A bicycle odometer (which measures distance traveled) is attan 6y3gwhuwk )l-g )6bwched near the wheel hub and is designed for 27-inch wheels. What happens iug)nhgw6)6kw-bw l3y f you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a dfv/z1w7r vug)p6* kkpoint 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 magnitude of either component of linear acceleration chang7 v6k fw*)gd1pk/ uzrve?

Could a nonrigid body be described by a single value of the angular vf sscc)k/41pt elocity $\omega$ Explain.

Can a small force ever exert a greater torque t l. r u;ip)doy)p 1ood8jp68xahan a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behin ew7v)zfng (f f+lp3zvv4z ;+nd0 ebnr0zxq2.d your head than whenwz vb) n z( .0fefe ;fp0n2l73z4n+gvxrvzqd+ your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rea0co+f2 5xzzjj r 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 sprocketczfozx j+05j 2 or a large front sprocket? Why?

Mammals that depend on being able to run fastfeo4cm,n3cx4 k* ldk;agn5y0 have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational4kka n od*3g04 xe5n fc;lmcy, dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry amlwcbie+k;)s. zo)9m8 ml0sh long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net a r7slnb n753ftorque on a system is zero,a5nsbf 7l3rn7 is the net force zero?

Two inclines have the same height but make different+yq hnr63 f+(l0t :k7psl 9mwjgskq+y angles with the horizontal. The same steel ball gy+hl+ 3 7y(:wp9nmrk0fj s+q sktq6lis 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)xrjbl:m9rsds r: (ac2 zi8g3. down an incline. One dxrrlmi :bs8j9:.s arg 2cz3(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 total kinetic energy at the bottom?

A sphere and a cylindecge:-*p 4r f*m f(zawhr have the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom-(mr*fg cwz 4h epf*:a? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. (bgk i77taglgm42qk cb 2e:1gYet most moving or rotating objects eventually slow down aatq i14 7g2g:2mb 7e(b cggkklnd stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wok55gc y/ ct/a)m1cuiyh+ i:c xuld this affect the length of thci 5ctc) x h1c+mkuy//yia:5ge day?

Can the diver of Fig. 8–j( *xscl.hwsmckpt boui6 2p0) 77be,29 do a somersault without having any initial rotation when she leaves o weuthbl (c2,*jk7 pcps.7s0)bmx 6ithe board?

The moment of inertia of a rotating solid dia y/ttb 9(ak0jsk about an axis through its center of ma a0jtkbt9a (/yss is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in eac 6o:aft-z)mt.eqvvvpddjb5 :9scf03 h outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decr v f.f:tm-5v o)jqd3d:c6azebtvp0 s9ease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hoyal 6id64mcx g uk-l4990iowmllow and the other is solid. Describe an experiment to determine which is which.i 4 6yik-ad w99 xl60umgcoml4

The angular velocity of a wheel rw*vt/yg dd u:,ktu /l/mf 52rmotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular /*:t/ gturvmkmly 2,d5wud/ facceleration 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 larytj 87pijhe4bn) 87y zge freely rotating turntable. What happens if you w7 b ytj7 h8epi4)8jynzalk toward the center?

A shortstop may leap into the ait 3b-x(erzc )zr to catch a ball and throw it quickly. As he throws the ball, the upper part of b3 etr-zc z)(xhis 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 conservation of angular momentfti6 )+ lx5wvnum, discuss why a helicopter muftl)5 i xvw6+nst have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radiagb:k,+me2lsr d7 y. vjns: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, using 95wcpm21 tvix j1bds2the information inside the Front Cover, the angular diameters (in radians) of t2 2 s1wi cvpjx1m95dbthe 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 bew+afbt br28 7lam diverges at an ang8wt rlf b+ab27le $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rota.ww/z qwe4 4ctte at a rate of 6500 rpm. When the motor is turned off during operation, the blad4z4wcq.e/ww tes slow to 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 floor3e:- +p(kogqx 8gqi xb 3.5 m to another child. If the ball makes 15.0 revolutions, what is it-b(ogi:xxq8pek3 g q+s diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km.gdy :x 0+2)jwpw,agkh How many revolutions do the wheels g0:adxgk hw2jp),w y+ make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2 j f)id9nfkt/h;v, aa.huyv41500 rpm. Calculate its angula v4v/thyn ihkdf 9;uf. a,a1)jr velocity 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 k u6/:my-mdsoxcqmrgov 3xk q;4) 2b6revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from th4 dm)omv q-gxkuc 2xm/6 s;o3yqbr:k6 e 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) la,(b+5y )kz jbf)b irin its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point 7g jp6l gcg8khclgzr9r258s.
(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 p u99kn 44dsvrwarticle 7.0 cm from the axis of rotation is to experience an acceleration of 10 kwv4s99d4unr0,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 1aa;wbpv2v.we k 46y5j 30 rpm to 280w4ep ;yvv5 bw ka2.a6j rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu:o iy3a ji9c:9 ,ftmjds $R_1$ 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, astroa1hpo6 -y;ti* u9wvf hp7nh 0qck,.ba nauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time intervay;a w qh1 ,ip vnb9hh0cp6kto.fua- 7*l. 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 uniformco 7 5;82sqvsgv /orrsly from rest to 15,000 rpm in 220 s. Through how many revolutions did it tur8/s 2s gov;ocvrs7q5r n in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 ; 1m2mlyv:neczavottt1p v q52y76 /ws. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a g .bx*x.a6hbj8n: tzqv9n 0hk whirling “human xav.xbk* gb0n:h6.9 hn 8zjtq 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 accelerates uniformly from 240 p,tbe8-k tc.cx( hf *trpm to 360 rpm in 6.5 s. How far will a point on the edge of the whf*t,(tp - tk8.e chcbxeel have traveled in this time?    m

