A bicycle odometer (which measuren4c- hotkxt,1 s distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch,4 h1kcxtno-t wheels?

Suppose a disk rotates at constant angular velocity. kye gqkjhwa4h48 :8 1gDoes a point on the rim have radial and/or tang1hw e 8k qj:kh4g8ya4gential 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 of the angular vek3bu k-2g+ n(b-co xumvu8d9 qlocity $\omega$ Explain.

Can a small force ever exj-;kn-vx,6i *nukq(frwb8arert a greater torque 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 your hands behind your head tha51ruquko7qv- r7 ger:n when your arms are stretched out in fror -g:r r7quv5q1 7oukent of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprc k 9rfwch0wg()6qj atx3y3l+ockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Wyr3cw9 jk(fl 0+c6g wa 3)xqthhy?

Mammals that depend on being able to run fast have c,i( 3f5czw .xivhbf7slender lower legs with flesh and muscle concentrated high, close to bh f5i,fwz73(cc.v xi the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrucs4:q6ju y3z ow beam?

If the net force on a system is zero, is the net9k- y nv*wujq. torque also zero? If the net torque on a system is zero, nv.uwy q-*9 jkis the net force zero?

Two inclines have the same height but make different angles/cvogm )t9;0rp fwe f- with the horizontal. The s)c p/vfg90;t fro wme-ame 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 g*g3/bi;yehye2 -dsi 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? *yd3hige- ig 2/eysb; Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder 5)mkq3h )v+q h (jys5hrjzv 9 :t84m4m ayhhnqhave the same radius and the same mass. They start from rest at th4nq 8j95 vk+:)r4 jma(yqqhh5m v3 tsmyh)hzhe 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 croa-a *mjp2jcqg:0q 0g nb 68ld91mxangular momentum are conserved. Yet most moving or rotatinclcxg*mo:qg rb0dn62a8-p 9jmj 0 a1qg objects eventually slow down and stop. Explain.

If there were a great migrationsmv8r m-:7 cx+vaf: sp of people toward the Earth’s equator, how would this affect the length of th mp+8:vs- :xvma rf7cse day?

Can the diver of Fig.n69ydt .ulw- e 8–29 do a somersault without having any initial rotation when she leavesn-uyw 9delt.6 the board?

The moment of inertia of a rotating solid disk about an axis through its centl5(,fcsd t(rn er o (dlrsnct5 (f,f mass 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 -y-m9nwg afy it+ly2,in each outstretched hand. If you suddenly drop the masses, will your angular v +-ngyiw9 ,l-a ymtf2yelocity increase, decrease, or stay the same? Explain.

Two spheres look identical)u ev 7dkj4sm5 and have the same mass. However, one is hollow and the other is solid. Describe an experimmed j4v57)u skent to determine which is which.

The angular velocity of a wheel rotating on a horizonta.;d gn gdud3u8l 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 point atgdd ;8udn .g3u the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the m a. cu3;4afpoap4e d2edge of a large freely rotating turntable. What happen2cpmapaed a4 ;f34 .ous if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw izpog dy2o94 k:t 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 direction dko2g9p4o zy: (Fig. 8–36). Explain.

On the basis of the law of conserkw 7 la5;:pucpvation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep t;u7 a:lkpc5p whe helicopter stable.

  Express the following angles in radians: ( ya,.bs72yjeb5,tzkva) 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,qwwphir 0tq *43/dm r-u g5ah because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (w -4 / mtqrhudhp53w qga0,*riin radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at thez c+3fapr2jb+vnq, q2oqp3j 4 Moon, 380,000 km from Earth. The beam diverges at an aorz2qj fa3 pq42 ,cpvjqb 3n++ngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rot+n /*awmyc4 ncm2jmw k1)v4vuate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the vu mc2w) 1nw4m*yn m4kvja /+cblades slow down?    $rad/s^2$

