A bicycle odometer (which measures distance traveled) is attached near the whfhwl.1c(w:oo x1-d*s n* dgk geel ho(*:c1.lhs -fkn1 x* wg wogddub and is designed for 27-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 point o*wx*ul fy4 ah8q*+-)vyoi odxn the rim have radial anda*8y f*ohw-+ d )ui*4xvlyqox/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 change?

Could a nonrigid body in -ml oo+n)n+bp6f1rbe described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torq-zn cok al((:lue than a larger force? Explain.

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

Why is it more difficult to do a nlptw (igb,32h pf q6,sit-up with your hands behind your head than when your arms are stretched out in front o,bw23fpp,hq lti( n6g f you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel1* ;:zdzcmxt45jl huc m s7z/k and three at the pedal cranks. In which gear is it harder toz7;*k4 u/xhlmz:jc c1mst zd 5 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 ,tb cz91s vyk0/rgu ga9a7hp7 on being able to run fast have slender lower legs with flesh and muscle concentrated higha09gs/ yt7r kc 1,p9v bzagh7u, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers ( nq kec*;j7j)vzwn/ /9sdkq4hFig. 8–35) carry a long, narrow beam?

If the net force on a system is 36 teziuzakdpn9 +p54 zero, is the net torque also zero? If the net torque on a system is zero, is thee6pap3 n i4tdkz+9uz5 net force zero?

Two inclines have the same height but make differen:x fkmwmrv 1f1f: i(x6t angles with the horizontal. The same steel ball is rolled down each incline. On which incline will tw6:vmxr k1 fx i(:1ffmhe speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (fr7s0 xe l3dth3mom rest) down an incline. One smt03l d73 exshphere 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 cylinp)5t0d- lkltv der have the same radius and the same mass. They start from rest at th-dkvpt)50l t le top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most m:h7z. fsfi5ta oving or rotating objects eventually ziah:s5 7ft.f slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, ho uggw/j3*+ywh w would this affect wyg* ug+w h3j/the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any ini lgvg- v5*g: ekwfke, nhq)v:v+w0- lrtial rotation when she leaves the)kvq,k::0+l l*w -weg5 vvvg rhg-en f board?

The moment of inertia of a rotating solid disk about an axis through its co 6; zdm;m-t2bsla i;kenter of massz-ds; m i6bt;klma2 ;o 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 holdi9 apff0)9cyj;i 0qd luj ,ekg9ng a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your ac90gqjfu;ald 9,k90yei)j p f ngular velocity increase, decrease, or stay the same? Explain.

Two spheres look identicaxh-e:8k 1u mbrl and have the same mass. However, one is hollow and the other is solid. Describe b1xh8mru: ke- an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontalogttvh +8b.zy:udk4+ d4vb d0 axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angularu. yho8dt +v4dzbvtdg0 4:k+b speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable.e (+klw b:(hmm What happens if you (k:w(lhm+m eb walk toward the center?

A shortstop may leap into the air to catch a ball and7xdp- wa7ditad*n +: b throw it quickly. As he throws the ball, 7ian+d bw7ptd :-x* dathe 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 conservation of angular momentum, discuss why a helckxnk2*-h j 4ynf/pu5icopter must have more than one rotor (or propeller). Discuss one or more wayn-5*u2kx 4f c/jhnkpys the second propeller can operate to keep the helicopter stable.

