A bicycle odometer (which measures distm*y)w ngm50dwr z5o v:ance traveled) is attached near the wheel hub and is designed for 2r55 mgw:yzo) dvw mn0*7-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a lma+e rfl8 d6d*i:1h vpoint 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 would the magni+6dvae l 1:i8mf*rdhl tude of either component of linear acceleration change?

Could a nonrigid body be de c onobp 8h3c2;vg05aso+u p/escribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forc1+e2fyxo 38ivs y-h ywe? 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 than wh-+3sn8qork 1 bl+ aflmp-q kr/en your arms are stretched out in f+ ra18kllq3+pos-f r/ k- bmqnront of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at tph3 (*;0f-5j 4mqtt f bimvzmche pedal cranks. In which ge5fct( qmhmz 0- bp*vij3m4f;tar 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? Why?

Mammals that depend on being able to run fast osjrqyolj(3t 3 7-pf8have slender lower legs with flesh and muscle concentrated high, close to the-j7ft3( joq3py rslo8 body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig.z7kg ss 1,(y a/uzei:g 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zer viq kr5l6t+4yo? If the net torque on a system is zero, is the net fory64+iq r ktlv5ce zero?

Two inclines have the same height but make different angles with td .t h13x yxnne*xq:7che horizontal. The same steel ball is r:tqh1 c.yxxx 7en*3d nolled 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) pdczj0a3vd2wx fv+* 8down 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? Which has the greater tota f+0jvd2 vczw 8dpa3*xl kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the o.7nk 9 ,b jgaarehs22same mass. They 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 j2 gn,k2oea 9h.s br7aat the bottom? Which has the greater rotational KE?

We claim that momentum and ang/efga1we 1b e-ular momentum are conserved. Yet most moving or rot1e1-wab/ eg efating objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Ea +kd;m+lqw;qerw;kh9 rth’s equator, how would thlw + 9mkwq rq+kde;;;his affect the length of the day?

Can the diver of Fig. 8–29 do a somersault withou5gbd98olq5l hijn+ +4egedo0apj oc ;1ey+9k t having any initial rotation when sh+q4jye5oo9 0+hkcilenjgp l + 158gob d d9;eae leaves the board?

The moment of inertia/gd +aci q :oywbr5y46 of a rotating solid disk about an axis through its center of masir5co:dyy+ q /64a bwgs 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 salm8o8zk ka ywe-:b3 ,tool holding a 2-kg mass in each outstretched hand. If you su ak-l bwa:y 3zo88kem,ddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However,)gx 4agdw6*n m one is hollow and the other is solid. Describe an experiment to determine wh) dn4m agx*w6gich is which.

The angular velocity of a wheel rotating on a horizontal axle points wes)+fx u.:dg*ng(q8rxn j eqei,b7,9sr)g tgsh t. In what direction is the linear velocity of a point on the top of the wheel? euxg:thnq gr).d )ern s 8gbgi,fsq(, 97*+jxIf 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 ,3op g*fh 4flcof a large freely rotating turntable. What happens if you walk toward t4p 3ff h,o*gclhe center?

A shortstop may leap into the air to catch a ball andnxhp;.7r* )ot ay 9gcf throw it quickly. As he throws the bac yfg7r) n*9x;pot a.hll, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of kptngzj +56ir. mw5yy bt. *t4conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more wa.npyy +.4mri tg5w6bt 5jzk*tys the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: r57ofm5sq :tz0rk:z s(a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of ao6-q,dh82uwx/ jv lx tn amazing coincidence. Calculate, using the information inslo uq/v- dxhjw, 8tx62ide the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000,gp*;7p(o w uwstf1 zm km from Earth. The beam diverges at an ap(z 1*;t ws u,wfogm7pngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotateum rwvr p6sao.(5( dx8 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 blades xsw(m6.v (oadpr8ru5slow down?    $rad/s^2$

