A bicycle odometer (which measures distance traveled) is attach4y bo3lhq jb/:ed near the wheel hub and is designed for 27-hq4:by3lb jo/inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angu::(9d jt jfdpil-jq cq hn6)5rlar velocity. Does a point on the rim have radial and/or tangential acceleration? If the )9cj5- qfi tlj6rdp::(hdjqn disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a sn9rv + qks5tr.n,i dambl/,v/ingle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque t30 tpx ,as:p* u4htfagln,q:*qri/ag han a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head thr)hzxbaq/qr 2 dp+3oi.6l kn: w;fxc5an when your arms are stretched out in front of you? A diagram may helk wz q 63rohxdc: rfp;52l.+na)qxb i/p you to answer this.

A 21-speed bicycle has seven sprockets at the rear whe.p ( xdys4g2z5-flogjel 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 i g yp2sjdz-o l(g4f.x5s it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower p)gxy3ccpy tyz ev4fz+ ;i8)(legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass;c pg4e+)f(p)yyzcvxit38y z is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, s9cq hqi-h-st rfy*(9f+fz ; xl; /auqnarrow beam?

If the net force on a system is zero, is nlovt w)5 f652eejxo7, aq.us the net torque also zero? If the net torque on a system is zeron t5 6uj a e,v)s5qxo7w.2eflo, is the net force zero?

Two inclines have the same height but mb wh ;hd(ix97pake different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explaph7iwhb(d9 x;in.

Two solid spheres simultaneously start rolling (from rest) down an incline. s28nvxr r ,7pgi6p;itcq .g,,gti7xzOne sphere has tw6n8zp; ,.gi i ,tgg7tx,x7r2 sqcvirp ice 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 cylinder 0cc 65t)ywro ohave 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? Whico6wtcy0 c )r5oh has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving orqc)yonl8 4r h-hj/j)n rotating objects eventually slow down and stop.)no -4j r njl8cq/y)hh Explain.

If there were a great migrap36 sefou sx,w74bsw2tion of people toward the Earth’s equator, how would this affect the length os2wu6xs f4 w,3b 7espof the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotat(9s m h4zymh,tion when she leaves the boam 9y,mh4 (hzstrd?

The moment of inertia of a rotating solid disk about an axis9v/+- 1lv* wgnu2hxs,b xemal through its center vmu1,lblx*gs - +xv anh/9ew2of mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass vqqk-vvx),v3 vi;pw 9e6n ib5;cl: spin each outstretched p;,;qq ik l5vbvi3px)v s6nvv:9ce-w hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and h(1r-x,sauwn pw 1x89pa1rh yhave the same mass. However, one is hollow and the other is solid. Describe an experimexpsw9haw-ah( pyx,8ur1 1 1 nrnt to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. Inll.cd/rl )zh m )wx0f* what direction is the linear velocixc) l/w)0lzrdh ml .*fty of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntaoyx+ mv:+jkb3qm/5 uable. What happe5:+m/vxa u3mk+bjqoy ns if you walk toward the center?

A shortstop may leap into the air to catcc4ly* qp0qg*gh a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that hisl*qg* 0ypgqc4 hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conser *vgrldxkn93n+n k-m :vation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second px39k+l-gnnknv* :rd mropeller can operate to keep the helicopter stable.

  Express the following angles in radians: (v) .zej b-njj8a) 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. Caotpwchn;z0t(4a a*8 flculate, using the i*h(4o;zata8t p w0cnfnformation inside 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 km from Earth. Thbrt:r j bb-qng 1ba665f97pane beam diverges at 9 b tq rjpa5 6bn71g:ab6-bnfran angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the mod 4.f: rxf3j lrxd6u:ptor is turned off during operation, the blades slow to rest in 3.0 s. What is the angularrp:f:f4 6dulr3xdx j. acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ballnslz-:5v dx0:ywu 8pa on a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is it5 nwa 8z0s :uypldv-x:s diameter?    m

  A bicycle with tires 68 cm in admhlo. d,m. -:wr .b4qb3wkjdiameter travels 8.0 km. How many revolutions do the wheel:m d.orbb 4 kw dmwhq.3.laj,-s make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates dgf hs 6azv..*at 2500 rpm. Calculate its angular veloca*dhf.v.g sz6 ity 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 on bmmxr e6,hg39e complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m frommb69,rxe hm3 g 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 around the Sun uv0 6jgixla7wsaw+t)u q7/1y    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speek lq6k6*bsex 7d 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 rota y4nwdff+z 2tn0 am,a9te if a particle 7.0 cm from the axis of rotation is to experience an acceleratz0nf n942md,a+yafwt ion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accele *gg-v ro-h-tz ay4(tyrates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determioatyr*z hgtvyg-( 4- -ne
(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 radius +dcf 6l7rdh8s$R_1$ 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 teulh w)l t)usxw/uwn46e.q/bw /)50io1yfbn hemselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their in50w/ )bnh b)wf6 1eq )./euwys/wulx4t ulotrip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Through how9biawq 8p7y0r9gu/ j 2rssfa4 many revolutions did it tuwi49a7f 09u8sj srpg r byq2/arn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.)mh5 jjptn( /b 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 .db0y( )zvmfdlz 8b+y-0bp nx4yvq )kstresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachiv+04qnpy zb(bd)l-z8 0kbdvy .my)fxng 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 accelerat84zjjc ,* gpzyes uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this *cy j8jzz,g4ptime?    m

