A bicycle odometer (which measures distance traveled) is attached near the whex59df -+il6o3e why stel hub and is designed for 27-inch wheels. What happens if you use it on a bicy-xhs3f9 tw6y +e ol5dicle with 24-inch wheels?

Suppose a disk rotates at constant angular vjlqz-2rno 0q ha9+2 jp- x.cijelocity. Does a point 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 wouoz qihj2 .la+ pr--q0j92nxcj ld the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of thc6vm ,ovs yi7 vbnpxh ./c)y*/e angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Ex oe7;jos ibqs/b,2g;splain.

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-ugjz4w7ei rm ke0+bvgop ) c746p with your hands behind your head than when your arms are stretched out in front of you? A diagram may help y4ke6gm rgc e4owz )i 7+7pvj0bou to answer this.

A 21-speed bicycle has seven sprockets at the rear whe zs1it.l8bf;y 4nhkn9 el 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 8. t49ysnblhkfin z;1 front sprocket or a large front sprocket? Why?

Mammals that depend on(xiw: qqi*z2a being able to run fast have slender lower legs with flesh and w(aix qq2:z *imuscle concentrated high, close to 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) n 1qz7fb0z2 4p0v inficarry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net vx)dxao /8.q btorque on a sy v/ axqxb)o8.dstem is zero, is the net force zero?

Two inclines have the same height but make dif -6xj9f -.fonrf nj7fxferent angles with the horizontal.ffo. nrf7xjxj9- 6f n- The same 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 et9cvv- /rtq r 4go/cn9xz 2nx2s z,)gstart rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Whichc2n, 2eqzsn- 9gtg)v/xt r4cr v/oz9x reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same ht(p5q + pk 2uyt(-kxeradius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first?xtt2 p+hypku 5q( -(ke 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 conservet9 i 9gtot3kp0h1y fkiw.ey s2jr q009d. Yet most moving or rotating objects eventually slow down and stop. hoy9k0 fpt qg29kty s3eiit0 .r091wjExplain.

If there were a great migration of people toward the Earth’s i)phu88 ,,yjp mt i,nuequator, how would this affect the i iu8pm j8 )uh,p,,ntylength of the day?

Can the diver of Fig. 8– cl2-v7sp2o-xuzt,v w29 do a somersault without having any initial rotation wvvosuc2 pxl, 2ztw -7-hen she leaves the board?

The moment of inertia of a rucc eehhh17:o0 x9n2hotating solid disk about an axis through its center :eh1h9 o2xch7 nu0ch eof 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 s+m 3 3h2ngv8p y,xy1r- sd)wtkqkmabo-o(q (mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Expltwx rh p-mo ,y 8qg3dv(2y+akbq ms)os3 (k1n-ain.

Two spheres look identical and have the same ome6oirf) z(5mass. However, one is hollow and the r5o6mf z i)o(eother is solid. Describe an experiment to determine which is which.

The angular velocitylhd/ qz6 36m iraluvf02;px0* -tvrcz of a wheel rotating on a horizontal axle points west. In what direction is v/63lc2z*0pq hlrix muz vdt-;rf60a 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 at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large zpnmahdkn)b3b(12 ,0)1omlifiv u.bfreely rotating turntable. What happens if you walk toward the 10nzu2f(b 1o )m.k hbmb)nl v3p,diiacenter?

A shortstop may leap into the air to;etuu ljy jy+kt:d)*6 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 htj*6yuk :+ye; u )tljdis hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conse p: n6r yvr;dc8onk7 tyqf49j8rvation of angular momentum, discuss why a helicopter must have more than one rotor (or propeo6 7nq j48ky v r;ftp9c8yr:dnller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (zv azs7cplzsd di9w d (3:x4m*d+;(pba) 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. Calculate, us*pjw+;,emi da ing the information inside the Front Cover, the angular diameters (in radiaa mdje;*+i,w pns) 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 beam diverges :+ wlglm738rn tz (q:hr)bzcp at an (nt+ p3lzw::qzr bmh7l)c8gr angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. Wh.bm .e,9dfhwzen the motor is turned off during operation, the blades slow to rest in 3.0 s. What is th9bhz, m.fd.w ee angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m82v+mxcv b7deo1 *xj(c eo.iz to another child. If the ball makes 15.0 revolutions, what v.joeb2vecxozc(+m87d1 x* iis its diameter?    m

