A bicycle odometer (which measures distance traveled) is attached near the wh0 9 lhdc;m racusov py;:uh1**eel hub and is designed fo :p rscum01yo v*u*;9l hhdac;r 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotatr vhj211nzbd1)su7otpt ka8g9 er3 f5es at constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’srtaj1vfpd1ku 3ns17zo h )2r5gbe 89 t angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angulae wh.kw2y5*qni p :lo4r velocity $\omega$ Explain.

Can a small force ever exert a greater torque than j6qe.yao,u ebz4 +qdh1jo ;u4a 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- f9wp- qbien ggt.4-1,wm z:bq-uakk0up with your hands behind your head than when your arms are stretched out inwme -4a9 f-k,bg1zqgw: .itpuqb -0k n front of you? A diagram may help you to answer this.

A 21-speed bicycle has sek5l 7wel2t;n9gd r hg:ven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or 5d2t herl n:ggk ;9w7la large front sprocket? Why?

Mammals that depend on being able to bv3w2smrih4. run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basisr 3w2im. v4hbs of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) cas:gf t/ gew62-zpg5o *5byyl drry a long, narrow beam?

If the net force on a system is zero, igcm (z.3 .zsmms the net torque also zero? If the net torque on a sy3g.mmz cmz(s. stem is zero, is the net force zero?

Two inclines have the same height but make different angles wit drt eb73a88cywz rh)x 4(dzjxm- f8)s k,ukl*h the horizontal. The ez r8rdkthd8 w-bm),k*a3jxs4)cu7z lf8yx( same steel 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 rolling (from rest) down an inclin*;t, ru+wk9eezoa(ank v 3 rz+e. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the oa+ek(erw+3 , r za uv;9zkt*nincline 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 mass. They start f)1ay+z/ z:tod6hawqlqc2d +erom restdaqotl6 z2dz e+):yca1q hw +/ 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 an wb3 cdpjcm.3(d angular momentum are conserved. Yet most moving or rotadwj p .cb3(3mcting objects eventually slow down and stop. Explain.

If there were a great migration of people 3:3r csn)hk a7oqr:( nxpcn:ftoward the Earth’s equator, how would this affect the length oonr ( nnqpf ra7c3:s:x)h3:ckf the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotrjp733k0kju g ,*7brzv(3mk*oques w-u 8bwqation whe e*3r qzur( 7b7wj0,kw-qjv pg m3 kou83b*ksun she leaves the board?

The moment of inertia of a rotating solid disk about an a31e j*gp *ocn emp)-amxis through its center of mass ismjg ma* )np-ep 13oe*c $\frac{1}{2}WR^2$ (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 qc4jpjzph *.yci n ,*7eql5 fd6b;*ca2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular vea6b; . 5q*peq c, 7jyhl4cj*nfd* pczilocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is h7vb oo bz2c0w.pu/,p nollow and the other is solid. Describe an experiment to determine ,vobnw7 zbp ou.p/20cwhich is which.

The angular velocity of a wheel rotatho 8mdgxe8i2 f+ v*vqa/b0*a ning on a horizontal 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, descrimanvx/ q*g*2a b8 ve8f+0hiodbe 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 fgqb jc)z4u1a 5reely rotating turntable. What h4 qgcab) z51ujappens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw iz1ng: 8lw:dpjxyf wcsac:6 ui8tc0.6t quickly. As he throws the ball, th.lf6 : dc0:accw8gtnz 6psjxu8yi w1:e upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, j 19tww lnxvc9lb8zx /.ev5 )xgu9+fi discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can oplzt9fli v8nxcg/b9+e 15)vjwu.x 9 x werate to keep the helicopter stable.

