A bicycle odometer (which measures vu3xoi3,utxt vb2y; g 8cq3 n*distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle wit2t* bvg;cu 3vyuon38tx,ixq 3h 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim havcvgrx9ym+4l9ti+.0 j itrp6 ue 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 the magnitude of either compon jg90v+y6.+ 9ipu c 4xtlirtrment of linear acceleration change?

Could a nonrigid body be described by a single value of the z(r(0opplqe +angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger1 9 mexi1z)mvz 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 behigu xuowumclmuj+ b5:;, w/fe* l.)4kjnd your head than when your arms are stretched out in front mg*/o ;5ukcuu wxe4:w)+ .jum lj, blfof you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the9z*7bm+ , 5e 1z zvsiohigqtt0 rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large re5gsi+* be, tzi1 h mqvto09zz7ar 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 wioy03hp 08ire cth flesh and muscle concen 8h ciop03er0ytrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers pq q5:2 m9diwxm74 xdd+d9o 0jyfjp3b(Fig. 8–35) carry a long, narrow beam?

If the net force on a systez)hnc j )wg u+h-h bre3c+bm33w. zxxis) ah)(m is zero, is the net torque also zero? If the net torque on ab3x(+ 3nh)r)ias cwzc)uxgj-e. m zhh+bwh3) system is zero, is the net force zero?

Two inclines have the same height but makk56 - -x(ajziu0nqcm ke different angles with the horizontal. The same steel ball - mjik5k6quz(c0x -na is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaner-w: r xcu8vx*ously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline firu rr:xw v*-xc8st? 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 mabkc 0b 3c1:w2jjuc.sz ss. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the ukj0cc cw2:1b.bzjs3bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum a(a wdo*q/q9:zd9zxd hnd angular momentum are conserved. Yet most moving or rota:* qo/wq(99d h dzdaxzting objects eventually slow down and stop. Explain.

If there were a great migration of p*+ y6(hygd+bxdg nt n6eople toward the Earth’s equator, how would this affect the length of the gyghxdn *(y6nt6 bd ++day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotf)mbm idm0 ,nu rbk6-.ation when she leaves the kbum, 6b0-m i)nfd.rm board?

The moment of inertia of(/qm-m3 pzq aj a rotating solid disk about an axis through its center of maqq( /mma3 z-pjss 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 holdipe3e8pu lbdps 88*3 voggt )r*ng a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or sbespogtu8 *rgep3l 8*3pdv 8)tay the same? Explain.

Two spheres look idenpx6e5uv-j+ ei0z*d feb6biu, o9r4t ktical and have the same mass. However, one is hollow and the other is solid. Descp0tviu6 u,*oj5 ere z-+xed64 f bb9kiribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal ax+h* 4 jgv-k3kpexfgy .le 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 increasing o+g 3k 4jhveg* f.-pxkyr decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Wha+vahf +o w; uu.gu6l7kt happens if you walk towgkh+v6f+uw a7o uu. ;lard the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he th--u,k wwlpw(rm i7y z+8pmao/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 direction (7/m-l zawpmi(r -uw,k8y p+ owFig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why,-6kowta 0f6lq * aved a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopq6l,v0 wa e kdfa-o*6tter stable.

  Express the following angles in radkdh5 nzjs97 3j/dt)frians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. C+jd,x1bxy-r))a 5vh i4ko uqoalculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun andrkh)i4x+a x ub od q51)jvo,y- the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam di+p2k,dac5x h kk8rew)7n6 yqsverges at an angle w2k,ks876 h5dnr+aqe kpcx)y $\theta$ (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 gqz :0oys 5.umturned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bladez qu.:5s mogy0s slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anothez n6vo ka0q4rx1 6gye:or; ivj +f(1bir child. If the ball makes 1( o:vo01ix; gijfaenb6kq1zyvrr 6 +45.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutu ng-ebqpywgjc 17)) 7ions do the wheels ma)q7g g w-yb c)u1ejpn7ke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm.5a u*g4 * hx/0.7rwzxlriwrivy, 9ngv Calculate its angular velocityr.gvz 97x5ir/l* *w0,hiavugnxrw y 4 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 o:j5d, b 9dx wk)wo,iey3o,8 e:gdqggzne complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the centergjd:)q iy 5 g o,g83eod,:e9k zxwbw,d?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity o1p;o5wv+umdrwgi3* b1 r 1gvc f the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spe; c9y 93duwvzted 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 centrifugz o3zkpzh6/gw, fo(p: e rotate if a particle 7.0 cm from the axis of rotation is to experience hp oz(:opzkzg,6/fw3 an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centeub t-d6b*h r+ar from 130 rpm to 2806atbb +h*r d-u rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius(i )wk nk.)rc1g/sghy $R_1$ 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 a- fi vqb*a(7khboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thoughvia q(h7*b-f kt 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 rpmk0e*vl n7e 1pg in 220 s. Through how mapvlek1neg *70 ny revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 45(v nm ucox fp94 uuns5u1v:w6s;c3ua800 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 highspeed jets ib6pprmby7txm r4 ,h3 .n a whirling “human cent x.7 prrb6yht 4m3pm,brifuge,” 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 diameter .(h7q k3/m565 k mdz kfyjpxitaccelerates uniformly from 240 rpm to 360 rpm in 6.5 s. Hof3. jk5kpmq zd6x(yt5h 7m/ kiw far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 a4t,8 qcdxrem 2ed v)co2p96 (njm: vrrevolutions before it comes to a stocp2) o,4q2 t( edja6 v89cmrnmde:rvxp.
(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 uniformlo/d2ry qo*va+z54za d y from 95km/h to 45km/h The tires have a diaod 5+2 v*yzdo /a4qzrameter 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 it8bq2ccu w 7v9;k im;krs speed uniformly from 95km/h t9ciu 8qb;27mv rw kk;co 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