  Express the following an:3:mj ks1wn eggles in radians: (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. Calculal lw3i,twe,o+ te, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen oni,3ow,+tlle w Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam2sdn.h; y. g guv1vl.s diverges at an.glv;uss1 v. d ngyh.2 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 v, qr+ avhx,*icz pf;+rotate at a rate of 6500 rpm. When the motor is turned off during operv,zi,rp+fa+ qhv* x;cation, the blades 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 leve63 wsr2+xowgrl floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diameter? rw xgs2+6r wo3   m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How ma+k6h 0z7 to .l ku:as)dtiw4mrny revolutions do the wheels maka s)uzw+.tki:6h kt7 dm0olr4e?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Ca6d4poble0dl gb4q.d )feq 97klculate its angular velocit6b 0ke dld4.7pfdlqbe)q4og 9y 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 compl nd6b5 ophi/+t)2a)n tp vl(,l1adaos ete revolution in 4.0 s (Fig. 8–38). (a)p)aavnh a 1t+5/ob) t nsll,dp(i2 od6 What 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 aron4fri pt.)+ wgund the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spee e* psod;4t*vl;rlr2 vd of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a p5j r+5c) ps)u /)h8zinoxc;)xbsp lfiuf mi63article 7.0 cm from the axis of rotation is to experience an br)u ) x ix3/sfoc6 p5fzin)umh 5)psij cl;8+acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center frombnn):3i)l;/: w;ayq p 1 f( x vm+otidb1bldwu 130 rpm to 280 rpm xw1 l)wvp; bn+o1mub f)(d : bdiy;ait:q/l 3nin 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 radius zzxe/3a51 gqh v1rxqhm/pza. t;*yi- $R_1$ 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 spacecrafuxw4: oe+ajb+ k ;tl y *a-x:xt:sfhtwh8-u,kt 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 interval. The sp as 4 ehttx:k k-u:8lby*+hwuoxwt;f:x-aj +,acecraft 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 accelerylx0 g 4gtgd8;ates uniformly from rest to 15,000 rpm in 220 s. Through how many revog0y g8ltgxd;4 lutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5tfe- my 7efa5) s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a wh29;x3 0d8tcmtdxnw xpirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachip 9t0dwx8mx2xcn 3;tdng 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 atm0j ; yod9z)kh;5g tsccelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will 59ds; g;)johttzymk0a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runn.mz43u;1n es agy-e luing at 850rev/min It turns 1500 revolutions before it co 4 1nu yee3au.mg-zsl;mes 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 red.(oeah:a1 xgxj xs3q(ej60 zpuces its speed uniformly from 95km/h to 45km/h Thaqax ge (o.z e3jx( 0pj1sx6:he 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 car reduces its speedym(61f0hxtr i uniformly from 95km/h to 45km/h The tires have a diameter of0(if1xhmt6 ry 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 b7+:d 59wpveh r;.nxtwib;- pjn)nly dike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 97v w rp hyn)bdw;:+x;pn.nid5ljt e-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 wide. Whao/53 y tw5il m1op ba*iah8hs3t is the magnitude of the torque if the force is e5 hh3/3osa*b oymitpl1wa5i8xerted
(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.hco : v8kpkx +i/s95lb1tj3nv 8–39. Assume that a friction sk pcvjk15i3t/+ln9 : x o8vhbtorque 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 massless pc 4v)nq c+8/w6 haucjrod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then releas 8w+nu c/cv6jqa 4p)hced. 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 t2(2 xiflb)ocuorque of 38 cbiof(xl22u)$m \cdot N$ 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 10.8igouv h3xbdlm z*6oa;u/ 1i2: 3y8it h-kg sphere of radius 0.648 m when the axis o/bx:o1yuoh3g3 m ;iiudz 682*avithlf rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertixwf3x6* g5;j) p phtaxa of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of t6t*5 );wx3gfx jhpaxphe hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end x0 (vdcwt-u(n v 7nd2gof a thin, light rod is rotated in a horizontal circle of radi cn-udtwv2n7(dgv0(xus 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant 3k0b.gsiqu *h angular speed (Fig. 8–42). The fr*3bghkui 0s.qiction 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 obje -e qp+ wz0v*jp3xj re:yx,)qjcts shown in Fig. 8–43 a+wq: ej ,xz0vp -xryqpe*)3jjbout
(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 mao-pq(;2yfm xcss 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 sa 4l k*vi+,uoyptellite 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 the required steady force of each rocket if the sate,*k+ly i4pvuo llite 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 radiu9i:.s aq5q zy ( lnrgtfz0ka)-s of 8.50 cm and a mass of 0.580 kg9 -5yzf.al t0 q:sikqaz(n)rg. 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 fy-7nc,wby0 ciweb . vqx/ce(en 0mb-0rom 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-. nzh/nde.z/(c o.rrt driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has.dc(r. / zz.ntn/ heor a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually brought )tt *teli4ho* uniformly to rest by a frictional torque of 1.2 4t th)i*oet*l $m \cdot N$ 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 accelerrmv5 322wgrh yates 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 6b+a/*cw v ensf5w3ntt waz -4thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. nnwtts 4 caf6/evzw53*b- w a+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 shownb6lbwd.vbzlfg29 7 ob,c z67e in Fig. 8–467 bdgf6bz e.27ocwll,6 bv9z b.
(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 ma95odmwh/w,fn.:t y *sj0: axzo pb7xqsses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (revoin s9 gzehkvj9ex7dl;w9d 59f/y x11m lutions) and releases it fj/ke; m9l 5wsv h79zde1ny1 igx9d9xat a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of k11lbi0*) veh: iyzww$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develop k0ri /zo10p+ d tieqp6nc/7nbs 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 szk3h(v n6x dbjm60 87cd gi4q;vg(yj 7.3 kg and radius 9.0 cm rolls without slipping down a lane at 387y4czjbi(66dvmkg (0;nxs hq djgv 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum oazd fpuab 46c3dob9--f two 6f3u4cdp -o9z a-da bbterms,
(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 net gx tdz :(+2d u4v1edqb 9udrii8ge,;twork is required to accelerate it from rest to a rotation rate of 1.00 revolution bgdt4 2q dtedud;e,v9(i :xgziu8+ 1r 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 and rolls (a9 c ov4ildx3l05nq eb2qv3m without slipping down a 30.0 m05cld4 9vo3 vx 3ebq2al(nqi$^{\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 start l8-ndamzb(m 5cdf7ms/ zs8p8s to fall and its lower end does not slip. What will be the speed of the88ds 8ml(7 zcmn amd 5sf-/zbp upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a i s-lx5za (oz-thin string in a circle of radius 1.10 m at an5zoz (--xa lis angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindi;oszwwvls;+v0.y zmm)4e +z i6 l5xutng wheel of radius 18 cm when rotating at 1500 rpm?ze wvwtzui5;zl lx .+ 0m; ms)sy46+vo    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at mf5shebe qm8(d x1w fgd 7k+10a rate of 1.3rev/s If he raises his arms to q8(em1ds5 0xffkehb7dg1m+w a horizontal 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. 88 7t5/)x 7st ii2ep8giqkigsu–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)ipugk sxt2 8giis57i7 t/q8e 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase h ) /sdxl:mvsy4er spin rotation rate from an initial rate of 1.0 rev every 2.)s y:xlds4/m v0 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 around a vertil)jb ,axem69qfg 8n;r cal axis through its center at a frequency of 1.5rev/sm;n8q6jl)r xb,ef ga9 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 frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angulay sb8s0 z ai/7ilm:n52e utz0mr momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Eart b0pfx7;k tm85fvjdd8h
(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 ik3:t n-:f*alo 7rqed/z 1 lgcrnertia I is dropped onto an identical disk rotal 7kq/a*z3rr-olgc:t f:ne d1ting at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2x)j qk:, /m7g tkefv-ske /rfz:2o.(6zqvvm p.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 cente-bp 4aorllz2q(7 ;fl jluv t-,r of a rotating merry-go-round platform of pa-lq o(u l4,j;-l 7btvzf2rlradius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity ofuj.hquktm 1m udm6z-+m1b7* d 0umtd.1mbd6 -k hm*1+ juq7uz m.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 *da h ymqv() eaao/,1dcollapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0,/a d1e*v dmohq)ya a(% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120 sns+weob *q3hy7/i s-a3 v*kx$km/h$ 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 asv,)sg1j )4tv yczq3 $ 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, tha3 e /wt: emnem64lg0rvt can rotate freely without friction. The moment of inertia of the per glm06ev /w:nt3em4e rson 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 s a*ex:z0uh-r-/ dcsqq tands at the edge of a 6.5-m diameter merry-go-round turntable tuadc 0ze rqxqs -:-/*hhat is 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 -b/fdoai ;:jw rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs thejow;/:b ifd- a 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 move?