  A bicycle with tires 68 cm in diameter travek; p ;1xnrhc+ayl-r3k agg,(rls 8.0 km. How many revolutions do theglra( h; nk-ra1xk+y,c p3rg; wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2 y1 287iqdngwe500 rpm. Calculate its angular veloci ied8 n71wg2qyty 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 4.0 s (Fig. 8–i-u kt4v pgjz*-)j:ud 38). (a) Wha*4 kjtudiv- u gjzp:)-t is the 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 Earth (a) in its orbit aroy; k s+l,y tnniqq)m9*und the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poinkd re vx7n*a7*w:b7dd t
(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 7v/ie c2gwdnt3 * eq(iparticle 7.0 cm from the axis of rotation is to n e (iv37c dwiq/t2eg*experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniforml+ap/gy 4 czi d*nyx6i,y about its center from 130 rpm to 280 rpm in 4.0 s. Determi iy xd z+pgi,y6n*a4/cne
(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 radiu25m,jws wcshua88 ,gbtk 47 nvs $R_1$ 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 to( y/bgay0tj 1hemselves into a slow rotation to distribute the Sun’s energy ejy 1atyg/o(b0 venly. 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 tcizh6 7s. ks*y1qzq8 15,000 rpm in 220 s. Through how many revolutions did it turn in 8sc.t6hsz iyq* zk71qthis time?    $rev$

  An automobile engine slows downn +i;3ru9lifl8w ;kon from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed je*7 v(ghkg8fodb+h 2r 2sjcpt 9ts in a whirling “huma coh+bf grk2sphv(g9 d8 j7*2tn centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter acck f mwxn b16b(zcq9s0 l97 xorm,:j.kcelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time,01jb r mskkf(:7onbw9xm69cxz qc. l?    m

  A cooling fan is turned off when it is running at 850b qrto;-f .hu0t0 t-+:-hsi 6huuftnerev/min It turns 1500 revolutions before it comes to a stop.oih- -0su+0bqtntthf u.6;- r ft h:ue
(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 revolutionso* :6io0na9 afrb *xdl -1wmiy as the car reduces its speed uniformly from 95kmy:-n9ilwo a *d0a 1mofb6ri* x/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 revol8bvhp i4erre*0;g h 5zlgx+v.utions as the car reduces its speed uniformly from 95km/h to 45km/h The tir hlr;.0e g4iphb58*xegvrz+ v es 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 pedals82 ya, s5pfjx*fu,wr when climbing a hill. The pedals rotate in a circle,5j,*yp8uffx s w2sra 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)p, g1 jckekm;;bnpk2n49mcj door 74 cm wide. What is the magnitude of the torque if the force is exert,k) pc 1jc;g k bknmpenm;29j4ed
(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 wx-v7dsgk7mns;5.djzi.kjpd5a h 7 c) 6o 6zjgheel shown in Fig. 8–39. Assume that a f xag.-ds )zhp.d7oj66cgn mj ;vkd75i7sjkz5 riction 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 ls 07vf3 wpw(bpt-pj8g2+ern to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is(l n7tr8-bsp ev32wf w+pjgp0 held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of 12ws . a5rclbvcl)3sj38sj la3sr)w 1vl 5.2cbc $m \cdot N$ 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)+.cdm+vk7xp;w t(y:uxgeo y of radius 0.648 m when the axis of rotation is t+m uov xyyxt7e(gw. cd +:;)pkhrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in di+ q(rodlcmzz 1e d+5n mo*-/xn9tzyt )ameter. The rim and tire have a combi9z oz 1x(+tqczty*ndremn)dm o-+ 5/ lned 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,w agr ki41fs78ndn06w light rod is rotated in a horizontal circle of radius 1.2 m. Ca isfr 084nadnw 1wgk76lculate
(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 /sm 1 nn exvsp5blf/kh9ok :x-2 /-wsdat constant angular speed (Fig. 8–42). The friction force betwen s /e9k2/slf-hx -5:vxkw/op sbm1nden 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 point1- vkpgg6t4o u objects shown in Fig. 8–43 aboug14o6 kv tupg-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 consis zhgat2+q02 a39i9hex*uapj vts 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 satellite spinnijl4 a rtcm(*cuo/h(b)ng 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 rc4/m)lb j( ao(*h uctrocket 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 c t+zlsq57m(gbylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculatst(ml75q+ gbze
(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, acceleu6gs )i 74g, o dpa1+ahookh5wrating 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 merrbd ;xmnm-* i*k8monq7sp*:j my-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 un**- *xm idnmb8n m;spoj qm7k:iform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at i63q3j,vvau1d)d;fu) wr fxq 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 13qfx6 ;wq d d)v3)u,rj1fvuia.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 an;4bppc 4v,a:d*xy f8a b2kb pccelerates 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 baw( .n a:u3biy1+w hvisll is thrown solely by the action of the forearm, which rotates about the elbow joint under the+: ibuhv 3n(a i1.wswy 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 thin rod, as shown in Fig. 8–k a/d6+5owmfe 46. 6a k/+m5wfdeo
(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 consid0cecen6 lc h7jk .1g j c3b85rpxxfd:5n6rx 8sts 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 hammer from rest within four full turns (revo7b9 c;i:olz z0uud4ou lutions) u04zb;i9o:cuz l7udo 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 moment of inertiaeqy4bk96y w6vg/r 1h. vos:xg 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 torquemr9b +av n8(n2mnzq /m 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 slippc6b3v0-2gy3 yqp gez e:t/t raing down a lanerqp-baz2 gce6y :3 3et 0v/ygt at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun7xmp+8 rfm ily.ver:) as the sum of two ter7. v+imlrmf) er:xyp8ms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How k6) yd/ p*fskemuch net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per p/dsyfk) *k6e8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm(u/s5.wx*g 6 twd.imxmj 6pnd and mass 1.80 kg starts from rest and rolls without slipping dow5xw6i6.n j m sp. wg*umt(dd/xn 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 6zctnmfraf5vt 8w 6) .h+pki(k,e/ gbstarts 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 conservbc)iwkekv zagmfh8.nrp /+t6, tf56(ation of energy.]    $m/s$

