fast have slender lo1 +sy7ju z0hgqwer legs with flesh and muscle concentrated high, close to the body (Fig.y+uhq0 jzgs1 7 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35/* o)zpa2*ri xmm 5*czhucn:9lxa p6n) carry a long, narrow beam?

If the net force on a system is zero, is the net torg gh rka3 0qxi,upvb:7 0;98z ko(gvu;p dio0zque also zero? If the net torque on a system p73duk0g 8vip9z x (va b ok;0hqgo0uzr,gi;: is zero, is the net force zero?

Two inclines have the same height but make different+kj obx9s;l1x angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of thes +x l9kjo1;xb ball at the bottom be greater? Explain.

Two solid spheres simultaneously t. uf)nxc80 ay/f. sfpstart rolling (from rest) down an incline. One sphere has f0)8/stpc.nu xf fa y.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 thr h cvz:o4e45b9 7ntvye same radius and the same mass. They start from rest at thec4vz5 49 thye: rbv7on 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 greater rotational KE?

We claim that momentum ciaf0bw:l( u,ps5ih7 and angular momentum are conserved. Yet most moving or rotating objects eventually slh w,5u7bls(ip: a0fc iow down and stop. Explain.

If there were a great migration of people toward the Earthv2y u;p7cxq5d sle9 /k’s equator, how would k su;dl 759pqcxv2 /yethis affect the length of the day?

Can the diver of Fig. 8–29 do a somersaf91z r-v5e,5pvtxhwma w1 3rl ult without having any initial rotation when she lea1v hx5zmrp 9, w3tral5ev1wf-ves the board?

The moment of inertia of a rotating solid disk uax8po ek.v3,.kgm/ gabout an axis through its center of maea/v. pk3xggom8,k u.ss 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 /ppzerz56nm 9 holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increezn9/z rp6pm5 ase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howeveitk,w+66ss(yt fc . +lm navf-r, one is hollow and the (- at .,wmty +fs +fcni6kl6svother is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontalfbgov 0jwv*p.2:z/c rq sy/ /n axle points west. In what direction is thf*/p /qcj2 b:0w/y vgor n.vzse 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 angular speed increasing or decreasing?

Suppose you are standing on the edge of a large fre-ari9 :-ssef ue.o;c-b) ios pely rotating turntable. What happens if you walkeri-b s:oc s .fi;-s )u-9epoa toward the center?

A shortstop may leap into the air to n xr.ycrr/0t -( okltxb48x7tcatch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and le(kr t48nxtcr.t0boxx y-7/r l gs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discu /zq:;8w apjkun,7pjf ss why a helicoaf;pp8/jjnu: wqz7, kpter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following tggqo+zb *c/( 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. Calculabiu3(; gs:ekq8 pauwr s; *c3xte, using the information inside the Front Cover, the*(se;3buksqarup8; wi3cgx: 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 3w()m +q fkoxruj lp 6/lb 7w+hmaq7.qr/m)dg, 380,000 km from Earth. The beam diverges at an anglwuwjg + 7qfhk/r al bqm 6+7mo.d)lr()/xmp3qe $\theta$ (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 a :ibh hk0p.9*4uf(g wrcea5fh t a 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 as the bc*hi hh0wg: ufa r5pk4f(.e9blades slow down?    $rad/s^2$

  A child rolls a ball on a 9a((q vq27f/ofdt ry ;eqybj 6level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is itsye79 aq(/dbo r(;yqv 6tq2j ff diameter?    m

  A bicycle with tires 68ca.vrf 2z 3/krae j.iar(j39 v cm in diameter travels 8.0 km. How many revolutions do the wheels makec2 f3ri ea(zakv .aj jv9/r.3r?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates alg(xos3z,4sr d5wvk4g01mh z t 2500 rpm. Calculate its angular veld0 mrg3(x 14gws, lkvzh5o4z socity 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 rev4fla 7j8avmwn87 i 0wpw.z3my fxb .4tolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 py34fw.. z087wi mjn7axlfm 4at wb8v 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 its orbit arouova) *k 3rn +,rn gl*.ikuqtw:nd the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of gc4 et yk pk(53dkk37pa point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from thpxl- stdmqo:du 0/bbs7+iq8ag iu 92. e axis of rotation is to experience an acceleration oi. sdia2u/lgq b-qpdb:89s mxou70t +f 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel a le.ppu8ish8r4h7 m9xg+31akao yt6fccelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. fh6r9ly8u.t 8xm7 a ks +eaigop4h13 pDetermine
(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 radiusa9k 1f8l)y hd o,5t jimbb-t:f $R_1$ 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, a3g :pq)p-v; gubqnu e+stronauts 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 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cbq3uvpg u- pgn;)+qe:ylinder 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 wjn2k( iw7h u5rest to 15,000 rpm in 220 s. Through how many rw 52nkihj 7wu(evolutions did it turn in this time?    $rev$

