A bicycle odometer (which measures distance traveled) is attached near the wheee),u)i. qa -q6 byunbrl hub and is designed for 27-inch wheels. What happens if you use it on )b. ) e r-abn6uuyqi,qa bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim ha)v jtpm(tzd5 7o57/o)ermarw ve radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential jva)7ep orw5m/ozr5 dt m7t) (acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a sin/yjo9 ozl0+o lkxa853bbslx*so ( z4qgle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger f 6rl6f/ .rwkxvorce? 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 y*m j9 1*8k u-kdtz9nsj3a ajibehind your head than when your arms are stretched ojt*a8zjkj 9im *uyd1 sa 9n-k3ut in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rk +1ygbh e* ,+z5irm*npjs/jfear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small f+* r y,jz h kmib/1s+jnep5g*rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs wi/majbeo7.)k x th flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advej7 k.)bxo ma/antageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bcm qybaqv*oz t,54i58)p* u yceam?

If the net force on a system is zero, is the net torque also zeroc l4(c(ttjl1 kz c./jn? If the net torque onj(n.tclzjl c(k t/41c a system is zero, is the net force zero?

Two inclines have the same height but make different angles with tmg 4:rfs0* pmjhe horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at thpmsrf g0 jm:*4e bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incli( chrq 8nhdwek:6,vvm nzif0m4yswz h7g.(8 ;ne. One sphere has twice the radius and twice the mass of the other. Which reaches twgkq( hs:( n4., ie7ndcz;v86wmrh0vfy8hzmhe 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 twdu. kbevlbey9 7 q(y15qyb7/he same radius and the same mass. They start from resbbe17by 5k lw.q vuy9(e/d yq7t at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving o2nqjc h d4.zr+r rotating objects eventually sloqrc.j +4hnd2zw down and stop. Explain.

If there were a great migration of people toward the Earth’s equ)lldkg 7vj 1h;ator, how would this affect the lengtj k)hlvg7dl ;1h of the day?

Can the diver of Fig. 8b7prug 3 kv1(gd c;f2j–29 do a somersault without having any initial rotation when she c;(vj21r7 u3dgbkpg f leaves the board?

The moment of inertia of a rotating solid hg(dnuhz) 7c6mcx+ b. disk about an axis through its center of mass isx6u+cm hdgn.c7 h)b(z $\frac{1}{2}WR^2$ (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-kgb,) izsrep. xmb i-l.+ mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, +)pmie.sr.bb-i, zl xdecrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howevergvb u5lmd )fc r+na40(, one is hollow and the other is solid. Descrburma5g)+ f4d c(vn l0ibe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horj1)pdf 5 yq6 1mqeqyu2/gbae/izontal 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. /e qfq)j12y5qgu1/y meapd6 b Is the angular speed increasing or decreasing?

Suppose you are stangqi i4xb9q 86-khp vq: ap4v4w wrwm1-ding on the edge of a large freely rotating turntable. What happens if you walk t v61k89pbwgwwvi q4axq 4h- :rim4p-qoward the center?

A shortstop may leap into the air to catch a bal:munm 6 pt0udq 73w2ow8z/fa ol 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 opposite direct:8m6w m0 /ow73p tnoqafzduu2ion (Fig. 8–36). Explain.

On the basis of the law of conservation of angular m4dzb0;:3 yv3wl ulc48rryvs1 i .vwe momentum, discuss why a helicopter must have more than one rotor (or propeller). Discvz 3w8l4d3 eylv ur;1mbivy.w4 sr:0c uss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a 5ck s5:sa.;iw uik+lyxq 0tq3) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, using th kq3m7d3v*vxd e information inside the Front Cover, the angd7vk3mqv3 xd *ular 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,uv o;7m5oq 0bc 380,000 km from Earth. The beam diverges at an c05qvm ob;uo7angle $\theta$ (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 turned o a2t5flbpm d(hlws.( d (rly91ff during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades sll(95dsr (m a bhf12p(tl lyw.dow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ba g( b*cbf:vnub lx+8p 5gc od*a*kh;5fll makes 15.0 revolutions, what is iuoh85gc;* x *g(pbnb kb5c*+:fdlfvats diameter?    m

  A bicycle with tires g1* d lg(oxc)prd:fj:d+lw5iz+ pv .y 68 cm in diameter travels 8.0 km. How many revolutions do the whee: 5rld (o +pjxzgg+.p)fvd:cdly1 i*wls make?    $rev$

