A bicycle odometer (which measures dist73t (j n /xpvc(-md);xz0tfv)xkhr yxance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happen) xx3phn)f m;v0/xyt7c rjx-zv (( dtks if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poin/.swd gnt:1*nzb yl c iqa4/1 oudq8v0t 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 wdq 4z8lcn1 yqtg.n isb:*/v0ud/1 aowould the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single f w eh:-9hg(wu9* odim5af;zy value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a ly:.yk29 56x*o ;u p huuskvhyvarger force? Explain.

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

Why is it more difficult to do a sit-up with your hands beh4+nw/a;qdcjlrvk 9ry/ *zs 7d; og9 toind your head than when your arms are stretched out in frontsd; ; kly9t/c7ng*doa/q+4 r o9rwjz v of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pe3 lg 6p v/03eyi;teccedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? gle6ite/p;c3 y0 3v ceIn which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on beinf, f69, sw zcttxkl2trnw+:9qg able 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 whytq6 f 9rtnz, wfw2t:c+,xlks9 this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry mvrp0 aa338aj(j xp4fa long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If th5m9r*hkts n(d e net torque on anm5r*t9 sk(hd system is zero, is the net force zero?

Two inclines have the same height but make different angles with the sh8ir.+cdf 0yvg gl16 horizontal. The same0 1ysrifhg8.g+lv dc6 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 rolling (from rest) down an ipuh 7(c lsj;volro8bd-j7f a./ zer 34ncline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has thez-lr j o aed7;4 bcoju87rslvh.( /f3p greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have + 0h. xd7tz;n.zvxl vrthe same radius and the same mass. They start from rest at thdlrhv+v. t.0x n xzz7;e 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 and angular momentum are con;q34 ys he;p- b, e7olumsku3fserved. Yet most moving or rotating objects eventually slow down u; ps33lf4-kusme he;q,b 7oy and stop. Explain.

If there were a great migration4*7qhx0 2pwb r h;koob of people toward the Earth’s equator, how would this affect the length of the day 0w*h2 b;r7pq bokhx4o?

Can the diver of Fig. 8–29 do a somersault without having kxm)m*- (n. ulek tp1eany initial rotation when she leaves the bo (l-)k1x*eentmu pkm.ard?

The moment of inertia of a rotating soln6 bhsplp g5i9iz:*)b (lt,oj id disk about an axis through its center of mn(pp:bgli hb9s lzto 6i 5)j,*ass 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 .:uqfwdyw p8,each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, de8:p wu,fdw.yq crease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, o,lye:w 0 ,-;rypskvnha*9nyaz0 g e- rne is hollow and the other is solid. Describe ae 0;yenr*-9 a,w zhg,l0v pkrya:s- ynn experiment to determine which is which.

The angular velocity of a wtr+kk)7irj, xjxvqc ,4j(pr: heel rotating on a horizontal axle points west. In what direction is the linear velocity o,) ,r r7:rkvi (4kjq xtjxjcp+f 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 freely rotdd zd,aw-e/.l ating turntable. What happens if you walk toward thea/ewdd.-dl,z center?

A shortstop may leap into the avs9h;:/*k1vzilyun xk1 ym,sir to catch 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 legs rotate in the opposite directio*y/sl,ys 1x: 9k1;znmhkivvun (Fig. 8–36). Explain.

On the basis of the law of conservation of angul4(soy 3 7zi7zwt3 lr +pw.ljwxar momentum, discuss why a helicopter must have 3jlt4 7p 3 wzzs l7xywrw+oi.(more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a)tao9 ih3zqo2+x ,lb )h 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 c/ qw;8ovb ;nqpoincidence. Calculate, using the information inside t 8 obq/q;nvp;whe Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Mooo*i3l4a -7lh :i 97atkhmq hn c0vnhg*n, 380,000 km from Earth. The beam diverges at an angh h i**9ah0 n7mvh7gt3:a 4co k-illqnle $\theta$ (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. When the motor is tf x3 ;5hqo/opkurned off during oo;k x53pqof h/peration, 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 balrb tt-0k8oz 2ll makes 15.0 revolulbt- 02tzk8 ortions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter 7kvdj.1g e3er travels 8.0 km. How many revolutions do the whrd7 e3 ej.kvg1eels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angqmv37h: 0m bux 8wk8igular velockg8b:0ix qhvm38m7w u ity 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 4.04lr)-j x,gu )ej*cb km s (Fig. 8–38). (a) What is tbr)uj,le)4xck*g- m jhe linear 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 Em-6 wghxk s66frs 7z29rewq0garth (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 point4+km/oj i ir0b.girr 4
(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 the axis ofc,xl;mvsfotn3 9/ 4xs rotationx4lv tno3c9,x;ss/fm is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 28dvvtm (d9yf, 60 rpm in 4.0dmv(6 9t,yfvd 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 radiusj59 zo wd,l5th2lejohd38j 5 a $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecrafv1;t zxu-huj1 1x x8okt 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 mio1 zv uuxkx h1x8-;t1jnute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to2yi ol3jnupz2d4cb85luv du*8 -b(ey 15,000 rpm in 220 s. Through how many revolutions did it turn 4bd(2vj3 eu*ubpy8uli c -o82ldnyz5 in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculatmxjvt5x -nc, 9e
(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 whirling “huv.tyao 21 3ehchqw(b8 man centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its finqb1 (oyeh 3a w8v2th.cal 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 36fc6l.hjz z4 kw2. 7kgd0 rpm in 6.5 s. How far will a point on the edge of the wheel have trzg kh.6wkj.zlcf2d4 7 aveled in this time?    m