  The Moon orbits the Ea l5d0)bj,r g 1wzmqi/orth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the z5 i bd0wqlo,)g/ 1jmrMoon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate ol++gycq ( rwm++hbjs0f 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 ux9icv(/dcxo uu5;twei82 1 ythe shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0 (xtu 5xyiud9u/ c1o;ic2 wev8-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 (:alcsene b91, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass:c9enes (l ba1 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 angulag-r k .f6nll d3xfnlv2 e0cp+;r 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 grea1eoe uoe35 4x0igloj28my ,qmt, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assumemqo ul2, e goex0 emo38y15i4j 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 automobilek ;p. 9qhaksh0 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 3asq0pk9hk; .h 50 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 illustratex: zo-g1yhsl (hopj1x *07ufjs an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) ugfee c9ugpq)zu8 f8v4;/uo4 is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pt()hp33-d4 d2eimhjda l gg3b+g ,kzxivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as sb3dki t3ggdahde l23gp z +,4h (xm-j)hown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It ir*o 5/ma)o-qdc9efoys standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against wq * d -9mf/oa)r5eoyochich it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling (owm i ;4r5mncwith speed 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 forcir;5 mcon (4wme $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 length47mgn),ba g 1x 0anhia 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, and where does the torque4gm7 xh1,aing aabn0) come from?    $m \cdot N$

  Model a figure skater’s bod6:f ::0ak:uzty o khviy as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for ykt :vaz f:ik:h6:uo 0a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, oux6 / ft.1cehzf mafu ./tx 16zcehss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough tracsj*x;htp - *nik of Fig. 8–58. What is the minimum value of the v* hxnt-j*p s;iertical 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 do not9p6h g4hbc+ti-:ajl 8hkdf-j assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the cayi/ ,o .:ojgfibp g;q3b/0t tyr reduces its speed uniformly from 90km/h to 60km/h The tires hbji figyo3 t ty.pq;g/0/o:b,ave 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