  A 55-kg person riding or 3 2hrap,qb-6ng(iia bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle o,an- hp2rb 6(qrgoi3if 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. Wha*yzw*)uifiy9+ hqc par-6 co:t is the magnitude of the torque if zarofi*6u w 9cp h+q c-y:iy)*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 trj:ho +b+u yy .byjc0 j (/qrjayi+8,qhe axle of the wheel shown in Fig. 8–39. Assume that a farhbibr/q8j0ucy y +.: y j+qj+(yjo,riction 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 +ci 2:zafz07fwffe7pto the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the 7ffpi +wze z20fc :fa7magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening towowy d*iw.8i6+ga i 4x;g evqld+1do5 a torque of 38i.+q a d6+gl5iydo ;wxv*o84ed1gwiw $m \cdot N$ 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 qqy9r,*pdu h(radius 0.648 m when the axi*ru9yhdp q,( qs of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle ss)14e q-ndou wheel 66.7 cm in diameter. The rim and tire have a c sn do4s1e)-quombined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light ro5hxjj jns9,t6t*b -- anthvl:sr. (k yd is rotated in a horizontal c tx 6h 5jjh,y.tbns*--(vn9alj srtk:ircle 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 pot (eu5spjs7 *deter’s wheel rotating at constant angular speed (Fig. 8–je ( 57suesp*d42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig. 8–;lr. sp owcrc:8bl,2v2bs cd *43 b2, vo8c ; lwc:*.2 clssrpdbrabout
(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 qjyl *a*xyzf( 3y09jmwhose 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 satec(. cn3ecnay5llite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satelli53anc.( e cncyte 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 radizi6ct- o bs3j0hn;w l7us of 8.50 cm and a mass of 0.580 kg. Calculalc 7wtnhoj -36sb0zi; te
(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 baj*vhwmy :4 l8:1o54pd8eyt k t hk0zoct, accelerating 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 n2 zh/nh* vpo(ke8j ps+ gp-)ra 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 radiuogne2pjprvkhz )(sp-8h+ */n s 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, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually bropp hqph u-/y zag/(k6zn-0q 3cught uniformly to rest by a frn hq p3h/ (gzz/0qk6apc -pyu-ictional 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 ba mdpouc48g+vph1+4d;9fm5skt tt y y7ll 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 s5ek. (tmtxgnd7jr/cm2 s; wu+35dq qp olely by the action of the forearm, which rotates about the eld+. d x;k 7t pu55 je/qwqsmtnmg32c(rbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can 7 mb (k;kxvm.nv/ .4ygsxx*bube considered a long thin rod, as shown in Fig. 8–46..vuy4x ;mkmxgvsn7b/k b x (*.
(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 coohj 0sla4lrr +t.a /4gnsists 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+d3 0b** qlpkznddbgaxqv+5h +lr 18b from rest within four full turns (revolutions) and releasdaxkq ln5dbv*+++rz hl3*0bdb gp81qes it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a momentfyt y;u-7 pyx8t0p; eu of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque t .ln);:kyntw of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mard74fp1d+; o76go9r q mzrz blss 7.3 kg and radius 9.0 cm rolls without slipping down a lane a+r dq;o 49fpbr7gzl6mr7zd1o t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy ol,mg re6a d1g wo,pd foc7vm8,w +9zn:f the Earth with respect to the Sun as the sum of two+ dmc1zrl w8,9eda76pomn f,g,gv:o w 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 1f2cnl/9var.4swu2 lg 1 nwki6640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume rlanl/2wv9fw4g.k i s1nu6c2 it is a solid cylinder.    J