  A cooling fan is turned off when it is run :tym: tf+hve. eg8rooi 3 85tjo63rjrning at 850rev/min It turns 1500 revolutions before o.rt8y+8 v6:hjg3trer em :ft oj5i3oit comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 htc)rh k g,z))i,ej f7revolutions as the car reduces its speed uniformly from 95km/h t ,fkg)j,rihh ez t))c7o 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unl,q (dr9u)gk5x(er - 9ivzc-mxd4 kxr iformly from 95km/h-x 9umd zel)r r-kdqvxg, xi(95 r(kc4 to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all:8 ddotf xk yo.,rs r,kq13p0m her weight on each pedal when climbing a hill. The pedad. d yos1r0pfmr3o ,8q:k,k xtls 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 thebvzi7txs/u *ngwo)k/ l f3y51 end of a door 74 cm wide. What is the magnitude /y 7gw* 3/zt kufbi)n1ovs5xl of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axl fdua3 0zc5.(3dev phhe of the wheel shown in Fig. 8–39. Assume that a(cz upd5 v0a.e3f3h dh friction 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 masslessfdf / +* .rf.i9xndcgn 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 ic*x.nf fgdnr.+/ f d9this system.

  The bolts on the cylinder head of an engine require tightening to a torq-y3n3iuh5 o9lx:jh l que of 38 yl:3 xin9-jh3oqu5l h $m \cdot N$ 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 momentbqwr32ho.*i w *m ree- of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is r eq2m* rb .3eh-ow*iwthrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rim.zno8 -iaj(d.9gb tshjfd ab0z9+5h s and tire have a combined mass of 1.25 kgh( a9z9 .hnf-0b.a s+8dj o5isjztgbd. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball o zhh(:i+ej;l jn the end of a thin, light rod is rotated in a horizontal ci ilh:+;zjhj e(rcle of 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 bowusf yk1m8/6vr l on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force betweemyurfv s 18k6/n 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 the array of point objects shown in6+ao5j1 h- o3alz.j lin9 8.apnvtwwd Fig. 8–43 about .8awa 1lnwaoi p+ 9jdz n5-6j.t lhov3
(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 conshw+3fg7x i9ulg)t ld*ists 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, unifore8 ,-ub7 idii*ukh t;;o( ullgm cylindrical satellite spinning at the correct rate, engineers fire fouol7;t uul(d;b *g8 ieuikh-i, r tangential rockets 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 unifor- fjo7qhenc4(lm/f (um cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calcue4uf ( 7m-qjh(col/f nlate
(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 dv 0kjg.ialru+ d1wbb(9be( / 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 hadea*4lp(c +0y eux-k zn*ttb2 nd-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+ uncykzax -e4**blt td02pe ( 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 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 broughtyl+ rb5g,j6 r d;k2g6l,p oyf1ga2lbx uniformly to rest by a frictional torque o,lgdpr;bao , 22b yl1 ykg x65jlr+fg6f 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 acceln,y)ly- :viw verates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm,,8 exwy ,agio 0o/ve,a which rotates about the elbow joi8aoaxi,o , /wg0,yevent 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 th(8tmzos hg zo5:sn1f9in rod, as shown in Fig. 8–46f9 ( tszo:moh1 5sn8zg.
(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 k oqzv858 4i+m qvuw 5 n)/5yw:,dygbdr(ttxk of 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 9+bp t;;b okzqr33nlshammer from rest within four full turns (revolul;3bnr;s9 +bk qz tpo3tions) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a m x;oj.1t 1hr4lf95rgx yz bhs:oment 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 280 2tv6/u*xa199s aerow cjr t4 9zmb*ew $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg anlc(dede5 4(qut9fr+ jd radius 9.0 cm rolls without slipping down a lane (u(e9j +r qtelf 5dcd4at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth ll 9vsnso/73gwith respect to the Sun as the sum of two term7l3n9s l go/svs,
(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 a 56(vnog9v+ up6sevp n3c,sg qnd a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 renve quvpsv 3gg+ 6o59csn(6p, volution 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 w0 c: 4hwfkx;ct()iev kithout slvt4:; )wx(ciefk 0h ckipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall;emfy3j.jp) dayl 35gghec,qep5m . : and its lower end does not slip. What will be the speed of the upper end of 3m5y,j53y;p.cee jda emqp:l )h gfg.the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular myfnew o 1(7b9s7 )jfxiomentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m af fe(jn os x)i71y9wb7t an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cj)y dczy*11 ))1 yne uyzpqc4nylindrical grinding wheel of radid)n1p4)yycycjn)q zue1yz1 *us 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 t/t2;facsp n-8 tyhj y5hat is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, th/ftjs pan;th5-c 8yy 2e 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 in Fig. 8–29) can resnee/3-czjycbzm s 3 1w j/s(6duce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If shec e1zjm/c-3 (ysjzss/36w ben 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 fr2,56 q+wp ,dk8a8a wwt ytzmshom an initial rate of 1.0 rev every 2.0 s to a fidt88 5qs2wtw am p 6hk,+w,yaznal 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 vertirr 6+/pwxz-ye n+z0wqcal axis through its center at a frequency of 1.5rev/s The wheel care ++qy0px-n6 zrz/wwn 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 momentum of a ye0ld68yrf a+ifu vtool -g8 ji*)5r6 figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular moment2y)m: xjfmlrq q,8pu4um 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 cylindrica0c(i 1zf/pqwv j9 znl0l disk of moment of inertia I is dropped onto an identical diw9qvj/c 0ln(p0 z1fzisk 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 2.48 h x3zo0khqeqz+as+ (cw(el 9 $rev/s$ 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 a rotating merry-go-dxyh50j*b 5ne round platform of radius 3.0 m and moment of inern*dyh jb 5x05etia 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 freelb1kr /8h r8vxv +spk:e izfm(1y with an angular velocity of 0b vi1ps: rk 1kv/+me8x hfz(r8.8 $rad/s$ 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 even2etjc 7 uy,c-a3iz*cy tually collapses into a white dwarf, losing about half its mass in the process, and winding up witui2 y*je7-tac, cyz 3ch 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 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 wi(ed o*g22t p5al;wjs3w nap)ends 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 2qveb0m94sd1e. e vz,y *jya r+pf z4i$ 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 caneb*d(ik s5mz* rotate freely without friction. The moment of inertia of the m(5z b*s*di ekperson 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.ic4oecq/o *pidx0a6h . ,dj4v5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a momentd/h,ooi*4 6.cdx0p qacji4 ve 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 thzy13;7.)cxh mb-pw)zlb )i lub av k7ye ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distac7luhwza i) )kmp 7lb. b3y1 ;x)-zybvnce 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 spool’s center of mass move?