  An automobile engine slownvum1-kx6f2s (x (e jhs down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whir6l(,fojeh2 ii ling “human centrifuge,” which takes 1.0 min to turn thr iloifj,62(h eough 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 accelu(jjcpkwl09c p0d w6* erates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on jj*pw9u( kc0pd0 w6 lcthe edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is -vylq6bo1v5twbi o x 9(ots-2 running at 850rev/min It turns 1500 revolutions before it comes to a stop o59it1yov vs2xo (- 6twbbql-.
(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 rev.)(ieem7dz o7 osd t/iolutions as the car reduces its speed uniformly from 95km/h to 45km/h e 7i7z.o oet)isdm(d /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 make 65 ckgilty t v4 (7e2l7d6revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have d 67k ty(evti 2g74llca 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 .i48krrc1b5yj s5a 5qrdc47r mf+vxh pedal when climbing a hill. The pedals rotated45sc5r+xj 8rfvkcqi 5 7hyramr4.b1 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.0oy*u * if3noo What is the magnitude of the torque if the force is ex3fnoo u**oiy0 erted
(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 shb t;8pw q)lmrq.z5 d4qown in Fig. 8–39. Assume that a friction torq;qp w.bqmr qz dl84)5tue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attach k/ri(b+ sjmq x47r/kwed to the ends of a massless rod which pivots (s x/k k7mr/j4w+qb rias shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tighof( g svqp cl+pl/7(/jtening to a torque of 38 fv+ cs7pp (o //l(qgjl$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when the aeep5g4w +3ai gcnct 6onhx7(,u* f 4vzxis of rotation e czv*i4e57, fnxghcwug (no643at+pis through its center.    $kg \cdot m^2$

  Calculate the moment of iq+r h8;ob*kc sxgac u 559 84hfhmp/nlnertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (whpc u ;hgoqm*a/4lxnsbf9 k8+5 h85rc hy?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a6p:o2cbsp.o l thin, light rod is rotated in a horizontal circle oc olb6:sp2. opf 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 constant angulqhd c/3h 5+:skd swq9xar speed (Fig. 8–42). The friction force between her hands and the chw+ chxs9 s:qd3 kdq/5lay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array)b4(l4t tpr:l td;y-z l ,neym of point objects shown in Fig. 8–43 abob ;l,ttz-n )4l pl 4y(redmyt:ut
(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 h1* kd* hlzzak)pk q(gkq/m+:oxygen 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 cylindrical satellitexv5t6z a;m*vs 13cccqh j68gg spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a6;g8 1qm6hz v cgx3c*jcv5 tsa 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 rax+valrq l820u 5xrb 9ddius of 8.50 cm and a mass of 0.580 kg. Calcula 5 2d0l 8qrbxla+v9ruxte
(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 swin-+o:v.5f1k dd gpibph h ,vrl6gs 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 tangentially on a small hand-driven merry-go-round and i e-t cmu r- ,u+/-glcx-ols3ohs 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,coeulhs----/x + cg ltom r3u 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 br phgkcmzi6ku6:0eg)pda*3x- ought uniformly to rest by a frictionak6kpiu a0*gdc h6e-pgzm )x :3l 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–maa0 /,dmoyj b+ r.:u) )djaxx45 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 14l 9jd lq zz k/)w1nocfk.e4saction of the forearm, which rotates about the elboll kk9/n fz o1dzc1 .sqw4j4)ew joint under the action 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 thi5a (j ;m l.a:fsj0p8xnp i5miyn rod, as shown in Fig. 8–46s 5m;(japi5 injyxap.m08f :l .
(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 x1dxv.oz*oy+ 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 o c0 :gyan7+v4 m,gumh from rest within four full turns (revolutions) anu h+cym4 :v0oga7, mgnd 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 moment2fkcvb, u3mdk2-1doq 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 of b s3z9fvbp)*l 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 rour,x -pao, v-klls without slipping down a lane at 3.3 op -a,rvk-xu,$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic ener8fdnf ok:8 uglhw9f/9 gy of the Earth with respect to the Sun as the sum of two te98:o ff9d nk/u8ghl fwrms,
(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 dtro513e3qp9ey-bkahq6h d 5 much net work is required to accelerate it from rest to a rotation rate -pyqek951 r6qhetbdo5adh3 3of 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 starts fr96awk lcyn/bp0ck; 2 ho;t feto upn.d5z*r- 8om rest and rolls without slipping down a 308r.e ; *cb f pn2pozk65;wck-dhtyt n0ul9/ ao.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 fall abl9yx4mplv q; arne0c,+ *,qnnd its lower end does not slip. What will be the sp04+bpvn;e,*9qcxlr m qly, a need of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin 1,a9k xriok ubm(j1qq/ o xv3 0/dm5bjstring in aiu1a j jd(vo1m3qrx5bk,bxq 9o//0m k circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular moment7,xi er s:z)nzum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rota,ei:)r7sz nz xting 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 siqpb4d yjd6fog kz ;0h3/6. nyt,okkx)de, on a platform that is rotating at a rate of 1.3revoy/0tg3 6;k donj.qd zh),fkbpy6k 4x/s If he raises his arms 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 shown b q9k v+oeto57in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If sheek vob +9o7q5t 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 increaselcvtyhz ;ke82 kbuf/y;b9o. * her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final bu *cf.lko/v8;b;h2 y9z ketyrate 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 vedxrq 81abpd8st9p)6z h8cu ;frtical 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 of the wheel aft schdrp8u6f8b1daqt9; )8 z xper the clay sticks to it?    $rev/s$