  A child rolls a ball tylf:rz5ck05e4p,w sh nm cj y(b29n ,on a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its ditcc:mr,h9 ,ef 2s5 jnb0w 4l(kp nyy5zameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many b sf3//gtf86-uydoem revolutions do the w//umo6fy fsbg83t- ed heels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotasy 50p etyik9;tes at 2500 rpm. Calculate its angular velocitsep 5kti9;y 0yy 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 oneutby 0jbmx vz4cc-, 75 complete revolution in 4.0 s (Fig. 8–38). (a) Wha7 cjcv5mbu x0-by4z,t 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 ar-x+oud zy lb s5cm f;/)pz.tw4y a8t:mound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pjy v6hre51 z8cdioo7r+7x heh7mj )l 1oint
(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 sb* 4,fq( drmfs 9bcfk/n*3 rpif a particle 7.0 cm from the axis of rotation is to d*fs,34rpbm ( k 9*r/csqffb nexperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cenl/b8 um7 vc.dctr4wxt,hq b 9)b+al9 kter from 130 rpm to 280 rpm in 4.0 s. Determ llhk+/ vbq7t99wmx.,c ra4 8udbctb) ine
(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 radiuset4l (vcz7 no1 $R_1$ 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 themcqr wa28q5iu 9ch s /c(9iaur*selves into a sl2sq 59rccw qh9iuu8cir*(a /aow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from reo* zz0fohx hchx 0+cp4 (nyc50st to 15,000 rpm in 220 s. Through how many revolutions did it turn in th ocp c(z +x*0hhofxchz05n0y4 is time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate s;ty 6pcg s0p80o*gwv
(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 st5juuh ytfd 0b6ghl 5h 92;x p1fvlp3v+resses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed. ;+f12phg9btxu jylp55 h6hf0v ulvd3
(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 frohap0u lg so gk;81y40mhe)gm- m 240 rpm to 360 rpm in 6.5 s. How far8hasp1-; e) 4m ggmkl0ghy 0ou will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revolp3s 0sirfgt/knk )up4bm6 j8 9utionsmrns4g)bp09 p s /itkkj 8f36u before 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 make 65 revolutt.) daz 33u:pg azwo7yions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.ua7zp3 aw.3:td y)z go
(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 r)lo8, 92qv sogz 6xiwveduces its speed uniformly from 95km/h to 45kmvqowg olz)98,xv 2i s6/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight 3d(echg/ 3gl zon each pedal when climbing a hill. The pedals rotaec3hz3 g/(d lgte 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 odh pqop y6: 7jk+/7ifpf 55 N on the end of a door 74 cm wide. What is the magnitude of thedyopf:hp +77 pik/j6q 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 whe9w ewdz r(5/voebb(*p6ipsz 0/na y3zel shown in Fig. 8–39. Assume that a friction t 9vze/ppz o5 zrbwi0y (en6sd(3 ab*/worque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, b2va o +irc;jj+/ldp 6are 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 of the bl/+d+ojp6v ic;j ar2 net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of v3z:e7pwrf 3xkidciq z13 v*8qz 7oj8387cidx q8o:jvp7z18kvif3 qe3*rwz z 3 $m \cdot N$ 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 sphevl6; c)st08 lm/rydymh.*xgw re of radius 0.648 m when the ax /l l)w s* yrv;xy6dmmtg.h08cis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of 6qata; 4zwon 3inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined ma63qzawn ta 4o;ss 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 in a1brmgt-xs-f- mj: g,s horizontal circle of radius 1.2 mbs -mmtg-: ,1js-rgfx. 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 i7kl7. vg pjm4bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her 7.gjvp7i m lk4hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown5ejrp::nxot3tjo/ f )t/ gsz( in Fig. 8–43 about xtpt/jf5sgojrt(o ):/3nz :e
(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 08hh zykr c6cs o3s:k,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 spinninga9ieo.ihgc0* at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the seagc.*0 h oi9iatellite 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 radius of 8.50 cm and a mass z807za o0c kk d.qjvo(of 0.580 kg. Calculakoz dz.(qv0c87 ko0j ate
(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 it q4 t* khjwfa8;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 merry-go-r7zf i fphb8g-ebpn xj-8:6 g8bound and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a ma g6g8- 8i7phfbpbzf x8e- b:njss 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 icv*+si ,:aibbrought uniformly to r:*b ic i+si,vaest 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 accelergbdpo 4i0(r5 o 3jm7 eiekb:2aates 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-kge()ukeq ee-zm-o- ;nm ball is thrown solely by the action of the forearm, which rotates about the elbow joint under thk--e ne-qezo eumm(;)e 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 b d*7)x;disw)ob/k2ndz5jebh ae )q0q lade can be considered a long thin rod, as shown in Fig. 8–4)j o;z/)dibd5qke2hda 0 xsqnw *e7) b6.
(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 ol)5;cl)u9x y uzr r4nuf 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 h ct1r 3(f8r9kd gaiawf12h;mb (i(dmmammer from rest within four full turns (revolutionrt2mia 8mk;h9( 1 m(f3rfda (wbd ig1cs) 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 momentdp e9r0:t:bz hz7e5 ny of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile enginec8pmlu8mknuqco( b+38;l*is7 d *m e u develops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cd(*ctn yc g57;np btk3m rolls without slipping down a lane at cd7;3 n* nypb( ckt5tg3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Ear2ofqv 60 xxijb9+ux(bth with respect to the Sun as the sum of twojbbux+i06x f2qxo (9v 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. How much netdvkmkxm/b 21ej c5ggz9 k(w3: work is required to accelerate it from reskdkk3/bm(2e czj: wg51mg9v xt to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and0pfmt) kc.; p..drm ee,o3sgq rolls without slippin fk0)..m3gc.otrd m e,e;s ppqg down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tipi xzjt lf56qmy7n0ez*+;9eqz. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole jus0zqeqt5x+6z z 7e9yiln*; fjmt before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momc sq99ds)gub,entum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed oscuqgbd9, s)9 f 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of apwt jpf ,-0;ce 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? etp-cf;, 0p jw   $kg \cdot m^2$
