A bicycle odometer (which measures distance traveled) is attached near the whwxyk jkg.x ).3eel hub and is designed for 27-inch wheels. What happens if you use it on a.kw) 3jyx kg.x bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular vels4e:j ps3* lhx3zghuhg ,-*t x w9.ocqocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increoxsh9-l3xj:ec* wth *3usz4.q,hgp gases 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 vel5; a9+pxleriwz6 bqd5ocity $\omega$ Explain.

Can a small force ever exert a grxr5/dmiv)bp(ie k-w i43nwt + eater 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 difficul8wz/y8) pb 5iinz* hoot to do a sit-up with your hands behind your head than when your a/hn8 i5z 8*yzpwi oo)brms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has s1 bice c n(i ysou5m129vtj+-meven sprockets 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(j9euy-b1it2 v 5smin+c1ocm ? Why?

Mammals that depend on being able to run fast have slender lower lb0vz30 gwcbfy vc4,+ degs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explcdbyz00b ,fvv+g3 c w4ain why this distribution of mass is advantageous.

Why do tightrope walbxqm-/.k1 vnr )jxmp 6kers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net tortl51 eovw +u12vh ew7bque also zero? If the net torque on 1woleuh5vv+t1 b27e w a system is zero, is the net force zero?

Two inclines have the same heo7* oyp phj(s..bj1g qight but make different angles with the horizontal. The sagb(shyo j 7.j1.*poqpme 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) .q1 qhna2vi( vdown an incline. One sphere has twice the radius and twice the mass of the other. Which reachqa1vnv( h 2.iqes 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 radius and the same mass. tey5)btus6,) e jf6ydThey start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Whu5te) ,syy6 jd etb)f6ich has the greater rotational KE?

We claim that momentum and angular momentum are conse hy/x mnn+p3,irved. Yet most moving or rotating objects eventually slow down and stop ,y3/xim +nnhp. Explain.

If there were a great migration of people toward the Earth’s equator, how wouldid77(uz8 nfbh this affect thz7(dn8 b7 iufhe length of the day?

Can the diver of Fig. 8–29 do(a 1w3m a;m cyu*skaq6 a somersault without having any initial rotation when she leaves the boarkwc* q;1 ysa(mua6m3ad?

The moment of inertia of a rotating solid disk about an axis throu,s i/inmybrnlq/n/ )4 pl 1+fzgh its center of mass ii,l1bs//i+ r znmnq p n)f/4yls $\frac{1}{2}WR^2$ (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 masshlxbfn -k97)r 7xhz1fjul8 1 l in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, 1fh)7xzb jx7nuh- l lf98rkl1or stay the same? Explain.

Two spheres look identical and have the sam,,piixdl7a t*zjwk1 1e mass. However, one is hollow and the other is solid. Describe an experiw1, k7ixtpd ,ia* lj1zment to determine which is which.

The angular velocity of a wheel rotating on a il mzvs4lj a:-zn,m-6 horizontal axle points west. In what direction is the linear velocity of a 46l-:, msiamzln vjz-point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntablf )5qn qg0w0cn(9qal be. What happens if you walk toward the celfq50ng0q9 qc an( wb)nter?

A shortstop may leap into the air to catch a ball and throw iiag.j( hxnq1kdf 2o(;mzpu):xt,9vf 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 opposit9j ft ahxzi;:(nmgox(dpk. u 1qvf 2),e direction (Fig. 8–36). Explain.

On the basis of the law of conservation of a mo7jq ( q(rgj4 -y7(f)xu8e4agxhuaxngular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propella m)(4qxu xy7 ua(oej j(r-hgq8gf4x7er can operate to keep the helicopter stable.

  Express the following angles in radians0no/wsoc h /78e7dw flfi*6 j0:dvkwq : (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 baqcb-buf* rvbn f-) r4su(m21ecause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as s fv 2unr 4b1q)crm b*-sbuaf(-een on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at thn/hsw vs t3kt 5f4 dv2(wk6k*ae Moon, 380,000 km from Earth. The beam diverges a vksh *k(/s6wv d32fk4na5wttt an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 3 ole 7s(t0qdj;3sqcp 6500 rpm. When the motor is turned off during operation, the blades slow d7s clqj 3tose0p(;3qto rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anoum)drmz (k ,;wqq i9.tther child. If the ball makes 15.0 revolutions, what isw) kummqri9.;d( zt,q its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How .+q 8mjbb 8hx0 or:yhnmany revolutions do the wheels m8hbqmno+: hbjx 0y. 8rake?    $rev$

