A bicycle odometer (which measures distance traveled) is at qb7( q9ryzxo8tached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicyx8qb z(qoy7r9cle with 24-inch wheels?

Suppose a disk rotates at constanp3ah3er8ic:p t angular velocity. Does a point 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:pr3ap 8ec 3ih the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of thed/m()w rb(wz i angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque thanle8c hgg 1t1w2 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 headb2e 2g * y4.yg80dfewpp( cohg than when your armsgh 28pdg ge(2yb04 y. wopef*c are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven spro.s *vs0vdnnr /ckets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a smalnds0v *sv/n .rl front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast hai-o3ojj nr)v2fd e +e 9wt3yn21p p9osve slender lower legs with flesh and muscle concentrated high, close to the body (F p1io)f jsno23-e93y 2ed t 9rjpovnw+ig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bejg;t /pnc*i4c sfy ov+2;8shjd3wl k 2am?

If the net force on a system is zero, is the net torque also zero? If ;z1f3 thn7/rll;lshn the net torque on a systerfhnz l/1sl l7nt;3 ;hm is zero, is the net force zero?

Two inclines have the same height bumvnirtwfq1i 41q1x ,9jbb ;9ut make different angles with the horizontal. The same steel ball is rolled down each incline q vbb1rnfmu;xt41jii wq9,19. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres siw;e)/w ;zz/odh0w vrtmultaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. W;wwz/ t;hw d )0o/vezrhich 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 have the same radius and thes1s:9 snr v93(; papv-wx lqfr same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the grea ps3n pv1f:99 rqwsl;xvs- (rater 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 gb/iq8cwi 58bmoving or rotating objects eventually slow down and sto/i5 8ibbqg w8cp. Explain.

If there were a great migration of people toward the Ei559+ng)ss zw mgo(c07oqaqu arth’s equator, how would this affect to9gs7ua q q05 nmc+ g)5ozw(ishe length of the day?

Can the diver of Figy p4 0eeo4ajig9 dn*m1. 8–29 do a somersault without having any initial rotation when s* e mje4dg0ona9i41 pyhe leaves the board?

The moment of inertia of a rotating solid disk about an axis through its : :gifwe5tkhr/(j99 qpjvm /q center of mass i ih jfg(:wt9v je9/ qk/qrm5p:s $\frac{1}{2}WR^2$ (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 am0;bwhq5)7y+ qlcq a a3wk1 yw(t m0rb 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, oby cqmky5hwlw aq(q tr )+m1w703a;b 0r stay the same? Explain.

Two spheres look identical and have the same7ve:2lh g f0/e c*jgqe mass. However, one is hollow and the other is soefe v :gl 7gq2jce*/h0lid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizzzj m jp+r v *j0igt;hs6fxegm)5 j03)ontal 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 angular speed increasing50j) vpm*i+esxhr jgtjj ;z0mg63z)f or decreasing?

Suppose you are standing on the edge o(pkow did*hgg6g1h; nznka h7d ./f/ (f a large freely rotating turntable. What happens if you walk toward 7 hi6kghngo(;afg//dd *.h wz1d nk p(the center?

A shortstop may leap into the air 5yz(0fnnd- k xto catch 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 his hips and legs rotate in the -y0nfkdx n(z 5opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of anguz asxq: /vf 0*3c4rdoolar momentum, discuss why a helicop4q/*3: 0rvoc fos adzxter must 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 radians: (arzlk qe .sdz.4dt,+.tem y (wd8v2ty4) 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 ambvhl3 .a(e.1cxj q r/nazing coincidence. Calculate, using the ince3 l.(1vrhba /qnxj.formation 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 fromz7/ vqls6z v0bz *ljq2h3 ygz) xe1/td Earth. The beam diverges at av62e0dzb s3v*l qyz lx1 z/q/ j7)ghtzn 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 motor is turne jr3mk);8otv-9t t fm b2rd1esd off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blade mok1r mtte8vb93f;2 -)rdstjs slow down?    $rad/s^2$

  A child rolls a ball on a level (33u m7fszjd4 jrr:wk floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diw47rzm( dj ufr: 3sk3jameter?    m

  A bicycle with tires 68 cm in diametebl* b+tio95/j:vp3swe tt n0cr travels 8.0 km. How many revolutions do the wheels mak+ ts*ov/pc3iw:lje5n b 9t 0bte?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2uf8zp uc d -d. j5pms3em56-be500 rpm. Calculate its angular velocitfbuu865j dsm-de z- pe3p5m .cy 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 s 8y*j(daaf6gone complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear spe(*f 8dgsaay6 jed 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 around the ;oz;:qxkqog/mr8 +-a e3wawc Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speedj0 v/ m;gnrelp43 n0zt 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 rotatebke jv e; c4o0iwby5z z*.3k5p if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,00zy5*;cev4 3 wkjbp.bzk50 ieo0 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unifosvdg kys8,86 ormly about its center from 130 rpm to 280 rpm in 4.0 soyg kv68 ssd8,. 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 radiuz 32r,p vatqjx2ksg-*s $R_1$ 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 Apoy01d 9.pgs1w4riw qx4jrbt4 dllo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotatio0 j p9yrd1 btrdsw4q4.1w4gi xn 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 uniforml8;jgvpxwx hitjds *5h ::3 t(qy from rest to 15,000 rpm in 220 s. Through how many revolutions did it tur:8xjh(wsjtx:hdgpiv* 3 ;t q5 n in this time?    $rev$