  A cooling fan is turned off when it is runnbfp a .m *noriwxw7t5:g*j(-g ing at 850rev/min It turns 1500 revolutions beforeo:7b mwxjw. afg*5*(ntg-rip 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 revolutions as the car reduces its s+( eq7qhwiwo;r kx4/g peed uniformly from 95km/h /oq4 7(w ix+qrkwge;h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the cs njze6.me44zar reduces its speed uniformly from 95km/h to 45km/h The tires havem z.s4zejen4 6 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 eac /cxc:g*w1, zd0s 4evd*+pc pe2yw xnuh pedal when climbing a hill. *cvdpewe w 2xsx/1c0 py*cz4ngd+, u :The pedals 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 forkwc;pw eglk1jy) 0ym ; ry70i.ce of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if tw)cyimy0y7k kr0.;;j e 1gplwhe 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 wheel shown in Fig. 8jzwyp9n31w 5w–39. Assume that a friction torque of 0.41w wy5wp nz9j3 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod whi.)qbvn,p l(mc lzf 71tch pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released1( f).cvnml zbql p7t,. 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 torqh0 u5q snvky39ue of 38v n09uy3h5qsk $m \cdot N$ 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 m8dt7 a(z .gvl.p f2mf.zcbg9z2a wu6of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rota.fg6d8 7m ( mlaavwc. ugz9.zb2pf2 zttion is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyclekf vz1 d)bfm2; wheel 66.7 cm in diameter. The rim and tire have ;2km)vdb1zf fa combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on t- 2y 8nif8qiisdv2 y9y9 7(iaxyxy;obhe end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculate 7fi- 9ydxi;x(ayo8v ns2 2b y9yyiq 8i
(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 qhg6 fj) 3rz9va bowl on a potter’s wheel rotating at constant angular speed (Fig h r)3vqfj6z9g. 8–42). 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 objects shown in dp q2l(lnz1m2v8 vie 9Fig. 8–43 about p8129dqzel vnliv(m 2
(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 whose total maa u93r*in5szs np3o.wss 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 rate,6qo5qzrspzl3ij 6,8p u.p vw8 engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radi 6 3uv,rjqz8psop6zpw58qi l.us 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 j e)ls8v ve.iirzegc06 70w5nwg :uy 3a uniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. 6ugw.8jv03)5 : 7scvlgiezwenri y0 e Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest to 31ec+0(je n bfngu2tag* r15on $rev/s$ 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-:i 2t(wj9pmk3r /rx yeround and is able to acceleratekpx /9wry:ter(imj 23 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 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 10,30.zh;a9h1 9r5:riy f qt)xl zju0 rpm is shut off and is eventually brought uniformly to rest by a f.r qrx 1hj9ul;hzayi)fz:5t 9 rictional 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 accek:j9i+ ,vb eoilerates 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 iefqr, vlz0/smb6h5 m5s thrown solely by the action of the forearm, which rotates about the elbow joint under the m lr ,b/q506ev zfms5haction 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 l) )- rq4ezfwfi+w fclux(/y1 fz46utgong thin rod, as shown in Fig. 8–4ut 4yfxzlf wc i61w)qr-fe)(gu fz /4+6.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists o1 / /7jb hccqvvt(yiz)f 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 fovjc*a+ o/r n.,0aezn n 7a*tqfur full turns (revolutions) and releases it at a speed o/ *n+.*0 ,nf7eanaraqto vcjz f 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 iner i/n/cx*1*+ojz a; apfb6xyfdtia 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 bm59alz 3xdg p/u.qn+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 cm rommuv2x.mkt t0 /dwjjgnci +:.-9ls i+ lls without slipping down a lane g+ mu2.ivs9t:mtw nji+/ml.xjc-0d kat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic zb3d;n;c hze 6qfv- 6eenergy of the Earth with respect to the Sun as the sum of tw6fbcz h ;3e;v6dnqz-eo 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 m 3 tg*t2d5p11gyi g kh)8mquts)wpe z0ass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotatio g)0tqthe 1 t8p*g1i5zdu3ym2ks wg p)n 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 6 x6u8mv(1ai x 2lus(mhk 9anzegg0;jstarts from rest and rolls without slipping down a xe(mi0l g hz2u 1g(s8nukx;j6v6m aa930.0 $^{\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 starts to fall and ,pqblokh+ue84 un1k, its lower end does not slip. What will be the speed of the upper end of the pole just before it 1 8ke4k ,uq lhou+nb,phits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg a 50j*pu db8ryball rotating on the end of a thin string in a c0ya8jdp*u5b rircle of radius 1.10 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 cylindrsttauubww.5u+ + o.-z 4dtjc (flkc 4.ical grinding wheel of radius 18 cm when rotating at 1500 rpm? 4t+(-zcfaw5ot d kucus.u.b+lj tw4.   $kg \cdot m^2$
(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 nimx.w/vp-pn2 as8*rthat is rotating at a rate of 1.3rev/s If he raises his arms to a */nrx-.n82ap p vi wmshorizontal 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.brkkzh,wqku1e6z 3i+a k5o 2r/r tu;mh8nj78 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what rrz3u7; r 5nj kaz2kh6tuheoq,ik /18m8k+wbis her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate frompvszz1h v 0g8zk6vf, m3k, fn/ an initial rate of 1.0 rev every 2.0 3,v8/k hv npzmf,zs0fz6v1gk 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 arouoxno5 0z ah6wk/ /tln2nd 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 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 frequa0ho/ozw 5x2 n/6 tlnkency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a2 1 w7dtmvwjt 5*the/ qcv0 c+o6wfhz9 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 momenxh4-x,nkp)nv j8.ld utum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

