A bicycle odometer (which measures distance traveled) is attached 15dsq*.i r6muel b vd(d m62zznear the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch whem16le(5*zbdir2 md6d. vzuqsels?

Suppose a disk rotates at constant angular velocity. Does a poo )tt +-fmvjkq(z 18vnint 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 cat(j n 1zvkq)+ot m8f-vses would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velrf2o, sr8nt9bocity $\omega$ Explain.

Can a small force ever exert a greater torque thv)1-gnb(g rg yy ecs(, (adv4van 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 your hands beh rpj64r i bnr;zxp*8o4ind your head than when your arms are strz8pix6b*r4njr o4 ;rpetched 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 the p83m 9f gvi:uyledal 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 lf8 m9g ivy:3ua large front sprocket? Why?

Mammals that depend on being able to run fast have slender l(u)sx-jz. z(ro bq5yj5o+r xgower 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 masqrx+ 5obgz xj5)zuojs((y.- r s is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narr2 /x9q)ff)ym 9ztclg8a q .gwwow beam?

If the net force on a system is zero, is 7 0vgl 38ejul ww*bvlzlup952 the net torque also zero? If the net torque on a system is zero, ivluw7e vb l0lg9 z23pl 8jw5*us the net force zero?

Two inclines have the same heighnr0av, x n*su/t but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at tx*au ns,v/rn0he bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down 1 .srpa.ga1b zan incline. One sphere has twice the radius and twice the mass of the other. Which rgap1a.1.z sbreaches 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 cylin9i:wuc g.ovyz fmc;52der have the same radius and the same mass. They start from rest at the top of an iumc: 5.zgcf2i v9oy ;wncline. 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 angularzmn ,7tev 4togia,;5e momentum are conserved. Yet most moving or rotating objects eventuallyomai 7tv,5te4en;g,z slow down and stop. Explain.

If there were a greatmirk e9/ya ;8a migration of people toward the Earth’s equator, how would this affectmri9 ka /ae8;y the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any zkdyu/y ;68zr initial rotation whedyu/k6 yz8r ;zn she leaves the board?

The moment of inertia (77ma4lunyac of a rotating solid disk about an axis through its center of mass4( ynluca77ma 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 holdinff+eqj bl3* 0gg a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease,+jbe flq*f3 0g or stay the same? Explain.

Two spheres look identical and have the same mass. How;5knv e2bel:m*)la4q f/qjhhever, one is hollow and the other is solid. Describe h/af m):e* v;e4ql njhk2qlb5an experiment to determine which is which.

The angular velocity of avs))xjfywk, f3eg;wj05 zz n7 wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this p x7kjzzf3gw0 vy,w 5n))sj;feoint at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotati0xxstgb5 o 9+ong turntable. What happens if you wal go+x5b0tso9x k toward the center?

A shortstop may leap into the air to catch a ball and trnf , vz17pn,m+3 h1;ggd,ig w5ixhc jhrow 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 rotazgh 1pghm 1+wd3rj ,,5xvfg ,ic nn;7ite in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of anb-1-gxxh7fnpm4r h( rgular momentum, discuss why a helicopter rbnm-pr1f-g x(h7h 4x 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 angles in radianvkyl* z 7+fzszz.jd ,4s: (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. Calculat;is j51p+jz+p/xzvry jxuo/ y+pdl6/e, using the information inside the Front Cover,d6 ijvz ;yj1/xy /sp+++/j5pl ozrxup the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam7 7v )2u3et:cqn5fb:lpjn qsj diverges at an aqj2b:u5)pln q :ec ntjfv773 sngle $\theta$ (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 ratesdx0/ f(i;dz e 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 asd0 esifxz/(d ; the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anouu (:f0+pioqwther child. If the ball makes 15.0 revolutions, what is i 0:u(i q+puofwts diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many v3ev *u 4dv as :nl7ik:7/x icq*sbnn9revolutions do the wheels mav sv :xknsca 97i4/v nq:n3*e*iubld7ke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpmraoah mc37g + d()o4 yqz:lk4j. Calculate its angular velalrojc kq oy(4g:md+ ah3z7) 4ocity 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-v*7.efbt 8q7mn ,bxw hround makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seat8 vn7fbqhmwt b,x *7e.ed 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 Earth (a) in iv;a/k 0bm bbq9(q/ 0dqwyzyx u3..owwts orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point y fsn/l(0dov8 : 19weuvz;j3*ece ejk
(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 mgx1jfi*f2(k2*x p lw centrifuge rotate if a particle 7.0 cm from the axis of rom** ik2xwpfg1xj2( f ltation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm jxc,+dce lu215 :iez12 rysoo to 280 rpm in 4 + le,2ozeis12rcyc uo1d:5xj.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiusc2io a f 2nivo,b/m;1l $R_1$ 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 spacecraft put themselvexo4nm:z:24 yfv .dzkhs into a slz4f4 .k o d2zh:yvmx:now 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 cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220x1wt ;qunx/ kn9)2, hgpf pli+ s. Through how many revolutions did it tu w)nxq1;9l/k,pxhi +gn2 u ftprn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm i7nahexah/ wdy 6,a7/ tn 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 jetse3jpbnr x ,uk82jl)x2 in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching il22ep x, b)3rxju8n jkts 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 accelerate m-y6lzn y2h8bs uniformly from 240 rpm to 360 rpm in 6.5 s. How far willm b6l-2n8 yzyh a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runnineo aae v,-n lmqo98c zzs+0j ,g5,ht4yg at 850rev/min It turns 1500 revolutions before izq,l89tas,j, c ene-a4h y0zoo+5 gv mt 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 revolutions as the car reducesqmpn6 aym y;gvm );lsu+/m 6d4 its speed uniformly fromgmm;mn+usd 6v64;/ a mlqyp)y 95km/h 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

