A bicycle odometer (which measures distance traveled) is attached near the whr.mvg y7p, +pbeel hub and ip7p, +rvybmg.s designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constanm qwdyj.za*9 -t angular velocity. Does a point on the rim have radial and/or tangentiaqa9.zd*jmwy - l 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 single value ogj6n xq.o 1:(nhxg7klf the angular velocity $\omega$ Explain.

Can a small force ever exert a greater tnl5; iqr 8tlj0orque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with yh81ud(zra s, mour hands behind your head than when your arms ar(smar 1 dzh,8ue stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at t4 qzd0uzf2e efx 8dy;8he pedal cranks. In which gear is it harder to pedal, a small re4q2dd 0u yzx;8 fzef8ear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being aynes2: hj:h: fcr s exq87q2j35 bayt+ble to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageouss3 :qreaebs:t58: + n2qfhj27cyy xjh .

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam?vbp2)l h17 1b*ymbinvm(ka m7

If the net force on a system is zero, is the net torque also zero?7.*mw dma a,of If the net torque on a system is.7w m,ofamad* zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontaltccj b-c-p-x*9zr ( nw/l po+z. The saw+o cxbz-- ptc/9r z-*c ljp(nme steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rosi,69kqpuz 4x 5l :ahclling (from rest) down an incline. One sphere 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 energs6hu,:i5p 49 qxcl azky at the bottom?

A sphere and a cylinder have the same radius and the same mass. They starp l .4z+tkqb 4qu:1g1krs8g unt 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 energklt1 uzqpng+ 4s1.8buk qg :r4y at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most 8k o-n2qvj dc/ s*aqx.moving or rotating objects eventuallyv/n*cqqjsk 2 .a -oxd8 slow down and stop. Explain.

If there were a great migration of peopl,d0)ym5fgtp5 x xa4pxe toward the Earth’s equator, how would this affect the length of thex5 fxpmt )gxp,a40 d5y day?

Can the diver of Fig. 8–29 do j-9:w7s7jp :ukzrgnmy xoy.j cq2g12:v ah1h a somersault without having any initial rotation when she leaveuv7cj1:a 9m:-sr .2gjg:pyqnh hy jx2w71z kos the board?

The moment of inertia of a rotating solid disk about an axis through its center;)h-xi8zugdfg. 0xmjnk1 e7 2 y oev0r of m18nm)eou fhe 0yj z ;vridgxkxg .7-02ass 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 holdin+2 na5q jjcm.3yf dl+ag a 2-kg mass in each outstretched hand. If you suddenly dr+yjn jf .q+3la5am dc2op the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one isu+ r 0bve;syw3azsq, xk;4 f7g hollow and the other is solid. Describe an experiment toyxfuv3,4gbz0 7r;q ;e ws+ak s determine which is which.

The angular velocity of a wheel rotating on a horizontal a2 ( gdw b6j.*vglf0-gt (lnae l-nn7kexle points west. In what direction is the linear velocity of a pointd2 jek blw(-lal g g6e ntf(7-0ng*nv. 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 freely rotating turn1(k9ad wouukd9c,-iftable. What happens if you walk towaru(doif-kacd 99wuk 1 ,d the center?

A shortstop may leap into the air to catch a ball a u.rip (k -;3 fwr1lu0.gen+anruh3zznd 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 legs rotate in fl;ep1k+hna.wi- z0r3(nruguu z r 3.the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, dis*iz3fisv rn - /c0+pvccuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second pronpv i 0ci3z-s+/ *rcfvpeller can operate to keep the helicopter stable.

  Express the following anglhy+rj- v*+iczes 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 ama8+la cbx k 1wsm25my amga-.g 6*gr2wczing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as -wy15s6. glmkca aw*22bga+r 8cmmgxseen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divergew5z8 tdwf-lq:s azdww5-lf8 t: qt an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. Wx 1em 2gc4 j 6f,tnmd-t ldz+ 8p2q:rfxm39kqahen the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow d, dqa3f :k-tm+9j nq4tl 8m1x r 2m26expgcdfzown?    $rad/s^2$

  A child rolls a ball on a level floor .q* th sni/pj93.5 m to another child. If the ball makes 15.0 revolutions, what is its 9p/tq*jisn.h diameter?    m

  A bicycle with tires 68 cm in diameter +wgrtt y0tcif ,8rj,8hp b::e5bc 0aptravels 8.0 km. How many revolutions do the y phfr5e8tc80t tgb,0 j: +awi,c :bprwheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its anjz*3* aup kua;gular velo pjauau3; kz**city 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 on+/* ao4gh esxae complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seatex/+g4oea s*ah d 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 oo,).q p/dgj mlfq68af )fad) kf the Earth (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 p/igaoizr .vq /ex3 :3v 5r5qsaoint
(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 ,c, au75ftrprl5joj4l6:gi;m a( mwg a particle 7.0 cm from the axis of rotation is to ex564m7ujl;mi: 5 rt rf ,a l,pgaw(gcojperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130)gi8pg1, h gqy4tn2x k rpm to 280 rpm in 4.0 gt8g42,kx h1n y)gqpis. 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 radius d *a 4ao;82fg7v6y+h *s 8swryfscxed$R_1$ 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 Mquwn *;wp0f x.hd)jj, oon, 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 revolution every minute during a 12-min time interval. jq;hdnpu ) 0,fxw *.wjThe 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 f fcx3+:)w:1 x3ejbnvbwylqlsp +i*8 uniformly from rest to 15,000 rpm in 220 s. Through how m+vy3+3l :*:jfx q8e x1) cpsnfbbw liwany revolutions did it turn in this time?    $rev$