  (a) A grinding wheel 0.3g *1x ;z5wahxv5 m in diameter rotates at 2500 rpm. Calculate its angular velocitxz5g1h*vx a;w y 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 completeo7,wsft o7c)ia6:buq revolution in 4.0 s (Fig. 8–38). (a) What iu 7b:)stqo6c7woa f,i s 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 v 8f,zfg2s4oqc 8)oq b-i mny9its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spear9t c+v)3o xa9ztlz3eiq cd r:0*e+ ced 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 ift 0q ws1e,k+id a particle 7.0 cm from the axis of rotation is to experience an acceleration of +is,w1 te kq0d100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its p5rrx3s8vvec/g/g v7center from 130 rpm to 280 rpm vv3 x7/gc5s8rg p r/evin 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 radiui08b jy cja6l8s $R_1$ 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 bq0vv*ns*v 5o;gxhk5 put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from s ok vx*hv5ngb;q5*v0no 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 frojd5iasbp) w:3m rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in p3 jsba5wd)i: this time?    $rev$

  An automobile engine slows down from 4500 rpm t+ jbo4apz*,v qo 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 ofi iti:lha f-): flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final slia:i) -h ft:ipeed.
(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 accelera*tw/yr1 9cx o jzsh;w7tes uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edgs*1rc tw/7j9hzoyx;we of the wheel have traveled in this time?    m

  A cooling fan is turned off(a a-o+lwvbmn3b: wm,gy +:wjv;nt, q when it is running at 850rev/min It turns 1500 revolutions before :mq;oww+m-v njy + (bgb,v,nt: wa a3lit comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed ud cds;t2u q9ap lkq/1;j*t p2uniformly from 95km/h to 45km/h The ts q altp;jp dc2u2ukt19d*q;/ ires 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 thmh b )i xdj-*kt2k//tye car reduces its speed uniformly from 95km/h to 45km/h The tires haj*2b -)yx m khdt//tikve 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 bikey;.xuag : wir- puts all her weight on each pedal when climbing a hill. Theigw: axu.-y;r pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What r /w2uiqcvwij )14tv3nx3( y uis the magnitude of the torque if thew/ (2 viuvj13qrtwin)u4x y3c 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. 8–39q+n/paht-4 zt . Assume that a friz4 t/tnq+ pha-ction 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 massl)/3rza qk8x/o,zoji-hf :oy.2 l, devp g afl0ess rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torquezlyorvaol/ ge,pa2)zf83,ifq:k0hj d/o-. x on this system.

  The bolts on the cylinder head of an ed a0ev- wyy:u4ngine require tightening to a torque of 38 4uw- 0evdayy :$m \cdot N$ 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 radius 0.648 m we ;dn:14p uejehen the axis of rotationd ;np:ejeu41e is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The ri x n*;*07ggm qajou7fjm and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored uxmn7f7oj0*g;a gq *j(why?).    $kg \cdot m^2$