  A cooling fan is turned off when it is running ato(;gt pqse* x7 850rev/min It turns 1500 revolutions before it comes to a stop.7qtp (x;*o gse
(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 rta9 dn(51wkg hevolutions as the car reduces its speed uniformly from 95km/h to 45km/h Th51 g(9 kdhwtane 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 a 9.oupcjw5hp q1)mh/y s the car reduces its speed uniformly from 95km/h to 45km/h )jqw.1ypm p/chu o9h5 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 alu;ww,90mat/bw uw4zamot 8/k o 1)gwrl her weight on each pedal when climbing a hill. The pedals rotate in a //bww;w9ot0uzomm wa ar,4 tw81) uk gcircle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wddy :f /5j(xaqide. What is the magnitude of the torque if the force is exafdqxy/jd: 5( erted
(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 s*kn +kn:hhyi; iy( a1jnid/7q 5,orx qhown in Fig. 8–39. Assume r;7hxh: aqn+di(1qy/o5 nkn yki*,jithat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massles mspkvak)8 nrx,4 q8*es rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontakv*sx )nk8p 84q, meral position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightet7 ay*.a9p d5to;wl sfning to a torque of 38ftlp.o5wad;tsy a97 * $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radiu+0i a2u93d g*jy0ut vrfit2kgs 0.648 m when the axi j uf +ir0k2gttid9vu32y*a0gs of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cwasm5;vo l7,-zfpyr+2p20g a ,afv wum in diameter. The rim and tire have a combined+ m27plvosr gavwu; a, 2,wa-5zypff 0 mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end -4m:+o-jy6vkzve g hl0l)hg8xc / ww hof a thin, light rod is rotated in a horizontal circle of radius 1.2 m. vhwl-)+:cgek84v-l/ x hoz0g 6jhwm y Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at cov8) rwi0g(gfgnstant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.g)i0f(vg8r g w5 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 Fig. 8–43rjtb/1t ly89pco) g v4 ag v18/t)b4 ojrt9 lycpbout
(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 tota 7crjl2(o ml7kl 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 satellitem ns6/jtej7e213 la- w lt*gc tg9l,nb spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is tcat9/ l l lj67 jwn -*3bmgnt2g1este,he 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 8ayey2i9;1 /, 7awb5k otelga m.50 cm and a mass of 0.5807a/19tmwb yya e 2,o;ige5kl a kg. 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, )u.th*t n 4qtiaccelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and is,020z7 vr0 ap/nahpfzj4lvxf 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 mass of 2l,/v 0hfav2n0 7ppxrzz 4a0jf5 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 x8b4 8ryrt9roab5blkh,3wo 9eventually brought uniformly to rest by a frictional torque of 1.2 99bb5t4xarry, blr oko8hw 38$m \cdot N$ 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 h0x32hiapga -accelerates 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 th.)fsof, n xrdrc5. ia5,jt. xne forearm, which rotatt ) .j, rfr55nx.ondcfasi x,.es about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown x8hgiv t8w3tql8,v.s9czix* in Fig. 8–4 l .8i3 tt csg8hvxvxw*9iq,z86.
(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 masses,zcg *1- n glnfoxx 8m:*lrdm/2xb aq16 $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full lht2z5/lv seb 9(htp6 turns (revolutions) and releases it at a speed ofvl zt/hl es69p t52(bh 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 h2h:,qxl,z+4ikhtq m cas a moment 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 engine develops a torque of 28e6* hga-p9a*wicf :dc 0 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg ak h -;bdooh.boo+.g o4ore:*x7jf zq *nd radius 9.0 cm rolls without slipping down a lane at 3.3*+o-.o k o4bj q;oxrd e7*ozhh:fgo .b $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the d)mu)y9iw- p:dmxug.Sun as the sum of two temdwp-u: .ugimdx 9))y rms,
(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 ma.9jhdct l67ha/65 ,t+rx3jexnrgc qmss of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is q j9l j,r 7hta6t3/gcrx.xm5+deh 6c na solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg stx) 7 9dh t5f+-5mn*djmehftjqarts from rest and rolls without slipping d5qn jf5edh7* 9jmtt-fm)xhd + own 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 ver5ay (a/ 6pz ,mfo k)thp*ewe:ktically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]) kp:o6pkw e *,(e5 ty/mfahaz    $m/s$