  An automobile engine ncamak.)up8m . 0 3kcpslows 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 jelrna+ nxchwni899m 2.mrb 7 (rts in a whirling “human centrifuc9 ihrln9n8 mw+b r7xmar2n (.ge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly iytcgak(zcg w8. -85d from 240 rpm to 360 rpm in 6.5 s. Ho(agi t8d-cy 5 zgk.8cww far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turnedq5a,,j )hay)ql w,cop off when it is running at 850rev/min It turns 1500 revolutions before it comes to a q)pcw,a5y a, ojql,)hstop.
(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 makenjj4 yh2fp zq),/,fcb sg09 uj 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/hfzhqpj )s9j/4b f,jyn0,ug2c 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 revolutions as the p b. h(6m09hpt, wlqhgcar reduces its speed uniformly from 95km/h to 45km/h h9 0(h blgqm6tp,. hwpThe 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 kby2),:m-yb,*xi0 dgo mqk bkputs all her weight on each pedal when climbing a hill. Thk:k)mb ob- 2*ydqx,,iy gbk m0e pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a doew qjpwg )j6.x*w t-*.jrmii 8or 74 cm wide. What is the magnitude of the torque if the force is .igt -wim* *. erwjqxjpj)w86exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Agc/j- n9j;wt20 rden gssume that a friction torq92-gent ndjrg w0c /;jue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attachr86bt9b x)ck oed to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system. )r8t6cb 9xokb

  The bolts on the cylinder head of an engi8g0rzsbx9/ zsbtb6/rne require tightening to a torque of 38/r6 zx9b0/b st8brzsg $m \cdot N$ 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 1 u4oxq;*4wzf+miy gh when the axis of rotation is through its;z4q io1m*y4gh +w uxf center.    $kg \cdot m^2$