  (a) A grinding wheel 0x2(sh)umpt,em o(h2 k,rln2n.35 m in diameter rotates at 2500 rpm. Calculate its angular velocity in ,2(o hnpmt,su2x en)k 2 (hrlm$rad/s$ $\omega$ =    $rad/sec$
(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 8. x;eb(xrxcf in 4.0 s (Fig. 8–38). (a) What8x.xx;b(f erc 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 aro)vvl+7 px,gczyr* xt4und the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ly08is0gq t10de;ohx 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 if a particle 7.gk4k3satho,pn u js(/t5e6 ( z0 cm from the axis of rotation is to experience an accelerati6nkg(s(5hte ts kp/,3 oj zua4on of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm t.htr.cit/7 j-o-aodz o 280 rpm in 4.0 s. D jo/7t. .atzc-rohdi -etermine
(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 radiuse 1vikl , m6 y(ona9.pfyp4t0b $R_1$ 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 themsb)6yt:j z)y+(c jxf zuelves 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. Determineb zzx+ t)):j(cj6 yuyf
(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 i::;97yd msnl5 brufynn 220 s. Through how many revolutions did it turn in t5mnbfu sy:lr7 y9:n; dhis time?    $rev$

  An automobile engine slows down from 4500 .bjv(r djrghm-2e8x 8 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 jets il yn+d7q po.e2 f/m3xzoxn18rn a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachin8n /7oxlor p2e+y. mz3qdf1xng 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 rlf.4hz hx54x ueqns2h54z1ao pm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time25h aqunshxl .oe h4zfz44x15?    m

  A cooling fan is turned off when it o lz5*5s p0dgtis running at 850rev/min It turns 1500 revolutions befp0*dltszog55 ore it 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 maw1ionsv ae x2,k;8 x:c -iq:p7sdc3go ke 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of:wpcs ai73qc8- e1;o kxgd n,ov2xs:i 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 unipy.gu :l-1sdeen(+hkw ; ( ftdformly from 95km/h to 45km/h The tires have a diameter of 0.80 -tf yn1ku gdep d( ws:(e;l.h+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 an-kn(b + cygj+(- a cbn.xpni5 bike puts all her weight on each pedal when climbing a hill. The pedx+ ganc (kinnb-p c-5(+j .ynbals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 a8 *)ijtb9ojd N on the end of a door 74 cm wide. What is the magnitude of the torque if the force ijt*djbi8 9 )aos 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 t)y)hrb xstt+ +s51 b4vp utn3bhe axle of the wheel shown in Fig. 8–39. Assume th ux1nr t+ 53bst4sbv)b )t+hpyat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of 47fosqmq*+i 4e+c cugmass m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction ofq c f+7eugi*4m qc4s+o the net torque on this system.

  The bolts on the cylinder head+dr( -f yv/uxjtvy;c,;jdcgj+e 5 zm+ of an engine require tightening to a torque of 38/m5+tgfyz+ cvy ,de ;+rju( ;xd-vcj j $m \cdot N$ 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 inertia2nrp*4zth gs6m/ww:o of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through itsom/4 6*wpt : hsn2zwrg center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whu ff:sc4ai)3q8 wse1hw9r t9ueel 66.7 cm in diameter. The rim and tire have a combined mas9t4 wwcfsui ahr)1feq 39u :s8s 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 rod is rotated inrok- t2m,,y8 ets2vc) w( azij a horizontal cie)(w,c2v yt,tkz 2s 8- jioarmrcle 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 rohp;sd)z0zn q9tating at constant angular speed (Fig. 8–40d ; zp9)qznsh2). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objv-wwl1v/ j+vj ects shown in Fig. 8–43 alwv +/jvj-1wvbout
(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 tbmt.- a.v5k svy d16xc8ynre zmi3j23wo 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 spinning at the correct mu1 .8 .kuiq;3zox 4qxl nm6wkrate, 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 rm 1oq3kkx6zlxm uui48. w.n; qocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifo65 a*o4 0ovmbpynt2rdrm cylinder with a radius of 8.50 cm and a mass of 0.580 kg. C5 o4ay6mnp*rbt v do20alculate
(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, accelerating ib wo*f kvn/4/y pj koh35;za,ut 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 mervg, updekz u9t:sk 2;)ry-go-round and is able to accelerate it from rest to a frequencge,d 9kskzu:puv;)2 ty of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 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 bro*9bg tb4uw2 enught unifon9w2tb 4*ube grmly 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 ack rt*8cjs -0zgcelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, whimz/rm+lg q)au) tic -fo, ;h*bch rotates about the elbow joint under the act, cl* -bftg;om ) q)/rzm+huiaion 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 sho/frzc7dl( 7 qvwn in Fig. 8–46lfzqvd7cr /7( .
(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 two masgo i0xk*hapz.f2 /w-:kg3wwa ses, $m_1$ 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 accelerayd6t5jh2 2nnx tes the hammer from rest within four full turns (revolutions) dj256nh nxt2y 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 ip n;txfl d::c(nertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of y:tf1igxd +b-0wg vb9:asf)a 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 radz(q lk6*mot d.ius 9.0 cm rolls without slipping down a lane at 3 6 (ktdmlo.*zq.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as e ;,*xk.5c ivnc0nps oq lvq0)jmp8o)the sum of tn)*,j0 p vxv) spc 8iqo;kqcen.lo05mwo 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 m. t)qfoe ixqc:(- +2smy. jrjr( How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assux (it.- qqy:rfrm2+j(ce) j osme it is a solid cylinder.    J