  The tires of a car make 65 revolutions as the car reduces its speed uniform)fd,y wjc6ko 1ly from 95k)df,w cjky6 1om/h 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 her weight on each peda;:bqb)nfr5y l ygm-r0 l when climbing a hill. The pedals rotate in a circle of radiusnr5:;yy0qr bfbg )-m l 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is the mukwuq li2 o-9 ein-k+4:ajff+agnitude of the torque if the force is exerted 2wkl :n++eqfaj- oi-4f9kuiu
(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. 8–3a;6 v 9rhv:ymjb /hxw7/h(olk9. Assume that a frictiovovhm (lkr:h6yhx/b 7 wa 9j/;n 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 enj-zzb , oxbjh3v*c9do/ub:2pds 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 ofb v: 9bo/z3 2dc -u,bojzpj*xh the net torque on this system.

  The bolts on the cylinder head of a0v 3kjwpn.lq)u ytl06s 9 noy:n engine require tightening to a torque of 38 69sp0 :.tloy nkjwvuyqn )l03$m \cdot N$ 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 sca:t 3+bzya50.648 m when the axis of ro ya+zab5:3st ctation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of 45xilf lki uu 3+fg064zq) dppa bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.4x4 +izli5 g3lq0ukdu)6fp fp25 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 i4gtj9zo)myt) k )-eyon a horizontal circle of radius 1.2 m. Calculazm k oy4j)eo-t9 )y)gtte
(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 l,2ql qw; m7 j-smxj: wxr0p1ka potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her ha,lx7j1-xjm wl0r :k;sqq mw2pnds 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 j ef n5yb)0jtpbnq0i8 xxb/,9array of point objects shown in Fig. 8–43 abqtbb)i8 jpjx9yx/bne ,050fnout
(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 co7gqv7-2+mqzy0x4jmiinz . - g8v ax nensists 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 cylindrical sate h-qa ,m20 x7yhhzdjv9.nfm5l llite 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 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 mih,zv 2fj 9yhm5.mlx- 0q dnah7n? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radf0.z.phb+ v3nl 9pnjuius of 8.50 cm and a mass of 0.580v0 .bhjnfnl.9p3z + pu 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, accwj udt7i7;1acelerating 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-driveh +fm-v 2 +g74k7j2mflg tompfn 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 f2-v tjfl g24om+fm+ g khm7p7a 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 +94vgetmn )jxg/8wis shut off and is eventually brought uniforg/)+n9 tse j8gxi4vw mmly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg balle2/x,kz ta dewkt5u 35 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 t xid (3/8ybkgghe action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The baldk8b/ xg yig3(l 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 b k 4h6j s+wuc2(k2tyhae considered a long thin rod, as shown in Fig. 8–46ty2 c huw4k (2aj6sh+k.
(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 con gm)(ggzfoa (ea3e:p 0sists 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 hamme- (yijfqzrw up9agx13/lv/ /9 vcdk6p r from rest within four full turns (revolutions) and releases ik9lw i( g-dav 6pfc// r /9x3vzq1puyjt 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 of i:,cqv( d)*l:e tnasjwnertia 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 develop1htnqo n,9l/ n(wr5q ds 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 rolls without slipping/,glcq0qw 14uq;i tws down a lanqsw/uq0 lq,c1;wtg4i e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun3 3py+/q vth+ wldn4hy as the sum of two terms, q+hh+v/lpw ny3yd34t
(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 rq q-, j jbxhgr048rb7sadius of 7.50 m. How much net work is re7jxsh,rb gqq0-b 84 jrquired to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 2 wj h rtm7+ew18.yzum.b18 lum0.0 cm and mass 1.80 kg starts from rest and rolls without slippz 7rwut h. l+ju8e8my.b1m w1ming 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 vertic ,fnmv/lo 1-)zi+srp,h 2fwv yally on its tip. It 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 ground? [Hint: Use csnf/ov-w,2 plz v)h,1fmy r+ionservation of energy.]    $m/s$