  Express the following angles in radians: (a) .,+ /9efnl,mg1l hg .xf s ,6jdvonncy30 $^{\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. Caus bq aj+l3g6fy,v4f/lculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun an6f,lbvy4s +g jf/ 3quad the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed aqo94rhez r5x /t the Moon, 380,000 km from Earth. The beam diverges at an anglez / 5qr49rxheo $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blendi 8z*+lm 6gp;lj1o( b2 yysraaer rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular ac;*yl1a zp8yb+riga 2o(j6ms l celeration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. Ipy2pzn+ jl nqq2:-: s.kai o w2;vmac/f the ball makes 15.0 revolutions,w :ynpz2vmq2aq -;.ksic2+lp/ j:an o what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Ho/3k z8rmtpt* aw many revolutions do the wheels m8t/*mt kr paz3ake?    $rev$

  (a) A grinding wheel 0.35 m in diamet1cnx u-q 9l)gxer rotates at 2500 rpm. Calculate its angul)n1-ux cxg l9qar velocity 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 revolutionrg,dh c oxfg+wup3k )k/lvp 7r5ts+5) in 4.0 s (Fig. 8–38). (a) What is the linear speed of a cphop )/5,)fk7ck x3gg+ws +5vrdtrl uhild 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 Eaewja-rn0r(r-uip n: ouju. 2/ rth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speezrmfz,- b/t y.d 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 centrifugen..cru, on1* t+v. shkpw q9ps rotate if a particle 7.0 cm from the axis of rotation is to experience anvntnsow qs.*r c .+.p 9,1upkh acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly a,44 :hkf l1*rsl ovdf vtg:sm8bout its center from 130 rpm to 280 rpm in 4.0 s. Determi d:4 f rsv1vmhot:,*k84gl lsfne
(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 radiusjae3y *6) nh 9 k6ztwrtbrbr;) $R_1$ 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 themselves-eqh:j4 ycqzzi2 a8 k2 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-a8hkj2 z zyqqi-4 :e2cmin 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 in 220 s. Through xyi4 pxt6v*z+ how many revolutions did it turn in this tvzyi6 x*tx+p4ime?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm zzpnn)( 7ck b4in 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 j) yj.c)vnn+egc0 7hhhye);kg n0z1pjets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete rev e 0cyjn)n;+ 1ck geg70zhj.v) nphhy)olutions 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 diame : t89qn/hfdfed -.m(eq iqa:mter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edgehn/:qqam:ft.q9 8(-ei m dedf 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 rro j, 4ll i2 )-eonr/p -emf1)kfbfs2hevolutionln) oei2 )f s4mhb--ej12,olfrpk/f rs before it 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 the18 p/znvuhb 5r5tpu:0yk i7xw car reduces its speed uniformly from 9:8b/z x5hitu 5 knuvy170rwpp5km/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 m ;i* a(qroxcc4ake 65 revolutions as the car reduces its speed uniformly from4icx a*;r q(co 95km/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