  A small 650-gram ball3wg c4v7fqq n6 on the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Can7q4qw fv63cglculate
(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 angulyhq2bavv89;b ws;ke0w gad kpl20p70 ar speed (Fig. 8–42). The friction force between hewe07vyq0b 9s0;awdbvph8kgal2 k ;p2 r 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 ofz9y5(oop vcnwh2d 2 ;w the array of point objects shown in Fig. 8–43 ab5o2 nh zc w2;9(opwvdyout
(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 ms(jbfi ;h(jqre /kf2co p.81iass 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 th2py g*/ oox:k3:qodnj e 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, 3pd2:oy :*gq oonk /xjwhat 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 89 e*8hfso(nul .50 cm and a mass of 0.580 kg. Calculat9 8elh*snou (fe
(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, acceleratin9a. m-9ii7tivpl; ut rg 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 tangentiallyxg31rrsl9m f mr2 :0jl on 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 hagr 3:12 fjxrlsm0m9rls 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 eventuala3 b (p7et3 ya7p1pryvly brought uniformly to rp33ea(y ar1p7t7bpyvest 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 ball at 7p2g-re,6noaf 0a dt7a $m/s^2$ 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 soleldsx39e q.z.j f9ap9 rsy by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerateds .pxeqz9a9 rj3 df9.s 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, ass)yx6/h)q;l+ xwwirg shown in Fig. 8–46.yi /q);hwg6)rx w+ lxs
(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 lp0xz5yv wnc,y:2 j t9consists 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 hamm e*a11nv mmed9er from rest within four full turns (revolutions) and releases it at a sped anmve1*e m19ed 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 hasa0s3jhq4 3ilif*7k ) strap6 n 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 torqj 9xj.r abdmrqw v,y2l6-3 jr:ue of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg ano*: qa.i3 9wep4(ya7b09 lw odr; canoddq(ptd radius 9.0 cm rolls without slipping down a lane at 3.0o;b7caqw i4.y dwapna*d q3oo(p(99:rtel d3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy q y,kic6 1j84hvhr:vd,d-;i i :vv ohoof the Earth with respect to the Sun as the sum of two termi ci4hvd dhov6y-h v ;:1vj:o8, r,ikqs,
(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 andy5bj 1et(xjp 7cq07d r a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolr jq cj71yb( xtd5pe07ution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg staygv:h9t8 c)z , ;rcxwt2 ):ozy8il 8mp+lceuvrts from rest and rolls without slipping dc)etpvot28 )r x+;h:mg:l,lc8c zy 98 yiuvwzown 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 ep4s.w .jg4ectip. 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 ground4pw4 .sc.eejg? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg b(zp u*etvycbp3i 8rtj70 ad96all rotating on the end of a thin string in a circle of radius 1.10 m at a08( 3 6uy vibztrc*9ptea7d pjn angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2eqyt6k8a4 3p ytkqi*2.8-kg uniform cylindrical grinding wheel of radius 18 cm wheniek8t2tq6 3*yypq k4a rotating 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 atqmb j/2o6qx 7lih 20jg his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horb/qm 20 6 jql27hiogxjizontal 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 nf)y 8+c6r6,83w nbx6 acpte ce9vgztin Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in +txe3ay 9p66gc,)czfnw6v8ecb tn8r the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increaserryoig j h88)p3 fr1i yj(sm;( her spin rotation rate from an initial rate of 1.0 rev every 2.iyg r()prmf; (rjo18ys3 8jih 0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical a.),l4szodrq .ngze ;p8sqa /y xis 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-kqnq8esa. zoy). 4r,p;l/s zg dg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinnin8i2+cq8 qs2ncmdihd)6zl8z ftk yqg188e 4 bjg 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 Earthca,dyud7 ( zxujj5 sj/i i+1t,
(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 sw w,b v3i)2enof moment of inertia I is dropped onto an identical disk rotating at angula v )s,niww2b3er speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at1wf m -pl1,kul 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 rotating merry-go-round plae5so )udv o(ple 7f(b5tform of5uof(pe75(bv lesd) o radius 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 frev;idj tfm) 9x-.utf*i ltbm8qw;7mz4 ely with an angular velocity of 0.8 ffj79iz4u8 )m d vt*;t. qw b-mmix;lt$rad/s$ 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 dwar.2l.wemv- 7 fbfm,cen f, losing about half its mass in the process, and winding up with a radius 1.0%bm. ec2 ,.-ln7ewf mvf 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 wd zuttl)8n ub72u i;55 pe9drwinds 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 r9z5oc:skhqis 9d e1.$ 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, iniux/.c53nv.wab,6j r pfcms korku 92 /tially at rest, that can rotate freely without friction. The moment of inertia of the person plus the uk.nk/,ccw mvs6 u5p/ or x2.a3rbfj 9platform 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 stand q-bj. xt0x(tqs at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a momet b(xq.q0tx-j nt of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of xfbi49 t rux4o,d)(eithe 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 length of rope unwinds from the spool? How far does the spool’s center of mass move? re4xof)( 4tix,b 9diu

  The Moon orbits the Earth such that the same ;sioba1p 8f8m side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbitai8so;fm8 a1b pl angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at 4ifa jsg(5 5xa6z vqj9a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radihz 5dzgfn74w; us 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate t ngw;7zh54 zdfhe torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.05v/l64 c)s prkpel)h8d6 xlu x30 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released fromlp ldlk3v /6s4))c6urh px x8e rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the 2+t+.aqr pkfx angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rfg( i 5(bebkd.otating 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? Assume that the star is a uniform sphere at all tb(be g(i5.dk fimes, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutiz4lif*1i-j umon automobile is for it to use energy stored inlzu*ji1- i 4fm a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a 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 an1-t7tax96pxr ) zkcux f eb:3r $H_2O$ 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 r) nedva 14t5lkolling 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 pivot freely (i.e., we ignore fry-e+0kj3 s8t)h li,hujz4 uru iction) 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 ,hzj +)ti8hk luj04yue-sru 3acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It iz/m1gn jv./ n7hqln2vs standing vertically on the floor, and we want to exert a horizont/. /mn hnv17gjqv2 lnzal force F at its axle 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 :6fud ;-n9/ ypwfhaste)tg: nv=4.2m/s on a flat road is making a turn with a radius The fnnpf ag;)w 9 :f-uht/e 6y:tsdorces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling o0hclbuqy (rm; 8f/ 9* (;nxihjlxfn d*f 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 thelx8 lhc0*x;(;b/ 9mdyfn( ih*n u rfqj torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rodss6b7g; d ;i3hvg3kn op, making 3; pbod3;kggi6nh 7sv reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindric6udo* id;7nr y 5* nzy,ufdk+4mya:tval plates, of massouu+;d,:dazkt i n5*4*nr fyd6 vy7ym $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ansj.wvmxa-mz8+ k .s x*4bsi -zd radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume im z--b8szjxssxwm+4 v . k.a*$r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not 3)pjkhi 5cxkssj88z - assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 z+ xbm ch 36l0 pdoevq*yp,3w2revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.xwe doz*pcyqmpv3 hl 0+b ,23690 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