A bicycle odometer (which meaarft z9.dbw3;v6m,n vkj)d0ep 8 sf2fsures distance traveled) is attached near the wheel hub and is designed for 27-inm bnvvjs0d6z 2 d 8w9r;3p,fae.ktff) ch 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 on the rim hyg8 /caq l+9c:cepe9u yd0x-cave radial and/or tangential acceleration? If the disk’s angular velocity increases unifod x/qc 9gy0 8 p+a:yuecc9-lecrmly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the8i3n7 xdohxme qx3 t5/ angular velocity $\omega$ Explain.

Can a small force ever exert a great ,mo7orn2tb,ker torque 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 sit-uv wy ijyc;l,9,p with your hands behind your head than when your arms are stretchjc;yi,wl9y, v ed out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel vq65xx cr67ra4kd4 cvand three at the pedal 4 k7 6xc vrdav5rq6xc4cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slenx ysqhy k2ucbs*ql 9e8:v xvec1 (f165der lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this di8 1x*vyc2c fk1qshu ys956 eqle:xb(vstribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, n;wz: +gm zj4 o(lrv8szp4kw3qarrow beam?

If the net force on a system is zero, is the net torque alsouyg*27ep hg l q.(w4no zero? If the net torque on a system is zero, is the net fory*(uhp4 n.2wlog7 gqece zero?

Two inclines have the same height but make different anw p3e0cqzdl9+ gles with the horizontal. The same 0z3e lq+dc9w psteel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolbd 44e5k yan1tmb7ik+ling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which readkbam1it k5 +eb ny744ches 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 the same mv l56 dgvz5u sl4lbq(da30gs5 ass. They start from rest at the top of an incline. Which reaches the bottom first? Wgl 6ul435 qvads5gzbl5s(vd0 hich 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 conseryx :25b c,vnquqef; 1r.lph) dved. Yet most moving or rotating objects eventually1 qedx,yfvqlp2) :unr .cbh;5 slow down and stop. Explain.

If there were a great migrationx(2 phv6mw 3jp of people toward the Earth’s equator, how would this affect the length of th(w63x pp2vmhj e day?

Can the diver of Fig. 8–29 do a somersault without having gfzz3ws aw n59c6d6r5any initial rotation when she leaves tz6df5w6 s3nzgw a5c9 rhe board?

The moment of inertia of wg/a d9l9rm-8t ( 4p/jog58xcforu uhjway92 a rotating solid disk about an axis through its center o5(daga lrrouo p-t9j /u 9xc82w/8 fg49mjw hyf mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each out0ku1 chb wvq .q(zmvn8/7ny1. jerpv9 stretched hand. If you suddenly dr/ uwcnvqy j8h p110bzv7q 9kvn.rm.( eop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have4t qj2ztpds 3duq lo5la)6)p i h*82du the same mass. However, one is hollow and the other il5hp 4 z)td86o3pq jqd2usu*ad)lt2 is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. I ha3,304v s i w)krxq)m.ovl/6czc lddn whatz osm3 vl0qaid,. /rlv)kwcxc 4d6)h3 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 increasing or decreasing?

Suppose you are standing on the edge of a large freely rotav2w*v rv0qj 5yting turntable. What happens if you walk toww*q5 v yv0r2vjard the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he the+4rm7,k-px5d:y ftn:yol io rows 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 directio f:7erd l45mx- y,iop+kto:ynn (Fig. 8–36). Explain.

On the basis of the law of conservation vn81h*hn,8jt4bsn ov of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate v4 *88nhn jtnv1,ohbsto keep the helicopter stable.

  Express the following angles in radians: (a))lbnlyn,n4d*q5w/ r d 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. Caovt0:(l. y eadlculate, using the information inside the Front Cover, e 0:lvd.t(a oythe 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 f/ .lxg6pxvc h1rom Earth. The beam diverges alxp vcg.h61/x t an 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 turnejokg*w-e0zxo h. ywa -u4275d l-phebd off during operation, the blades slow to rest iowdy0 7 5 g a-xjlebh -2kz-p4uoh.ew*n 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on ,4 fbbdmp8 eu7tvtj1*tdmm1t0h 1sb 4 a level floor 3.5 m to another child. If the ball makes 15.0 r 7 jebbm 81umftv,pms thbtdt*14d041evolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km.5 lj np5cw4z.e How many revolutions do thn545. wlep jzce wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Ca9 uvzon/upram) (f0n*lculate its angular velo0u u 9pn*v /nformz)(acity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolutiod,h(uwn;h2 4 gxeg3bmn in 4.0 s (Fig. 8–38). (a) Wha d4e,(h2 wmbngg hx;3ut 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 it nud7s 1;jbj;i3fp+ass orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed owk3s38dpsr-)5m ;ca 1 hqk fkof 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 particle 7.0 dpd u9:6naga q1p ekl6n:i:(cw-e k*ucm from the axis of rotation is to experience-pqawdenk *:a1:iu klu6p 9nc:d6e( g an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 283pkbk v;qtz ;c7 i71k w6bukaf2a yb040 rpm ivb;23kb wai0zk6bq uy 1paf77kck t;4n 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu axa,1 hjo7uz9/i was,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 Apollo spacecraft put themsel-rgtp4ml8b n.ves into a slow rotation to distribute tgp84m- lbt.nr he 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 spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm sq )wl4 -e g9xxdy.c4zin 220 s. Through how many revolutioz4xx4. q-w yedlsg9) cns did it turn in this time?    $rev$