  A 55-kg person riding a bike puts all her weight on e m3ypvq:c kea.v1djxjm ;-5ar4:o t(lach pedal when climbing a hill. The pedals rotate in a circle of radius 17 l3ackm(5r dqy 4vj:px;tm jaoe-.v1:cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a forcew)y i;it;yl bj 1xv+6m of 55 N on the end of a door 74 cm wide. What is the magnitude of t6)lw+; yb;1jyi mtivxhe torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque abona8 *uq,fl; gffkos2kb+tn 6j6+no /uut the axle of the wheel shown in Fig. 8–39. Assume t, qkn + ;sf u8btjuo/a*nko6n2f6g+fl hat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of ma bpe3m4i46 blsq) r n6knao3xz:;r o2ass m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initialqoe2 bxm 4a6)3:;kn abzor4pr l3sn6 ily the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torquey1 s5ninpax3 * of 385 3y1insp*xn a $m \cdot N$ 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 /ttl9 fj fy,yp 7f;4xit+up* tradius 0.648 m when the axis of rotation is throfj9tu;l7f ypiy t,tx+t 4/pf*ugh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm inl qcpy+ c a9 6d.l(c46ow;+pdpfgbgn+ diameter. The rim and tire have a combined mass of 1.25 kg4 ga+l pldbp . ncypf+6wqc9(c+6go ;d. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball at vf/s nu;j 9sy;8 1bu-u8v 4t7otwaton the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calcul ;tjv-t88bwfo uass7 ut91;ya/ vtn u4ate
(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 consaa5 fixo4ef,6tant angular speed 5a,oiea 64fxf (Fig. 8–42). 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 objecoen0m;.ab4 gu7fcr 8pts shown in Fig. 8–43 ab aeu4 8;o g07mrbnf.pcout
(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 ofij8 (6btwk,j f two oxygen atoms whose 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 5y, 1dyg,ijx7 naea q3satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the sateln,ji5,7e1g 3 yaaxqdylite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylind 2*og+ zqp obuax9+xh1(dm 5vkp8dmhu kq9o4 ;er with a radius of 8.50 cm and a mass of 0.580(5;d muo+k* + qxqgoz 9mbpp8u4kvaod921 hhx 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 fro s nwtki66utpz54(d2g m 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 pbr.(:fasdl 1a 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 unifordblfrp1: .(as m disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, 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 9c j m(wpwd.z,and is eventually brought uniformlycwm.(9p,dwjz to rest 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. 8–4s 8v*x*kem wi45 accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by thdjz4z,eesnk+ c2 *jfbl2:ir6 e action of the forearm, which rotates about the : fnic+szee2rd,z 6*ljkb 24jelbow 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 bladxe rq n 5dugs7-dy9z.-e can be considered a long thin rod, as shown in Fig. 8–46.dr7 sy9 u-qd.ezg5n-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 consists on iz77naoye(db, 5e /xf two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within foure/-bpqzznw)oike1:g qt j6dy5 1.0jc full turns (revolutions) and releases it at a speed of 28 jtcz qky be-)/d56no:0 zwiqgje1p.1 $m/s$ 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 85axvqboz zxm++ d8(0i 9doaq 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 txky f)8 cb4-ya torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of ma q0q7-qtw6 jhbss 7.3 kg and radius 9.0 cm rolls without slipping down a lanj0qwht 6qq b-7e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energ.bcchjj /m*5s qx(/x u3a+p10n boougy of the Earth with respect to the Sun as the sum of two bucqcax+5*(1./n mjghx ouosj3bp/ 0 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 mas4c7frusk-uaz. k,3j b 8dqh;l s of 1640 kg and a radius of 7.50 m. How much net work is required to acru bk-dc a4z sl,qhf8u37j k;.celerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls without ji6+um(.+ f+mtba iyl slipping down a+ ij6buym.+ai(fm+t l 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 o2y-r :m5 4hmkh:xb4 klkbg c4tip. It starts to fall and its lower end does not slip. What will be th:x4mk m4b bk 2lg-yhh4:5ckor e 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 mom 3qtcr9lb iz6f l 3:pfm2l4g-xentum of a 0.210-kg ball rotating on the end of a thin strin 9x zfl3 :lclip2g4rtbq6-f3 mg 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 mox;,bbqo a(y 6xmentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating a,boxy6ba; x(q t 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 plat 6oa4eq*1+d wiv aakr3x4yi,oform that is rotating at a rate of 1.3rev/iqa4 x+ywikroaa*1v,4d6 o3e s If he raises 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. 8–29) can reduce her moment of ine3 kbgkc;(, tawrtia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations inwkg 3ck(b ;ta, 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 increasfsz-62.obg u2 e8l g1a kiok-je her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a fin1ogs b j2g2u izko6-e- 8f.alkal 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 throug(eh1acz94n ,8 sio xrl8zb 8elh 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-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotab( 8h,c8z i4srxaz 1e lel8on9ting wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of axnv kh9gt*gvd -oqip+9 pe*-4 figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earrz d+zl (qms4m .+6vrrth
(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 dilfg s7vul e2 /e,k/:fisk of moment of inertia I is dropped onto an identical disk rotating at angular s7lulevgf/ 2: k,sfe/i peed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2, hjz(6t a8sjq.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 merryxc7qv wo 5d tse-w0:f*-go-round platforo :0tv7cqw- fs5w *dexm of 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-rzm 4y 4(p2sa:bqv t2;qxpq f/vound is rotating freely with an angular velocity of 0.8x zp/sqmv:yb ft24 (;p4qaqv2 $rad/s$ 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, losing about half iinu,plm* (kyi e0/.a lda m40bwa4n+pts 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/ u ai+* 4dak0w(pln lmy4imebp.,0an’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excessf6k+/xp8/m9gm civgu1wyl5z3p 6 zuu 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 sjpx3 d uw*hfjrf(/ v;4u7ec, $ 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, initially9 *8f +zghn9xj91hee;fkk qgb at rest, that can rotate freely without friction. The moment of inertia of the person plus th b1 ;99 hf9n jeqkzhg8fgxk+*ee 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 thb.nht: rh+iz9 e edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionb:+rh tzh 9n.iless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying on th) ox.pg1enhy pj *(zcx9m4tn1e nmpz 4 (p go 1yxc9*jetnh.)x1top 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?