(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 rotati.;pg .me 1tvt3b qzua5ng at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8zq.;1au t.g 53vmbept $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the oxn6w9x zme7 :vne shown in Fig. 8–29) can reduce her moment of inertia by a factornxw:67m9zv ex of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can i*n gf*h af *qg s-v:e+whveo y(p0u8m1ncrease her spin rotation rate from an initial rate of 1.0 rev eversu*-0(m fvh eqpog:1 gw*+*vny eha f8y 2.0 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 aron9 ,j w-c.jwzhund a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and dia9,.nzjwwh- cjmeter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skate -iz /p5oy)69mbj t(3m(xhh uy rup*vwr 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 mom 9e:zk m1so:ux0nf- psentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertix-y0 9rkbx*tmofc6e w2p 2yk- a I is dropped onto an identical disk rotating at angu-r*29- 6mwcepkb y f tx0kxy2olar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 hzn--f6 +tim:b;mupl $rev/s$ 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 centerf 53oy /d+oiwa of a rotating merry-go-round platform of radius 3d5f+3ay woo/ i.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-rba 1t bnx b* /5oift y97nmls7+wpyk/.ound is rotating freely with an angular velocity of 0.bn9+5ayo7tx/1msb kyn 7t *filwbp/.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white degz3,ua cbof(s1 x/u7g2 ueejwt )73v warf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest iuxugwc/1go3fe2 t je7,)37av(buesz nteger)$\approx$    $rad/s$ (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 w9q88xn )wbou oinds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass ,;-hij jlk icf1 v3b.h m+yk3y$ 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 freely withou0.bs ;:bm vqtd r25 mrtpb/n3swe.s8tlh6h c 3t friction. The moment of inertia of the person plus thectr l bmqt6.sp:etd5b2sbv .r8sn h;03/m w3h 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 stan1dpw b9;2h2jrqw4y pwds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless beari1j22b4rw9;d wpp y wqhngs 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 o:w: 26hjnvckx r(ww/ a )x9fjwn the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig.(njvc) jr:ww:x/kw6 x 9awh2f 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 such1ab;it-4g1gk j8pj gl that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about1b8-ip;a1lg 4jj kg tg its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m/z) z76jaajk uv dpaq /7rqr*4+$s^2$ 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 raxb0rw6x wp ://ae 2neodius 0.20 m acquires a rotational rate of from :0bx6 epr/ o/2wnwxea rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg a7 e-ff fb(er*ond 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 calcu*7e (beof-rfflate 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 erc8h9;ow/vi zb:x -nis the angular 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, we( l4jd hxcv i2yu:2yn7re rotating at a speed of 1.0 revolution every 12 days. If y d :yi2u v2xh7l4(cnjit were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to p sq.srk)b e.38l9e7 jdj8)(9dp7us oviyfca use energy stored in a heavy rotating flywheel. Suppose such a car has l8(of)j9j ies.dkpb.)d7q 79vupy sr83 sa ce 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 an xwooza;8mf1 li/q 1s9 k(qaz8 $H_2O$ 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 shr 6c s9vrg61loxr+: ( ygbr/zpeed 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 95hhubkik9jt :bh + 2oand length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod+b k9hjh2 iht95:obku is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vmkrs hfo3;,:f qrtz:z4: kz /qertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, whtqkhq::3/ :r z fmkz,z;rofs 4ere h

  A bicyclist traveling with speenk*h l 9t*l p1p2 /9ucbuqwkj0d v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal forlb2 p9ktk/p l* q9uc0u*w nj1hce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 leng yqsz9*31o)vnrz4fkm0xa3u ;ynq8 rmth 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm1zf3av 3y4q; qm s8zrnu*rn0o x9ky)m 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 and her arms as thin ro:;aqjkt;0x f3c p;h n(:9ubctyw-dig ds, making reasonable estimates for the dimensions. Then calculate the ratio of the angulabi;t(fk -jcwy;xa0gquc3n: :hp9td ; r speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clup1 op 4n2w 4wvhejwx2bhrr,0 6hl8g4 utch assembly which consists of two cylindrical plates, of mass ,rwr2we4 wh2v8 b6n1 hhpl40 g4xp oju$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rg: a4 ky v3.b-+eishkholls along the looped rough track of Fig. 8–58. Whgh +k3a:hkse 4-byvi .at 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 leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dop1l7ncv) or p.c5q 3rq not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutionsjphr0s vr8 nfh;*uwl)h- :.f y as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.9hrsv*h8fl .j)up 0-f;yn rh: w0 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s