  A sphere of radius 20.9zxm ql;zf80m 0 cm and mass 1.80 kg starts from rest and rolls without slipping down a 30.z9fm0mz8l qx; 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 v.-zpc2bdegcj ( aur :b5g(y4certically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper bczb2 (d(jeayrcc4g-g: 5up. 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 rotati kbd uu6.ysyq g:-o o- vt44ztcuf(:h9ng on the end of a thin string in a circle of radius 1.10 m fco4 y4qdvgb(- u zhtk.6s: to:y9uu- 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 cylinehy71i i)n0ejr 8k8 lzdrical grinding wheel of radius 18 cm when rot0njez)781yl e hrk8ii ating 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 platfol+dw55 /mnwab:v8 dinrm that is rotating at a rate of 1.3rev/s If he raises his arms to a horiw5/:dv dla 5i8w+b nnmzontal 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 one shown in Fig. 8–29) can reduce her moment9x/ ,g-nak5djk+ xt)rjb npb5 of inertia by a factor of about 3.5 when changing from the straigh5jdk+ ,)t abjg-np xn 5k/9brxt position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase h/ij q cud-6he8er spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final6ei- dj/h u8qc 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 agm ;n3tnb4n gcj6rq1 b(ip8/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 tr8/ c1; g3qb (bnn4pjgiman 6clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinntsc3n+.1f yqkl521vo iu f4ej ing 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 2ug5ji jh)w( wthe 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 dropped on207vufim. crnto an identical disk rotatin2vrf0inu7c. mg at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns r3 ldsq1d6rk 8r-3ipe 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 the center o)vv) f/6rc ksf jw 1yfl8ed/*uf a rotating merry-go-round platform vr/8 /j1*c)kf) 6ws fdevlyfuof radius 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-round is rotating frej+s (akli0af7gsh8z8 :v1r kuely with an angular velocity of 0.88i0r 1zja(agvkus l+8:k 7h sf $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing9) 8mzhib 6 piper-ybvi6pema 3se:0 0 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 integer3 ra e y)bevb:p0i9 -heipipm8s66 m0z)$\approx$    $rad/s$ (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 120qh kw9-94ue1:mqpn 14pzfxjt $km/h$ 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 n4 *ugdy0aj3x $ 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 bb5jpw7.8ni hfreely without friction. n hb58pw7bij. 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 6.5-mzhl cl*m,51 fm diameter merry-go-round turntable that is mounted on frictionlesc5*h flm,z l1ms bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of thpkp t*;oe9tfo .h3ph -e rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds frtheo3;fp*o t.hp 9p-k om the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the samex-b5 u4k3y w hxra9/ms 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 pmw/9 bysk45r3 uhxax -article orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a5tp l4v;*unsot s p:6u 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 cylindt 1p(pnm7 /jiwer of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the t1i/twn( mppj7 orque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical jydq, (ncbq+ . dm9,uvdisks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of m(qcm , dudv.9,jqyb+nass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular spee/ ngys0.9zafunj.z 7yd 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 giamwc x):/oz;a )v3k atc -s2jreat, were 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 would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mas;m2ji/ at)k c)ao - scv3az:xws carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy storeb6o1 f v/dajth,5+xdm d in a heavy rotating flywheel. Supfmtx+hd ,jab/6o1d v5pose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates p 4g xgj/aw/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 horizontal surface at speed v=3.ewj8zt mesniq w-4+/53 $m/s$ 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..ms : /v wjqoiw i(h;pk)3 p(vwpb0we4e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54.i e(wws pqjv:h i4vbp w/o0k m)pw(.;3 The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R.uzz t(;/gu ,y)bl vqb* It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb ab *v,lut)uzz ;yb/gq( 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 makwd08ekz4 rk ea/ j.+x/ir ;pqjing a turn with a radius The forces acting on the cyclistx08iwrq .a dj4/rj+; e kpzek/ and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of lengt 9qet 2. 4g98kpucd:;hpk h2zveur +jlh 1.5 m and begins whirling the rock in a nearly horizontal circle above his head+k d8 ;z pe9 4rhc2q9ej.u2l: pugtkvh, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder anvbyom3dm/ /nn;i 9)fwdnik85d her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a//9mwf3 dy;nkv)m8ib 5noin d spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylqzu6gy 7n5f ql1 fey+:sp7/paindrical plates, of el upyn7+z/5 ysf 617agf:qqpmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alon iqd;(6 c)::iarpsyu ng the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must dropp sci i;nqa(6y:ru d:) 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, bx :tj,t /p73bu )*di .jtufts-w8rmoqut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car rx you-8rrk;8zs bvc dba*66ah f* slz k0k80-feduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the ans0 0rubz ho a 8fyzk;6s kc*r8fdal 6-xk-v8b*gular 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