  The Moon orbits the Ehh,yf7d; m0lxfj wo4,w4dn1 m arth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentumxw 47fd f;odh0 ny,hjm4,ml 1w. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of jab/z, ehk-3i 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 radius 0.2/j/mhn kf 6 b00z;3clf.y46fsbjkz rb0 m acquires a6bk/k;sjzf0b3 60lzfrb/m4f.j h cyn rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.rmr,20 )swmnh c8tnk ,k ;zz- 9k0kems050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0. nk0m hm -s0,r9;mzerkks 8wk)tn2 ,cz010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the real8+lo +o8 ca tqm4/ lxjfdga/:r 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, b spyp .7.tjv:i*rmfk nsh*,z 7ut with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergh yist.7p:vsz*.m knr ,7*fjpo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to u*zdpu(e xq2*lfi+ p;mi8t/fp se energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a unipmle fzd;*pxqi*pt+/(u8i f2form 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 anrry49l+ -8w1mymjio o $H_2O$ 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 surfa./9tpywmo vorz7 z2bw)m 5 j5j0* cxzjce 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 55yp2zf6,a1 bwzsw) us1ns rduo ;9mfM and length L can pivot freely (i.e., we ignore friction) about a hinge attacupau21n)woff916z;zrb5dsmwsys, 5 hed to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has rva7pbwl99 5y : tjm/br0-mvrxhn6ay0adius R. It is standing vertically on the floor, and we waj5prn bwy lay0bm7t6x av-0rh:99vm/ nt to exert a horizontal 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 s9is8 a:1t g q23 q ct+oiwq1. lh-xypo++vwjkjpeed v=4.2m/s on a flat road is making a turn with a radius The force:2gc qq+3sjha j9p t8 w-o1vtyql++w 1x.i oiks 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 of lenj( 8 zng2 mf4,yaqa;ymgth 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, 4,m; gqa(2n8jyzayfmand where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rod6tc38l,nkzfg +vu za1s, making reasonable estimatf63l tg,unaczzv1 k 8+es 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 whsifq3 ks9c1c9ich consists of two cylindrical plates, of masqssk 3f1icc99 s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough tralmei w,;xeoq.6t/5wp ck of Fig. 8–58. What is .5lqw/ eoxte,6i w ;mpthe 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 $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do notz340ntmm y co+ vd5(xs assume $r\ll R$ h =    (R-r)

  The tires of a car maker r 92ucw;g j;a/he8mhn32yfy 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m 9 8;ec2 hwjyhugmr/3yfr;2an. (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