  What is the angular momentum of a 0.spy p 5bpu;riem+vqxd;;/ s-7a/ q0iv210-kg ball rotating on the end of a thin string in a circle of radius 1.10; sbu qym; dvr;/75q/s i-xvp0ap pe+i m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of flk2* g cww9k:ps-6it a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at :i-wkpkws6 l29*gcf t1500 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 at2gw 3i+l b k,lq/x*ydpdbl 6f5 his side, on a platform that is rotating at a rate of 1.3rev/s If hed/,*5wkgq dll 263+fy lbix pb 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 o l(w4qtirjq;,:z;0qafpk :6+ dlqop fne shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her anrfpqlp, zl4a+o 0::kqq;ftwq 6dj( ;igular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin ro.do:d8p7af9rud;/4db.w n n;s pgcmttation rate from an initial rate of 1.0 rev every 2.0 s to 4:drcdw.;m ;9 sdpob n8d p7/ngt a.ufa 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 v mb ptm; z0yj5f1o6v(v:/zkdl)dao6p,gy o+w ertical 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 ofko6dvl 0+ /wygvo)jp5p,:o a;b( dmyz m6ft1z the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular mgdj(a 9w9q-s ie:0/bc.itec aomentum 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 angular moment ( xtn(:xpme3: oqnp.aum 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 aj1co*pheq85r k1:qqdropped onto an identical d:15p8qjaec 1 roqkq* hisk 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. m8xyr6 v8eg+prd1v 5q4 $rev/s$ 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 rotatingx+yr55 h(c in1qmm yng+ gcmhl;4kq( q768i uu merry-go-round platform of radius yqih4li k1+xc cq n75r8um+ny5qhg 6ugmm( (;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-rou6f.-5 a)gdsduf c e3imnd is rotating freely with an angular velocity of 05ic. 6d3mdea s)g-f uf.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 whi/aum e7j7/u8xsu5+kdkix p9tte dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest 7i/tu e mjk58pa k s9+/dxuxu7integer)$\approx$    $rad/s$ (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 winds in ex/8cf/hv xs1 wo;prf,7tn6bcccess 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 (/jy rt1 +-u dlbpcbynp,dr0*$ 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 rege bp)m:qw7u/ 4i7nmgst, that can rotate freely without friction. The moment onb77wmg4q mgp ei u):/f 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 th(lafxb5 e*l, aiw)x y)my vy46e edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment ol)f () iyv,b5lmywaay4x ex*6f 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 ground with the efo a6kgy h7 9uy ensvy/8/gg43nd of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distanc/nyh/os9eg guaygyv 34 68f7k e 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 such that the same side always faces the Earth. Detec,j :emj)hhw+: , v9stc+z jrsrmine t,,+h cvwjjm+:rt9cjezs): hs he ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates froe1iub y6jg;8z 0mdloga1 mii11 9y, ctm 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 radiusgf3- :p5x ms7sh,j vxvp evr hl:)v91g 0.20 m acquires a rotational rate of from rest o73sr 1gp ,vv se gx9h5l:vvhj:fmxp)-ver 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 solim5(jc(m p8ef3 n8yfqihex39 cd cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo whenmj( cec3m hiyqf89f 5 (x38pen 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 angoh +a3:o 4vysztmv*2w ular speed 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 lqt a:p7(flcds02o3 j our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days7lcp j l3safdoq0:2t (. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a lowtpd* 4,0xlsxu86)atc4 uqvfo-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should a8q,x x6cso t 4 *puutf)vl0d4be 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 illustratep0*j/ *6 v 2va,vvwzkuic yz7os 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 (hoopihl s0kcyqqmj 0/w+ 3nc1o4 0h) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can3s9f 8, fp)6j9pmmb:lnu3:8ulwv 8sp yxudhz 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 acceleration of the tip of the rod. Assume that the force ofz3hblu:p8 fj yun: up9 pl)8v3f 9s dw,xmsm68 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 on the floor, and we w7p(i8g f hyxh gc7)-vjant to exert a horizontal force F at its axle so that it will climb a step against wjp(fvc7x7 8hi)hy-g ghich it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a ke, v8vq):vk qm(kz p(turn with a radius The forces acting on the cyclist and cycle are the n , (k(vzm8qvk)pekq v:ormal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length fp011i bp3.p6 lgivjf1.5 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. Whatvpp. g p31 ibjf1ilf60 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 thin hc 2ce -cz7h*wrods, making 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 hc7- w*z hecc2her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, of9m*er pp4k;nk9y7 zi v mass 7;z k 99ynivpmep*kr4 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roljdl4cq7efb /oq(f8,wu v8 iw (ls 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 witho 87cfwqewj,vqo(4d/b(l8 f iuut leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume mnv- s/4c* vic$r\ll R$ h =    (R-r)

  The tires of a car make 85 revo ff)bc,wsw74:mh ykn8 lutions as the car reduces its speed uniformly from 9cw:fnhw8 y ,bfks)4m70km/h to 60km/h The tires have a 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