  An automobile engine slows down from 4500 rpm cf2oy upo:3: u1xx e)yto 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in ah :zzl7-xbipwgyj;(ot6 (*wmc7 tov,jvm 0 ,w whirling “human centrizw(p;*lmg 07v: om jvj(hw-yotw76xbc z,t ,ifuge,” 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 diam (nz(v8bns1vzhp: fl .eter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travelzn:v1vzb hp8s ( n(f.led in this time?    m

  A cooling fan is turned off k* e1j(a,6rknbvz fzwl*he -z4*b7nmwhen it is running at 850rev/min It turns 1500 revolutions before it comes to a w*z-mjzkb f*z krah4b, 6*n ene7 l(v1stop.
(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 asp-(trsy5 v,t p 7+tnxft/(dw k the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter ofx dst+pw t((vkp/y tf5nr7- ,t 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 th).9husiy2 nyaq1h6 tf e car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m2) yhfn. s61aiq9t yuh.
(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 each pedal whet+im 8 eourz0soz.g o8pd31n.n climbing a hill. The pedals rotatesp dn10+mr8 8o.guoit.z 3zeo in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force o) ti4cw)rjt9af 55 N on the end of a door 74 cm wide. What is the magnitude of ther t4c aj))i9tw torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8p;q079 2jkb0kv n kqzi–39. Assume that a friction torque of 0.v07b2zkq pj0ikn 9k ;q4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of massi49 n6nnc1 a6m(fdest m, are attached to the ends of a massless rod which pivotsnces dmf1a6tn 9in6(4 as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening tdch9gr ;eabv p:y + 2rwgp-w)6o a torque of 38 wc re+hyppwvg 9-g) 2r6;a :bd$m \cdot N$ 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 moment1z skc84 flvs* of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through itsszk1l c48vfs* center.    $kg \cdot m^2$