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

A nonrotating cylindrical disk of moment of inertia I is droppeag.x r fxzem4+ 7o8l85ib9pv ad onto an identical disk rotating at angular speed8+ar9f gpbvo8 x7 liaxmz5e 4. $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 y2mkcyv-q9ubnt h 0 27xg; ze9$rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a l ez,; kqror:61bj;gvw9sd.y rotating merry-go-round platform of sk;69e:rld; ,zy g w1.jrb oqvradius 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 merr8 9a2kzed ()wxnbu2kh eli,m3y-go-round is rotating freely with an angular velocity of 0.e(,ieadxk2 )nlm 29uwhzk 3b88 $rad/s$ 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 i:u(r3 q xn0 kqg9uuml*nto a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s n(mq k0: u*un gl9q3rxuew 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 winds7-cxn 6 pkz48.2qaik+ b njaq2kkya5t 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 8+iae 7lcwdk: $ 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 jnk)4 6jcjj+sch)pn,pu:cl: rotate freely without friction. The moment of inertia of the persopn s,ccj6 )l: nhu)pjcj k:4+jn 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 ,5jf8 roj.hgt;, gq6t b0)xjrxnnl; vstands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictib 6, x j5 njfh;jvo;tnq.0,8gxrtg )lronless 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 the rope lying yex+lr 1x5 y*eon 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 from the spool? How far does the spool’s center of mass moxlee +yx 51y*rve?

  The Moon orbits the Earth such that thl0d5g m(a::w gh ap-d y)ie*r nxzgb+1e same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular mome(mg+ay0z d5he)1n a:p: r ld*gxb -wigntum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest 3ir, oz4lqt*g hl,ir.q (g.miat 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 .np)ep unw8v7of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torquenvpp w8 .e)n7u delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.0506;smh jo: k.g9w e (51jjkihmd kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long strin9 ;h1koem5d jgmw(jh kj.s6:ig, 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 speed of the rear whe)3 ltcwp1pflzn* mcd*o3 (s8lel ($\omega_R$) 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, bui wcv (-3+ o xx36jzu/zr/yqyut with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it wericu/yo+jy 6xxzu-3rv (/z 3wqe 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-pollp-wal) l) bsk6ution 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 needing a flyw ll))s-ba6w pkheel “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 aafjx 6p- (bn5$H_2O$ 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 vo o()np +)vvdp=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 c (e xoqzcp 2mlit, 1ay(q:)q4 sxq0t3fan 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 ta: q130o2pqxf (l4m,yx qis qtc()zetip 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 vertically on the floortgg, j0:h-knt , and we want to exert a horizontal force F at its axle so that it will climb a ste0: t-gkjt ,hgnp against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with sp14/ snjj j5nwceed v=4.2m/s on a flat road is making a turn with a radius The forw/cn1nj45 sjjces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a slingqqfr7ks (k5ys1t hltza,;8dq4q d+x2 of length 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 rpm afterky;h (qfk q8lqadxs+rzt1sd7542 t, q 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 c- secjwruuo7:mqn x 04+.tjdj;tdm 9 9ylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning ;jwqjxn7 .uteo+m-jm0st dudr 9c 9 :4skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylind ifw op-kn zsfm/-/5i5(bbrm3rical plates, of masfp / 53mfsb-zmbk(n-ro w/i5is $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rfmk3tfonkd1.u6kp,abq.bo 84: m d h;adius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must dr fb4nhakumfk8.bmp:q ok dt.16d,; o 3op if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not(6vimq-4v-+kwuf uuik0vt j ) assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the c0c m h+92uryj2.r a e4tqqzgq;ar reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleratiohz+ 0 2j t.am2qgc9qy;u4qrern 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