  (a) What is the angular m x43hmopsve ./omentum 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 angular0xe +-/ +pn2j)htezl u 8wqywx 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 onto a 0fb u9dw2o;qdn identical disk rotating9buqw;d d20 fo at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at .;q:yc zr,1p/suznpm 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of m.6rf6wkfvr0p )y8xv a rotating merry-go-round platform of radr)mv.6ff p x0 8kwr6yvius 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 merr sgs9 ;)mx9tm7 rb:x whmqt5)q/f-refy-go-round is rotating freely with an angular velocity of 0.7m 9t; f )rm:sgw)hsq-x mfr9 qxb5/te8 $rad/s$ 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 + smzi4ty*q 5ecollapses 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 symzei* t54+q the lost mass carries away no angular 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 ly; -tw :lj l//up7qkjwinds 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 bxmz-917)cx f+ vaqku$ 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 row3m qm0t 78qxutate freely without ftm8q0q 7w u3xmriction. The moment 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-rouaai , ive4a 11vvhktkl2*p.6h2j ,kqjnd turntable that is mounted on frictionless bearings and has a , v*ij,p6 vkka 1jvi.k4h2 at2hlq e1amoment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the gror*3)tp 3gl 3 n(2yzbr6zb9de-xtdha u und 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 the u3 etz 2l3z(na9hbt)rd gp*6xdy3- rbspool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Ea28r cu v(obfory) h+t8rth. Determine the ratio of the Moon’s spin angular momentum (about ith u8r ob(o 2)crv+8fyts 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 from rest at a rate of 1cof3: e oh:+vb 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 cylinpv ck,jt2 +vt0der of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constanv, tc2tjv0+p kt angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of vzy9 nub6(qfr34sx xu2+5ivg 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. U vx(isvrn92qub 54yfzux3 6g+se 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 th+xqwqt x(p0)a l+a4w fi:)y)mnd 8jxme rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 tim+mfnxub;px 5 ywgv)v65 6vd1b es 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 t66bbv+ wm5y xu5gd fnv1 vpx);hat the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use htbon gh w,256energy stored in a heavy rotating flywheel. Suppose sg o5tbhn62, hwuch 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 illustrates -zgd(oo*li3 1mozlzm7.e/ )t x3jjgp 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 h, +tm-og*64e6) e7u8y lwst8rpv 2piccb bmzkorizontal 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 an)*rs (.a;npizz2yk. i eg;azk d length L can pivot freely (i.e., we ignore friction) a2irie(ask g;y. kznaz; )p z*.bout 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 gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius b;+kdgl 4: mx o+t-htlR. It is standing vertically on the floor, and we want to exert a horizontal f: d +xl;hb lk+og-4tmtorce 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 1gahqb7 klq*6 a flat road is making a turn with a radius The forces acting on the cycli*q abh7gl61 qkst 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- *h yj/ts9kbs gr8h,*pkg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 j s9ytgh 8,hrb**pks/ s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body e , z a7a(3ji9;a.hoq0k jhtnaas a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the a.z(aa hao,79qeij;hj n 0t 3kangular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch as,7g:cdijf w* juh4 iz)sembly which consists of two cylindrical plates, of ma 4* cg7uhzw)i:j fid,jss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ppx 9,k ,(o+j dzfe)b3alye6zradius 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 of the loop without leaving the track? Assu y9fp6+z3l jex aoz),dbp,(k eme $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, buc,-b 1;7psfntx; 5qhf(olk p ut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifqhd x2z , c09gxs.j4jnormly from 90km/h to 60km/h The tires have a diameter of 0.n4z90j,x j x2hgc .qds90 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