  An automobile engine slows down/z,4mk.wuzn 43cide(/e4v1 lrrjd e-okz1gq from 4500 rpm to 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 8wl ;yi(bh8kti y)jea8 6 l+rahighspeed jets in a whirling “human centrifuge,” which takes 1.0 miaei bj+)6 y8lat wh8lir8k; (yn 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 diamrcle lvc;n6 sr4; y/d-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 traveled inrvls; rcl -y4dc /;e6n this time?    m

  A cooling fan is turned off when it is running c( 15:trpqohx3gzmes;( iv2qi*t3z vat 850rev/min It turns 1500 revolutions before it comes to a stop.to s x(v3 v51t*q2pi; gze hzqr:m(ci3
(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 revolut*wpn,u,a z0g.az mdz4 ions as the car reduces its speed uniformly from 95kn0,mz4gd* .a pua z,zwm/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly frp4): z 6tt0in3xydqai om 95km/h to 45km/h The tires have a diametenad yxt3qi6i: 0t)p4z r of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike p 6r5s:utz lkvd mq;0u+rmaf+s2 cpr.4 uts all her weight on each pedal when climbing a hill. pt2q+rlr6cda5;u0s v m+ s.uzfr4m: kThe 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 555z +rh fh+kt0gllag j7gr;y58 N on the end of a door 74 cm wide. What is the magnitude of the torzlr y; lf +grkah0 gtg8+75j5hque 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 to ib)wmi.1gz.7 pzjiw9rque about the axle of the wheel shown in Fig. 8–39. Assume that a frictioi91gzi . 7. )bpwmzjwin 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 massless rod which l)/yn7et mvquvx4 fs d3/u2slo s92.g pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positiu3/. tv7vfe)lx2smdy4g un2 sl 9o/s qon 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 to a torque c lyb -33(1l:hwxotsaof 38lw3o3yxst:-a( c b hl1 $m \cdot N$ 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 radiu6c(4nz8 o) ooq uhyhd.s 0.648 m when the axis of rotation is thh6u(dcq )ohzo84.y onrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diame bfs:0p s:f l40:sifamter. The rim and tire have a combined mass of 1.25 kg. Thf: 4:slsifp:af0 0bmse mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a hu m3:qb 2eun2pxg w4frr30y f1orizontal cir 3:mr34x 0pq2wu1rgfeyn 2bufcle of radius 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 736yfv3kk)x issz++ofd w hi, angular speed (Fig. 8–42). The friction force between her hands anz ds +kk+6f ,)x 33iyh7fswviod 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 4 53egce0z:tepuw 7eminertia of the array of point objects shown in Fig. 8–43 a5e 043 wgm:7ze ceeutpbout
(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 who2c 1uyc p8g+cuse 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 cvrl(c *-81u4ipx ik7(s f+g n)w ld5aikkfzi4orrect 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 7kplr+(fi15x uik 4d v) i4 c*flz-wga(insk8required 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 anh+h su4cn6c 4azbjk;f 50t4w3 zivay9d a mass of 0.58c kht5avsnz3jhc y6 izbu4; f9 a4w+400 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest tdw/len b+ct.4 (:oi ego 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven m ,9ora h7z:5-p5lg0ok / hdhjoxgyjy *erry-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 an0d joy9 y h5ko5ag*x-/p,l7zg: oh hrjd has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 1 ))wzj. rm+omk0,300 rpm is shut off and is eventually brought uniformly to rest by a fricj.mw kz )o)m+rtional 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 b2( j, jj(exhdlall 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 isg rw: 1vp0rt:u7 kx*nefx1z67q -wjforearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is acce:vst 7 eqr0 1 ux1gjz-w:i n7p*6wfxkrlerated 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 considere4hziecwg83s :d a long thin rod, as shown in Fig. 8–4z84h:es ci3w g6.
(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 6ihp0uabo(ro( p o2f1j: +dl mof 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 fiu8 cl;0wq lk*rom rest within four full turns (revolutions) and releases it at a speed of 0 l8wu;*iqk lc28 $m/s$ 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 ik7-.h +0 mmfwip:swhssdc5 n+ lpup. -sv(n2vnertia 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 28)-zvb0vr wk(j 0 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without sl++fl -lpoxss )dj 9y2pipping down a lanejfsyp p)sdl +xo+-9l2 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 qxc5a(w5f 9xx sum of tw(5a 9 w5xxfqxco terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. Holzg3*xj g8g(h w much net work is required to accelerate it from restz (h gg3jl*xg8 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 rsyktl)gg --i,est and rolls without slilg,k-)- g ytispping down 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 ve3a)a*no tl o/.2wop lpt j2kl1rtically on its tip. It starts to fall and its lower end does not slip. What will oa. pnll231jot2kop* lt/w) abe the speed of the 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 oqle+6wl5 z w; *)ybr a*mee/nbn the end of a thin stw6 +q*l e)wre5 mbl byn;ez*a/ring in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheg;zrou.v0k-a 2.soppp/b/k l el of radius ba.-z/.2pl/0rpspo g kuokv; 18 cm when 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 adu 46h dsdg*:lt his side, on a platform that is rotating at a rate of 1.3rev/s If he raisesud:4ghd l*sd6 his arms to 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. 8h .*cwfz 6o, zwbp5u twjq:1e+–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, u w.65 ,wqpbzoc:z h1f*ew +jtwhat is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rae 89rqx+as 1nxfma:i/)vqon 3 te of 1.0 rev every 2.0 s )qnmn fixqa1:r 9+eosx 3a/8 vto 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 axis through its center at yri8q 3cj. j+us)qx;ya frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk o.+ysj3i)cy8 u;q rxjq f 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 figmhvn .1/d1zalure 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 momentumifz hjj;-;; v x7f:vm9, qvpza of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I i fe)q)6ar5g0pp wawc+jo7 w3as dropped onto an identical eqco0)+p ) 7wraw j65faag3pwdisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 8s4t.k gp:dm7a3;m p5poba llap/c 7f$rev/s$ 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 mebq es(.jrch+2xa+7 tgrry-go-round platform of radius 3.0 m andq 7.2j +xr+bseacht (g 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 wigly cpn29n qx)ywk(/6p 7zowt/,d/ qtth an angular velocity of 0.x7qp /)(z d w2,/gnl y okqt/pytwn9c68 $rad/s$ 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, los/9gs rhcqzmlg3 zj-40 ing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assczq 3gmg sh9jz0-/lr4 uming 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 invol)k 2lo j2a,lqjse5xu93qo. x cve winds 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 t i 4/(jm855qkejspgb *:ynig$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely withoud8 52zplscal8 4bm1u ht friction. The moment of inertia o8 azhb84mpl2 dlcu1s5 f 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 m1 pm/ p/dx4txierry-go-round turntable that is mountxit1/d p m4/pxed on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the cvyn1a 0,l unbm+vo-5(l, 6yzqeoi ) rground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unw vnb,lyo0c-en+o,q y1luarm6)i zv( 5inds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always fac.gts: m6n*zs8;ia z pr(1bp ehes the Earth. Determine the h*mz.zb18a t g ssp:pr ;n6ei(ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates rvdn95 lm.w/z 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 the shape of a uniform cylinder 8y2yw+,+hhgymw3vl i-z.hwg of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s y hvw2hy3y m+lg+i zhwwg-,8.interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made 6j0e6h q3db n ,l4op(p:cmvfi of two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentrih6 0:ov,(icf3 d jmp46pq neblc) 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 i22wxdaph/d 7dbz( qu/s the 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 1ds7 mznd4eb imkfw(6/o3ke0 with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, 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. eomd0ndk/6wi74m3 1feb zs (k    $\times10^{9 }$ $rev/day$