  Calculate the moment of inex .v(1 suyhsmdq0/7h brtia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1qbhs m7xv/s1d.0yh( u .25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on th031 pjo t0gjmy8h-6iix64du3 b bhnsy /nil /de end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculatenjpsyl16im43n/3ybbho0 6 i hugtix /jd0d 8-
(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 rota( nedl a4w1)rnting at constant angular speed (Fig. 8–42). The friction force be1w d( an)lne4rtween 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 objems, zn+c 9ol*icts shown in Fig. 8–43nm *loz+ csi9, about
(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 muod rifm.(4:9si 9sswhose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the corre- *+nn ac* ge,u agrmq)k+4pexct rate, engineers fire four tangential +-)xagnqp erc*u+kgm nea , 4*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 satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of s,qho0yj4ov7 0.580 kg. Calculh7o0o,s q vjy4ate
(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, acceleraz5 rk blky9fwng ()*s+ting 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 nbbu byf6t 0uk;d27 j6w3ngi+a small hand-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 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, yf;bbng703 d6 ji6nbwu+t2kuneglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor ro c6pub(ij( 0lgtating at 10,300 rpm is shut off and is eventually brought uniformly to resp((cb0u 6g jlit by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg bac(i: ki gtiuh7nojfnmf*/qn a4-5r 1. ll at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm,dgwn jn4eamr qy7imf6789j:) which rotates about the elbow joint ummde7n9 48)if7wy:jjrnaq 6 gnder 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 rol:, 4ljwfeza*yfeb* 2 d, as shown in Fig. 8–46. z *,*2lajl4eeffby w:
(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 consistc0 xzjy1g78, qe5 9v2ofltpmi s of 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 four full turnjs+ 4loka ;lo0s (revolutions) and releases it at a s;0k4oll sao+jpeed 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 inenz i5nbgkgq+ (lae3 ji:*s:8a rtia 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 280v85*b5qbj wpc $m \cdot N$ 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 rolls without slip 1s2q fsz*rbpxxj9-g (ping down a lane *fbx9xj s1(gqrzs 2 p-at 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 ofid 3w +2jv-rfvpdpdhbl o/8 3u9 0ejm6 two te0o3dvu+8d pel j6 hfwr-b dpj9/ i32vmrms,
(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 mvrjxg b1b1cg a j;xxu;y0*4)x. How much net work is;yxx1gb4j vg *)a xcjurxb 10; required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls wqzle/9u gsy*u-3zp;kithout slipping dow-k z/ supye* 3;qu9lzgn a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tr 0dst2txne*. ip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole junt *0er2 xst.dst 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 5g75/ch6oa7f ehh p2,i k-dnusp-rvxend of a thin string in a circle of radius 1.10 m at an angular speed of 10.4 hhx -sek75do7r/2fp,av-6i 5hp gn cu$rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical q2pb 8mp/th5r grinding wheel of radius 18 cm when 2 qt5pb/ 8prhmrotating 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, hank (h :grq.k1xv j)eq;vds at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a ho1.):k vvg j(x;k hqeqrrizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inhk9z mmf7y5e xp(n50aertia by a factor of about 3.5 when changing fr(y0mpa7m5z fn5xe9khom 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 inc5mli1y7;c dve6t+sd rrease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final ratlc7se+5 6viy ;rd m1dte of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis thromc p 2xh05kn4n gvn4b(ugh its center at a frequency of 2kxp(vb n4n nhcg0m 451.5rev/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 frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular mbt;fupz/ 54y 5bd:s;7odgopnomentum 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:1j4x jnd(e vk;gab8g momentum 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 mome-b koc.o5h,munt of inertia I is dropped onto an identical disk rotating at angucok5uh,b - .omlar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ath0p7d ce/+t mr 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 of a rotd5b pzopw+*v9; fd h:cs4 3gqx0yo)n aating merry-go-round platform of radius 3 ad 0 sfw9dbopy;3 +g hqz)xp*n5c:v4o.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 a j1 fpsev9 :xzu87,ugrngular velocity of 0.ev,sj1 : r ufuxz8g7p98 $rad/s$ 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, losinnvsph d3s d+*; tv* -p t8,xsnjm/sl)gg 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 momentus)s lvv8s+/ hjxmsn,d;dt* 3p p tg*n-m, 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 9gleni,s-l 9p;t b1 vewinds 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 :r5 fo-c uia -msg 28bkib(a1u$ 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, thatu9eb 0b9hw (u+m 0satov 0.,ksgh1uwq can rotate freely without friction. The moment of inertia of gkhw euv s,9qsh00 u9+ mut.wbba o10(the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merrm2z) slb cc -d35dhr5s6at- xjy-go-round turntable that is mounted on frict)da- tjr 26s 5hxb3 czcls-5dmionless 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 on m8 ionjf ;p3vko3ard,h. ,5jf 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, Fiv8pidhrko5 ,.mj33jf, a;nn og. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same sid0ewul,ert ;y d(5d a: mjus77c5yc6hv;lw -zme 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 camuyc5 h e07u7d;;jt vwlse(cm- z:y56rald,wse, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratedu u7li(( 4vhr+jser:k.y(wh s from rest at 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 t8u-nj-ccb 0 n)n8pwka he shape of a uniform cylinder of radius 0.20 m acquires a r-88aw0ucncnk b -nj p)otational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical.og 02r0;ow6kpo wryx disks, each of mass 0.050 kg and diameter 0.075 m, g opoow; wyrkrx0 .062joined 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 string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular spee g5l-z2w5lf*r vt x32dw+jqurd 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 7s1), ,ent f:dudqts04gqgd6fy1yv dvgt8 a )8.0 times as great, were rotating at a spe1d ,s:t1yqg)4dgfd 0u ,e6vt)7nf atdqvgs8yed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to usu:f ahx++j8(tbox 6 uke energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a (t8 ujhkx+uf+o:bxa6 uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates 2lp+xi8zu, pe an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed v=3.3*jfmv8s4rf+mbf 2- uhwy7, lu $m/s$ 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 pi .up*6rg *zd7lyy kk(dny 9gu;vot 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 rodkg nk ydy;z*(p7g*.lu d6y 9ur, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vepfv-d kozce .df9v77;rtically on the floor, and we want to exert a horizontal force F at its axle so that zep.f;7kv-d7 v9 odcf 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=4.2m/s on a flat road is making a turn witp k17h+6nhy;ldj il3gh a radius The forces acting on the cyclist and cycle are the nni3l+6lg7 pjhd1hk ;y ormal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and beginh s+26 auct4w7rr70wpag3awc ( s9 epes whirling the rock in a nearly horizontal circle abovear(04c7w+6ew7u h sc2ret a3as9g ppw 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 torque come from?    $m \cdot N$

  Model a figure skater’s body as a5qcn/d+f un x5 solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstrn+xdc 5n/5 ufqetched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consi t5/.x ;u/f:b bqgna93 zbjwbxsts of two cylindrical plates, of mab9 xqb;/ntja:gxb /z3b5f uw.ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 m*ild5q97vg0sj+d lm- c 6ev dr rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest poincdd6v0vml5- s iqmg9e l*7+d jt of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but d v *g,0hysafmi8btt12j 8kw(1mt do)t o not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed ung.wu0qpu 6x8kjax., qiformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) Whaq 0qkuxu .6 ,.pw8xgajt 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