  What is the angular momentum of a 0.210hcm1 ;zps:jw 3-kg ball rotating on the end of a thin string in a zmc;31jhsw:p circle 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 cylindrical grinding wheel4, n owid1xie.x7.eo m of radius 18 cm when rotatingie.ndmx14 ,o w.i7 oxe 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 xm b80 y, f )uaubj. /dcaecin09-.lrga platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of ro.l)m9gdc /yfx0bar8 ,iu.jun-bce a0 tation 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 moment of inertj 83xasvx+z8gz f5dlmb3)9 yj ia by a factor of about 3.5 when changis x+3zy5g)vj8 9bj flma zd3x8ng 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 increase her spin rotation rate from an io : t4tmsx yg(d;d.e-snitial rate of 1.0 rev every 2.0 s to a final rate e-;:mgdys s txt 4od.(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 vertica;(n* vdsnqagb, mp l+4l 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. Wh , v4nnm(s* daqpgbl;+at is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of akcu5gatmmvd 9d q24 vis13l/ 5 figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum o4-jf vu)cj4l- aq5nexf 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 dropped ontryy*x; nujhej 0a:qem:k+s l)p3ot+,o an identical disk rotating at ;o :x ,et* ae+h30k)ylryjn:q+u pjsmangular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atjcpviau-(q k 07w be.; 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.1 aag pz.q,kd;p y )e2e3jyarf a rotating merry-go-round platform of radius d.p2z,aj; g13 y.eaapykeq)r3.0 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 i2-t ltcf3x9n m230*kbt 0n asner wec+s rotating freely with an angular velocity of 0.8 nt tc -n+k02aebf t30lm9*encrsxw 32$rad/s$ 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, losing about half ittz6nk1k z8ye2. iltc8s mass z e2k88.lcytktzi6n1 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 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 wmeu-+)u snju):46l d n5xa xc7ll1smeinds 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 y(oqvocr 9;/ci0q9 sk$ 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 / ttz39dz c6qawithout frictio 96zta3tq /dzcn. 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 edge8d6nlh ;j5n iht81 ffc of a 6.5-m diameter merry-go-round turntable that isndl688h ;f15n ihftc j mounted on frictionless 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 j-+y ,pkq nz;4cs8 js:y*bb ayof 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. 8–50. The spool rolls behind the person without slipping. What lengy4z:ay;y8 -s+b sqjbcnkp,*jth of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces them8 v ,qw6kuyscvc;5i7 Earth. Determine;,yvq8w s6u57icmvkc the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rateh1d;s.b, 9z ,kmc k9.szm ezgp of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 mn5 p7q oubs7(z acquires a rotational rate of from rest over a 6.0-s interval at constantzns7 7 obp5u(q angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical da 9whn ;eq83yyisks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylin y;e8a9wqnh3ydrical 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 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 speed of g474e 7yrwiv1jk mz+u 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 wit e:;okv;+rfmfh mass 8.0 times as great, 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, losier; ;f fov+k:mng 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 use energy stored ibebam):fi/ :zb q fx..n a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindricf imbe:xf ba:q/b). .zal 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 awg,ap: +dj)lmn $H_2O$ 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 a/6c c+,rp( e9uqwz1nmnb r5;s 3;*g otg xhript speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore friction6xanvv/ 1:sxt:mcs : t) 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 acc :xs6:/a:csm1 nx vtvteleration 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 vertically on tj9 7d/es (n t9 qdrqo49es2fimhe floor, and we want to exert a horizontal force F at its a7mf 9 i ed (2/9sqro94jtqnedsxle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2,sei y7bgj9;7s q7w5iifew n.m/s on a flat road is making a turn with a radwf; ig9,77isj 7esiebn5ywq.ius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.506w4ti dra5(mp-kg rock into a sling 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 after 5.0 s. What is the torque required to achieve this feat, anir4t5aw6 p md(d where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinde:kdbvi ck,)1 ktv-fip,t20zdr and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of thvtdpdc2 :kz k 0)-1vitbik,, fe angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which +j) itc-zzdlp8z-eg m7fg ,0j consists of two cylindrical plates, of mass l7z8gz+ p0fji,dez)tg- m-cj$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along :;jgee)ij6d sc 8 bv(bthe looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marblei )c:v8de(6jsb bej ;g 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, butzthpum3 d66 yn*-w3qr do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its sperpzy8/tfot,3 ed uniformly from 90km/h to 60km ztfp3/ oyrt8,/h The tires have a diameter of 0.90 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