  One possibility for a lo u4a9kwseegp 9bg ft1 54ls2-uym22muxbd 14bw-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should 2gu4x d9s1g12lfk4b-u2suwebpemmy5a b9 t 4be 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 6 :tjkkv2 m:3dotgrcn) s:rd +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=q4ymk2r1 c4 .x b-kwzn3.3 $m/s$ 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 ;jdl ;u1yaohj2.tm; n 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 accelerlhday2t. 1;u;monj; jation of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing ir i9l7rebk2 )vertically on the floor, and we want to exert a horizontal force F at its axle so tha7r ilb)9i2r ekt 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 withw2+l ab)b me5z a radius The forces acting on the cyzm)law25b b e+clist 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 of lenkhb jz y),0r+fgth 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 k)r j,hb0zfy+ is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s bodyf7/7 . ucw6m6xc mohj0 +fgo-yv*j qgp 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 a spinning skater with outstretched arms, and with arms held tightg 67 o +/wj-cyup6mg0 vomhfj7 cqf.*xly against her body.   

  You are designing a clutch assembly which cj 9 .vat.uet1consists of two cylindrical plates, of mass ec .va9t.1tuj $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 kf,,q.e mekc )1,noh/oe4p b uthe 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 t1moq, ,bpueok) e,/ke.c4n fhhe highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but z u .)cdout2*odo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed 7vg(yu:..)l q mx2aw /z esamruniformly from 9) esmzxr7am:vu(q2/w .lga.y0km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s