  A child rolls a ball on a au v94biqq, v p)/f1/9 j5jtq5sbskxr level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its dq/bpq5/vq fj u)v5s9 x4akt, b9rsj1 iiameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many rusp8. l50yvli evolutions do the wheels mak0l.s5 piyvlu8e?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates a 6o)ti ,u1dlvs:lqs -g5wlw v7t 2500 rpm. Calculate its angular veloltw7gw) d6-,voq1l5vsu:sil 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 one complete revolup upwaf,9x +-ntion in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m f+ap w9,xu p-fnrom 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 ly*zfwqku d ae1*081othe 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 f o*z* g(fnjo-of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate i0o;c4ob gk2c ll,(d tmf a particle 7.0 cm from the axis of rotation is to expel ;mt 4b,kodlc0ocg2(rience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm t,*xsy10 q 7jb m:ld mdvw7lun0o 280 rpm in 4.0s,n7 l* m:vqu7jw1xddy0 b l0m 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 radiu6wa 5 ifwzk*8gs $R_1$ 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 aboar4zpn*zslp s+une9(nwfldm - kl h;; 9,d the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. u fzmpp-d+s;e,94 s(*l h9znnnllw k;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 rpmoqa7.0(b u 9w8zfigu o in 220 s. Through how many revolutions did it turn in th. f98ug 7ozuqi o0b(wais time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 .q;duwutzgkr3h.z 3( s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirlingo gi; ri01cvn3 “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions begv nr0; io13cifore 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 from 240 rpm to 360 rplji;ubv r;5;(9f w fhom in 6.5 s. How far will a point on the vwr u(jl; fi;95;fbhoedge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is ru2cvma+ cm*zy0r0) tn ynning at 850rev/min It turns 1500 revolutions before a*c+ mycrmv z00yn)t2it 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 reduce zu00(j8irxwa s its speed uniformly from 95km/h to 45km/h Thewu a80i0j zxr( 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 revolutio(x lsjvzudm / y99mr62ns as the car reduces its speed uniformly from 95km/h to 45km/h The tires h y/jrxsmm92 (d 9luzv6ave 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 / wmp.0zx7rq(gh ,olzweight on each pedal when climbing a hill. The pedals rotate inqxg,rzwl /7( mzohp.0 a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm w fga1gbnmd6yv(nxr *kz2vf/ lq2:76 uide. What is the magnitude ofyg 26k 2b*ar1 l(v76zdnuqnf fx/:mvg 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 axle of the; gqgchsgg59 + wheel shown in Fig. 8–39. Assume that a friction torque of ggh9q g5c;sg +0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached t b.l *l ;lic-cf,.v gvxmec,bb3hjqqi901v v:o the ends of a massless rod which pivots as shown in Fig. fcbcbl .e*jvl:vv-;l13,m,9gh iiq cvq.x b 08–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head 7-,ccan cclx7 of an engine require tightening to a torque of 38,7ncc 7lcxac- $m \cdot N$ 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 radihhh7;q9glm7p sac-po-5 c +ia us 0.648 m when the axis of r pa-gph5o-9+i7;q mhacslch7 otation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia oitn iz4bizr,-* s+9 iuf a bicycle wheel 66.7 cm in diameter. The rim and tire ha ziib+ zis,*- 4i9nrtuve a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light vv40y fg3f uuj 8kzi*vek./8zrod is rotated in a horizontal ci 4yg0 8zv /j*zvv3kieuu.k 8ffrcle 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 bowl on a potter’s wheel rotating at constant ang3vzt3 eccemk++2lo(hhl 3s+ u ular speed (Fig. 8–42). The friction force between her handcumz l+v2e3le+s3 3hh+(ck ots 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 plv)k5nx gz y9+oint objects shown in Fig. 8–43 abouv9zxgky5)nl + t
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms wnzjjnjtot /1g6bn3, :+-wxm 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 satellite spinning at thubz nt*5k(pw4pq)hq-e correct rate, engineers fire four tangential rockets as shoht4kupbp*q nq )z- (5wwn in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a ,+vjq6 stne- ka,l avu):vv0*a zzie9radius of 8.50 cm and a mass of 0.580 kg. Calclz a uvt:s*-zka+0e e vv,,q9vij)a6n ulate
(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 batq8 ja u(2e*nk/f:v.jr) ft rpx, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven mer c8rfr qx; tgvuhq39+*ry-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 qrv x3t+ hu8qgfc*;9rradius 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 brolecm-de 38* ut; p.+trjitz-w5cq h8jught uniformly to rest by a frictional to5pcezidr j .lt t8t qu3c-w+e-;8*h mjrque 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 ball a(0iu*)/e fl wiga5+ite uv53oogdq)wt 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, wh3rase mi*,od.ich rotates about the elbow joint under the action of the triceps muscle,adieo3m.* sr, 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 thin rod, as sh,yvjxy/z p2l )own in Fig. 8–4y,jzy)/ lpvx2 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 tv/8,ly( ba wxif*xe/ iwo 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 fourp 9 5br;euyt g(e3+x*aytes n) full turns (revolutions) and r+an*e ;( usryygx3 e )9t5ebtpeleases 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 moment of inertia of 8fg f(sggcu )kiz1d 2w)q-, qc$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque o93 ,k4 rnc n3tujbbc/d5;rmbhx 1de/zf 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.hmxhe0 ;y,(xjf-qvt .3 kg and radius 9.0 cm rolls without slipping down a la-,e.qmv;0fx hty xjh(ne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of fs fqapt)gtv4x(9p y psb7 t4 +gbq9+1the Earth with respect to the Sun as the sum of two +1pbt4ty4vg9q( q bp)97fa+sp sf xtg terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 mu2 o)fs5vt/3w7 f vwalk9i(dq. How much net work is required to accelerate it from rest to adv3f)o fiwlkq 27t /9(au5wsv rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cal0 26; sb cz(ronvff3(zhll ,m and mass 1.80 kg starts from rest and rolls without slipping 6,l (nf;sllfz3rcvz2 o 0hba(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 vertiydxhkdke3 shht81f kypr85m7(f 8*r) cally on its tip. It starts to fall and its rdy15 k8kfx7 )ke(mhhrd ps8hy* t f83lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating onsvq5 b a4qg-74htc,xn-exh1 n the end of a thin string in a -47nb q,hg s nxxct-eq 41a5hvcircle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular moe + w;f/t- yv/oo4h d3ebk-k yyofr7t0mentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 c3+fokw7ve-/f ty 0y 4r e oh-yok/td;bm 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 sb 2pgriw 3tr0/ s/+cmnide, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed o b3pim+st/rgnr2/c w 0f rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the oncxo1p/ ffa4: me shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the strai4 p1o:axm ffc/ght 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 increaseilsj.(bdx )hx+*o1cr her spin rotation rate from an initial rate of 1.0 rev every 2bcxr1ho+ji( xds).l*.0 s to a 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 through its center atq1lfpu.(dt g3gg 5z: )*hmkzjy.j o (j a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the gggoljjfmu k *yt:15zz.(qjd(h.p3)frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of f1id.cuaf+ :ba 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 momentum of t+2nqbd:8 ckrc :(sfy vhe 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 ilm rx*v ((u/s/nm;cejnertia I is dropped onto an identical dxj/;m/r cs* nu (mle(visk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnswj+zb86g**mysny x9 ( scbmw) at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at theeyog,vh0gn5 m ej+ 1t0 center of a rotating merry-go-round platform of radius 3.0 m and momen ne0gm,vh jt5ego+ 1y0t of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freelywdvitm ;(dbov u4s3*: with an angular velocity of 0.8dum i(s:vw;o* dvbt 43 $rad/s$ 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)iq* zr) mpd;i dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radiuip*im zr)) ;dqs. 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 winds in excess of 18dj,3 ittv 3vs20 $km/h$ 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 k1xjhz9h24,-c p5.s e:vn2kky yn h a05gjay j$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate fremjpbr;o 8bi54 ely without fm4;i rp8 b5ojbriction. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a g jxb(dxq8,u 5iev x0 9nda9y+6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a mome90ygb x8d( jexxua, nqdv i9+5nt 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 ground with the end of the rope lyiz3+u *cemdqfbd goq1j*c( ii n z9*l+*ng on the top edge of the spool. A person grabs tzju eo91*qb(d3z*++*cid*f mlg iqcn he end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth s ju:8c gc805kn cvxi.much that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Exccjunc0 g.85 kim :v8arth.)    $\times10^{ -6}$