  The Moon orbits the Earth sue,anh n1ngj0b4.k lyw(t )cv5 ch that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (ab (04h n,ltyk5b1) wnnagj.vc eout 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, j;:hmpljnabbh4x2 j 4*kmby.7-nvy from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquphnzvat ej,l.82g04 bires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calcu0l zjpe bv2t8a.n4gh,late the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical)l0zhqje wh:3 disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindricae03lzqjh :)h wl 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 sp hrz-qnhvj d;1rvh;65eed of the 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 times as great, were rzrgetw(1p- , i ,+ salm7:,ugrq;mz sfotating 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 the1:mzus gg,f a pwirlqte-z m ,(r7+;s, 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 is for it to u 2amkk1l1. okwd;7ytlse energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter awm7 l kky;2td.1lko11.50 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 anek1p;zc1 s7mn $H_2O$ 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 horizontal surface at speed v=3.whj b/nkch) 8 a3e+-k9xt1bm e3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore fric knhi eo,)/k4stion) about a hinge attached to a wanih)/ok, k4se ll, 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 R. It is sta,w)wj ym;flr 9nding vertically on the floor, and we want to exert a wl; j,wmrfy) 9horizontal 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(kt-r t1)z lqv,4 sity is making a turn with a radius The forces tq)z (i1 tvl-k4syt,racting 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-ksn3jcg4 u4 hqu(r x(v4g 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 s. What is the torque required to achieve this feat, and where does the tor4ujqrx((vhgc 4u34 n sque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylindt+autref1k:/3 -l y urer and her arms as thin rods, makin+y-31r: fae rltuut/k g reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of glkr 4()f ablt566 mytn yo+0ktwo cylindrical plates, of mf6l b40tytyg +k56 ako)rn (mlass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 zyba;tp zuj v2(k71,tw0 v/yvthe looped rough track of Fig. 8–58. What is the minimum value of the vertical heightpv(vj/0,1 y7t ka t2vuzz;b yw 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, but do not assz/ud98 ce+h- ite 7uafume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed ubys7z 8t2dukls-d0+ t niformly from 90km/h to 60km/h The tires have a di7 ysls b+8 kdzdt2t0-uameter 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