  Calculate the moment of inertia of;smlte m5ycn-ytna5 i6 3z2 5o a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.iaynnyom- ze c 5tt ;5s6m523l25 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 ho*kw.jga-24vxvh5 k lxrizontal circle of radius 1.2 m. 25a*xgk w4v v.jx-hklCalculate
(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 pp)t)0e ) unvnfs4me*iotter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1vi)pfm4 n0)steu* en ).5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in)prgr0y )za6)ou oua ; Fig. 8–43 aboutyao0 ;p)aurg6 )zuro)
(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 consists2g r0cbc+v d;c of two 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 cyli89ph5bxyts . os,q l)l3wujs; ndrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of h;y, tjqusl9pbl5)sx8 s.3 ow4.0 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 unil;c ef(p70lmh ty tb,29yqvj :form cylinder with a radius of 8.50 cm and a mass of 0.t9y, y;q7 p2hmejf b :t0v(llc580 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, acceleratin+)pm )4ey005 i2rqd4m1 pdoxfxvpsu bg 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 smallxk+ .zk/ 6)ct2wx75ti fnqv qt 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 7x ttxt/c. if)wqn5v k+6 zkq2kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is evensvf-mtm kc-+ -/+rfkgtually brought uniformly to g/mm--+ft+vk- fskc rrest 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 acceleratesx.a9dpi) c7ghzl:+kh 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 forearmv hxb8 2f:/k0z*kvupi , which rotates about the e: /k8*zfvp0xhivuk b2lbow 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 considerbrgj5. m h6(h hj1an78iqs p7ued a long thin rod, as shown in Fig. 8–41 7mpjbgjn.h8si7(qur5hah6 6.
(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 hxp83j;buo7a4lkk n t (hzk(4two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within jmx,(w 0 gi;sofour full turns (revolutions) and releases iwjmxs,; i(0o gt 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 moment o(7l nw0 r9 qhvn(sq:d-foajc+nddx/9 f 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 klym h/ u3.v4odebz1 .develops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolvz9 r+5dk4e0 ewrxfn6 u/h2x yls without slipping down a lane at 3.3 +r4xxn 9u we kdyzvh50f2e/r6 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respec7uxa./4mz kxbt to the Sun as the sum of two termsux/a .k4z7mbx,
(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 4qf.gx cu;txsw* rjg:1yhu q2 swba+4qu,h ,7a mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a sol,4ujgxq7bhyx.t;h u,: *+ r4gw1fwc suaq2 sq id cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg startuyb:ni i3ld-ut2 0 o(mte59oxs from rest and rolls without slipping52-x(no3ett d:0 ouylm9iiub 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. Ihrfiv njf06gy n-(ald n7,cu0/ 9n9w xt starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the g v9hygnuf 0fnd7-,(n6jw /n9x0irl acround? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on th1+6cigh ip moqf9 r((ee end of a thin string in a circle of radius 1.10 m oi(f19i+6 hc gmerpq( 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 hf+1ys jp3j 8fr. 4nvtcylindrical grinding wheel of+f.h 3 4nyvjs8jtfp1r 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 is rotating at a rati86( p fk4rytl f)9hlp.wo+ame of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed w9ppm8f i6fohl( k).at l4ry+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)egcafyr, :; uctj slnij(,:5 shown in Fig. 8–29) can reduce her moment of inertia by a factor of about j)es:aju:ic(lr y,fn;g ,5ct 3.5 when changing from the 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 froni +kan2fba5ni(g420 d0nun b 8l)vyom an initial rate of 1.0 rev every 2.0 s to a0n(8b 2uigda 0vln)+i 52f knnob4ya n 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 around a vertical axis 1d4qsjz )5 -t.sbwaaathrough 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. sdw-sa t.4jqa)baz15What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinninqi ) fx :)c*bwniux( y/to9uz.q8+m eug at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of thm)yc7;nxs*e r 7xdv:de 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 mlw w7il7h63btkzu4rvj)n-8gb y/v 5 j21px qe oment of inertia I is dropped onto an identical xuwv tw) 82by6b/lh4rj7l1jg q pn7-v5k ezi3disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4nf: atg3qv r7wsaw(y, jtb49 : $rev/s$ 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 stanu6yf q dsy6u82ds at the center of a rotating merry-go-round platform of s uu2qy6 y8d6fradius 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-roujg)liq-8 b1h gf80f9ci(bolq nd is rotating freely with an angular velocity of 0 b1 ojl0fg)8f ghii8-l(qcbq9.8 $rad/s$ 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 into a white dwarf, losing abm1v8bpa,z s0o out 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 rotation rate be?(round tb 1m,zs pva0o8o 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 involvedfskb ; x*a4r6k.sb +t 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 d (,0e48bohej y e5e6dl aaxk;$ 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,, :gz ko;v6irn initially at rest, that can rotate freely without friction. The moment o6v ,:i;n zgkorf 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 diamet m s+mdcy *f,n5d8hg4ger merry-go-round turntable that is mounte+ n8gc *yhm5df,g4m sdd on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the grra4+n v+8t jh pib1 e,3zgramj9p*3knound 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. Wha v 1 4a3k3r*ppatmn+9 h8rb,+ezijjng t 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 always fac(m 0t(i 04j aw7iphmgnes the Earth. Determine the raagmn(( 0 j4i7mw0h ptitio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from q*tlbn61)cv3t 1 wmlfrest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder lvo*67v y jpv7of radius 0.20 m acquires a rotational rate of from rest ovp7*6yv jvl 7voer 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 cylindrical disks, each of mass hib4:v)sqnb 30.050 kg and diameter 0.075 m, joined by a (concentric) thin) 4vbbih qn:s3 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 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 3uz8el,5pk6c uzojd 35jn-ir 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 timespb wy.p:gd/j37 5hxv6c p+ ijw;j w5ife:rq5t 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 rwdyceq.j p :x+ji p5r5twj/6ip fv ;h: 3gbw57adius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is3 (dg: f vrfw/++bsiiu for it to use energy stored in a heavy rotati+3ig wuf/r f isb+(dv:ng 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 illustrat49yurq tldcg0* * sojzt: 83fbes 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 smx gf8 li/cf/0w5 ,mzhorizontal 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 le-/0tzzve/vc ek./a drngth L can pivot freely (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 accelt/ea c.e /d k-z/0rvvzeration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically o fc jaygnj)v15at() w1n the floor, and we want f )ca(aytjg1v 1wj)n5 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 .vk 2ero (zc:xc2j3f wa flat road is making a turn with a radius The forces acting: jzexcf2wrv3.2k(o c on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of leng /r6bl/ecf hv3 2af/vgz6-gumth 1.5 m and begins whirling the ga/e6c/6 vv23zufl- bh/mfgrrock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin3;b4-bzc uf6y aytntong8eqxe;iw )bv 1y ,*) rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater wittv;x6n),eu4* y wyciboea-qz3f by)bg; nt81h outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindpxp82x g xzk) zhjgm)68.5gbdrical plates, of mass )g5zx6d gxp 8g8pk)h2xz m.bj $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fi-/gdp 15s aw 090p hww1ylqvatg. 8–58. What is the minimum value of the vp/ 9vdwhwws 1tg0l5qp1- 0yaaertical 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, bueg4 csym6 d,+st do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifort g.h,y wf0.6mel llm mp4q)z,mly from 90km/h to 60km/h The tires have 6.gp,,l 04.)etymz mlwmhlfqa diameter 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