  A cyclist accelerates from res1p8 *:fk9-6sc dbtnomra o) vwt 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 acquireszt8h)n xapj8d o: y *rx)d:q3v a rotational rate of from rest over a 6.0-s interval at xjdxht:8r na3o)pvd:8*yqz ) constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical dis c5 5qx5yrnq,dks, 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 when it reaches the end of its 1.0-m5 5r dnqxqy5c,-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 angurei4fb tz mchk+/*:u:lar 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 our Sun, but with mass 8.:f;nnvo/tiil2cf ;z. 0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergonftv2.; ci;i:/zfonl 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 low-pollution automob3o vwr43fpo uv;7sin)jf : ;af)drl 8mile 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 uni4f)urjw p ;fm 3a:niv8;rfd7) o3losvform 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 illustratesqkm( o- 8 y k; d3t,nl9;jyzzs-klok.k 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 horizontavjx 0k ( pal/+.3a/x-plmy jgol surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.42;2-uk zzojti e5lb nwtp 6q,e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. Atqjpezb2 l ; 5nt-t,wk64ouiz2 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 standing verticallo4 6ypykc+gu-omcf 28 y on the floor, and we want to exert a horizontal force F at its axle so that it will climb a oyg f-c u6+2pmy8kco 4step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s fbmdq7v + a06tlvcs5-on a flat road is making a turn with a radm5a +fqdvcvb0 ts-l6 7ius The forces acting 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 rockwsy0)ue*f4m/u+ul p x into a sling of length 1.5 m and begins whirling the rock in a nearly / lumywpxfe4)u u*0s +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 solius r ;d:g98:ks jyzs4md cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate thesy r4k9 ;:8j :uszmgsd 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 assemble / oaf6euh e0dtq0z6l9f-w /dy which consists of two cylindrical plates, of fwza60eut/ld hed90/6 -qfoe mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 r bc7ut1n;e / e7ny)qgfadius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of c ;ef)n 7yn qgt7e1/ubthe vertical 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, but do not assume(u h:*l j,ftz*yx 1ek 1ofya*k $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the0.yrpsa 9uq sxa2u)+-gl(u io car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angulau9x o+l(puaqs)air02gu-s.y r 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