  What is the angular 20ikdvadb./ umomentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.12vu kbida/d0.0 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindingip6 o xen7qpr,*a-t6p wheel of radius7pn i*,oe6-aq xtrp 6p 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate o rk.cia7/jqb;f 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreasejcq ai br/7;k.s 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 redc;(yh3 ux1iq65 ys esauce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tucu qhx5 1ei;sa(yc 3s6yk position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of 1.08. 9 e9z-4rdsgejfl lh rev every 2.0 s lh9 d e.e -jlf9zg4sr8to 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 o:;y cd j)hu0kcenter at a frequency of 1.5rev/s The wheel can be cony;o)cd j0uk :hsidered 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 m ;kvvu9b25jg,tz ll mz2v59kuomentum 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 momef2)8fypwv(sba; -rt*j8 yfdm ntum 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 moxp o7y s5t0;ghl(3hk kment of inertia I is dropped onto an identical dilhp x7(skto;3 ky0gh5 sk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atuy25chhtyoa,:4 r en / 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center ow mgba /p z-htox )vwe83h09w-f a rotating merry-go-round platform of radius 3.0 m and moment of inertia 920 b-0 )w9gheh a x8w3t/oz-vwpm $kg \cdot m^2$ 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 freely with an a )fo4 9v:rhuq (rij*zsngular velocity of 0.8 hqjfo4 *u v)sir: 9zr($rad/s$ 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 dw. f2rr j7qju 0kpq*o,narf, losing about half its mass in t0r2j qpjfqr7uo*kn,.he 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 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 1p4 ; ub jy,hmyg(la6vtr.z+3i20 $km/h$ 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 l 4qib19 fi n3bg2vn-i$ 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 platfoz8 dca*zu kf0boo ,j)2rm, initially at rest, that can rotate freely without friction. The mo0zj ,d8k *abzco2fo)ument 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 m1x)j9l( xpohn .lz s6of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment o zsl(9xmop lj )16hnx.f 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 rop.wmqgla ,qa c7 dbk:-:e lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the peq:-mlbac wdg:7 .,akqrson 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 Eart967trz* jppmxeb s/ f7h. Determine the ratio of the Moon’s spin angular momentum (about its own axe7rt9 jpb6mx*pfz/ s7is) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from r a;zs60 e;w,glm,lek hest 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 cy duh99 vqk17ywoq91xylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s9y9qu9h1 qwov 1yxd7k interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and di;px8 7 2yzkxmktu6,j)y xq9atameter 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 thezxax2 y, u)mpt jykxt6789k;q 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 an6j* ogf 5mitt:,-fz 4gme2ln p 8fq r17hyn/nqgular 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 8.0 times as great, werrlzm (isnnvsjoh-x/o .44* x8e rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what w lm -x/zx4inoj*8ssh(4v .onrould 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-pollw .w k;pc;wn*sution 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 be able to travel 350 km without nesp;wk wn;w c*.eding 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 an2xfpwub6 i81 s 1*zlhufa1:nr $H_2O$ 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 0q0ll/l.hcvp 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 c4b3gkd aszbfma 5y28w4bcf9ac 4;d x9an 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 of gravity acts at the center of mass of the rod, as shown. f9kd4ba4b38z cy dsc4 x g5fw9ba ;ma2[Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It iskido-ec 58q ghszwp)o s8++ f0 standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will -k)o fp5 soce+0 wigqh8 8+dzsclimb 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 is making a l pxaoj f 3r-9)(k6kwzturn with a radius The forces acting on the cyclist and cycle are the normal fo-r a(6w xzfolpk)j39 krce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 lebtwt:t z9:ehs)bz 2 ,l2aod 6gngth 1.5 m and begins whirling the rock in a nearly horizontal circle a:o:szttzgb 2)d6a w9 bl2,thebove 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 no6jyz d/,i: ;kvv e:jsolid cylinder and her arms as thin rods, making reasonable estimates for tv:jj: 6 oe vdikny;z,/he 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 wh-6zo fw7s dw)txdj2c, ich consists of two cylindrical plates, of mass ft wc ,6sx zdjo)72w-d$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough tra.fp 0rmd 6q4bn2v:vm uj:)b bcck of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without udcmj .:r64: n2b0 bpmvbf)q vleaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do n h8 ktps-w/5u jc59axmot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces it7av*gh3rj4,h qfu1)44r kf* ga wjwdhs speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What w4j*fq ra4fgdahv,3 ) w h*hwjr714 ukgas 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