  A sphere of radius 20.0 cabczf0fp g7 +kxrj+74m and mass 1.80 kg starts from rest and rolls without slipping down a 304 r 77j0f pxaf+zg+bkc.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 i ghe*r 8(oc bq vp89dq.g;brz; lph:(bts tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground(8hclg;d 9z: ;ve (pog8qrb .rpq hb*b? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the udp w rpmpp8lo28058uee4) eh end of a thin string in a circle of radius 1.10 w8lppmoepud4)88 5ep0e h 2ru 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 cyl l7xzi+u;vp;o3 3vzjp indrical grinding wheel of radiu3;p3jvlz 7pizoxu+ ;vs 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 at his side, on a platform that is rotating at a rate xm./b r.veva/.,mpza)yw; ms of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speew,s.vx r;m/. /.m)ezmyv apabd 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 . cn-fhb7nm2f in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from thnh.nc7- 2fm fbe straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin 36 i7jzn*ajc mj9qmt1e: ka(vrotation rate from an initial rate of 1.0 rev every 2.0 s to a finnam*3jqj9 e 7 ij6tkvaz: (1mcal 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 verticalz8imm m-n; 0:)yoyb gw axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The -zm8w0iyg:mm)noyb ; 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 momentum ofj-i r:juhz 6 sscz.p qja4;z76 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 momentumlayosgtz3 2/m +7 q,fq;a tr-u 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 rsohoa34 +hb 6 )ydbz+of moment of inertia I is dropped onto an identical disk rotating at angularb+s+3oh a yhorb6z) d4 speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.2k ta:nx e2:ub4 $rev/s$ 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 puqc4zx ju;7;/ ywr:q4z sgs5kg stands at the center of a rotating merry-go-round platform of radi4 jusxwspqq ; :;z4y7czg ru5/us 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity oftrk;5sdm xu g0i34 2qn 0. skd4n 2gi qmu0r;3xt58 $rad/s$ 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(re(;v4,p *suwyg2 0 sdeoxpk , losing 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 momentum, what would the Sun’s new rotation rate be?(round to the nearest(ep ge*r4k;2ywps uvs(dox0, 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 windsdyv(k23 q7py0,sa -izatg m,p 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 1hx.b14 f/0xgz8j zco:,wdnjhssj + w$ 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 with mr 5x2gipl(pbi ,6-ysws;t0cout friction-pi xls,2b 6cyp(5wrg smi0;t. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merryvq5-e,r-outyem, e+f -go-round turntable that is mounted on frictionless bearings and has a momee,+ rfyemevo--q, tu5nt 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 ropedwgi 0r o-; zudk2r4,w rolls on the ground 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 unwinds frok ord0i,zd4-r 2g;wwum the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that t 6h u y tizu/k;i3n0j1kj5k1hphe same side always faces the Earth. Determine the ratio of thez1ji;u1tujk5i /yk 3hpk60nh Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest jve -z-5g:io t ktcxr47e5;wl 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 scaw;,c0/fg*e1 :4rz eca-fx+y tu smyhape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interva1 *urfyy0s/;f a c,m c:tgxaz-ecw+e4l at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical c8,;9w: zxjgbd g.s oldisks, each of mass 0.050 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 sb dlxg ; jw.,8zg:c9oit is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the ang q)8edk8os(s tular 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 w 5u,(oyzd (byhith 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 zd(b ,5h(y ouy11 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 use energy store.4or yywfif( v+ r6gm.d 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 yi.rg y.wr+v ff6(mo4240 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 illustratvmz9 3buq 2kg9x6*yk+ v:oocaes 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 hor*kkp7- h ha7ppizontal 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 ,d0-ea rzm 0yz6bx c:t(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 ofdb6zcr0 et- a0my ,xz: 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 habxn fderp;ir:.v1;*h fna 1 re :ox3q9s radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle ; b i;pof1x1:e*qe hrrn:vrx3n.a9 fdso that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speecwkt *oht 8 m73h3g;tgd v=4.2m/s on a flat road is making a turn with a radius The forces acting on theht7mo *tc 3h;wt83 ggk 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 of leik+8ihpvmc x .d+h3:lngth 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does tmph8.3i:lhv+c +dxik he torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as vtr--y w +o* qwnsk/m:thin rods, making reasonable estimates for thk:t*wv roys-w+n/ q -me 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 ygb1mpi (u9ha vse4s 8.l7)n-y4igq-qr5i sjof two cylindrical plates, of mas(h9uy-7i4vjpq li 5r1-)ie.4sa y g sb8gqnsms $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the r;bfx e 2 *3y)ojag.9wdrwm .m9dis1hlooped rough track of Fig. 8–58. What is the minimum value of the vert rjamr2y 1h*g;bx9 owsw.e mf)d9id3.ical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assqk)*x( os:w+s5k brcp+ ,(vrootgz6( ypkh/ aume $r\ll R$ h =    (R-r)

  The tires of a car makwv857 z ktm(9ji/xmpd e 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of ea 9 pxvk5m7 zmw/(idjt8ch 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