A bicycle odometer (which m89v63f 2g lpszgnd hp*easures distance traveled) is attached near the wheel2g z3f6slh8nvp9pg* d hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates ljy ct r8 oye(bij dfg738uas54/8y9f at constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angu4f j /5fau 8tdgiy8s8bjy7loc9y(r3e lar 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 singlet0rkmkm73 b0) noq+ o1/v jfdp value of the angular velocity $\omega$ Explain.

Can a small force ever * j.4*tr0n. 5iknvgbc xx /wszexert a greater 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 amm .e0s xg-2qy sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answesym- qeg0 2.xmr this.

A 21-speed bicycle has seve 4dqa647mfeeul+ g bo*n 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 a large front sq4l 7b6m+uag*4odfee procket? Why?

Mammals that depend on being able t7yvde ss/ z/x.o run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, e /yxsz vd/e.s7xplain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35)qob:vgfvi fr6 hcj.0 61s6kf3 carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If,w:e8b6z.elhvw 3 wki the net torque on a system is zero, is the net force zerow le6k:b.ev,w8 z wi3h?

Two inclines have the same height but make different angles with th:m d2n6k8wd1yrsnn b+e horizontal. The same steel ball is rolled d1s8:n6rbd my 2nw dn+kown 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) (5;e n bitr-tndown an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which hai(-;trb en5t ns 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 from t eo4 bn3)7i ze76cublrest 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 gre63 ez7il toune bbc4)7ater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving2 00ethgkvv -o3y 7b(oe+ymeh cng c97 or rotating objects eventuallgehckc03( y-m7ovet ogyb 9vh02e+ 7ny slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how;y igw7x8jbd 5 would this affect thjx ;i87gw5dyb e length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatiowv(a0 *jkt )pbn when shwvbk pta0)*( je leaves the board?

The moment of inertia of a rotating solid disk about an axis through i52q sg+onlhi ;ts center of mass s2liq hg5;n+o 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 hu7 6t26g8jtb bst m2wholding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decreas26ttbb6 7hg8ujt sw2me, or stay the same? Explain.

Two spheres look identical and have the same mass. ) wdb5 htr7a6jHowever, one is hollow and the other is solid. Describe an experiment to determine which h 7)a5 j6twrbdis which.

The angular velocity of a wheel ro9z-e pl; pja+tk.w0f;g6 tgd ktating on a horizontal axle points west. In what direction is the linear v;p60gt9t+ep; gd a-flj.zwkkelocity 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 standing3.4kb w))mj fuw8ufvd on the edge of a large freely rotating turntable. What happens if you walk tu4)bk fd)m .f8w juwv3oward the center?

A shortstop may leap into the air to catch a ball a-q0s z wel1bjg4k, u;z.t)qgfnd throw it quickly. As he throwsjqeu 4 ,gz qzgkbf1.lw-t0);s 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 (Fig. 8–36). Explain.

On the basis of the law of conservation of angular mom0y./zkre ly v 6f 8zlnrw)* +91gcomamentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep thcrzwer/ zm016 f yk mo9vag*nl+) .yl8e helicopter stable.

  Express the following angles in ra mbkks y4+d4t( y:-xcjdians: (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 cz*vpa 6-yyfc * y+a8dooincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Eazyoy 6a*8-+fpacd y*vrth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divergejhgn r3z l5wox m 2 x/oaw9q,5,i-hrg0s at 5wl5 rar,qnm3w h ggo0x-2o/ihx j,z9an 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 rotatv+6gs b7phldy9bh 3e/ e at a rate of 6500 rpm. When the motor is turned off de+vp97bys bg3l h/dh6uring operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If ts6pz owslg9a/v2s4 n b;yz82 ahe ball makes 15.0 revolutions,2y / s6 za 2pss9ln4vgobaw;8z what is its diameter?    m

  A bicycle with tires 68 cm in diameter trajt2ng c7sfo* 1jt 6p0evels 8.0 km. How many revolutions do the wh p2tc07sg6 j1*tne ofjeels make?    $rev$

  (a) A grinding wheel 0.35 m i htb.gmz)mn ;5n diameter rotates at 2500 rpm. Calculate its angular;. g)mnztbm5 h 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 makesskphpwea 7dj7)z )0i (/bx nox,35 cvv one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the vxvje) /nxpo(7hi7c)0,z ab3k5sp wdcenter?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of tr03e t)icgn .yhe Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of az:,hb 9hus3fib4rwnsfau 838 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 cm froma8s 7;xbtdxk;r6l hmj5a0it ; the axis of rotation is to experience an acceleratiot; 5aija;r s0d l ;xk68hbtxm7n of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerajq rki3na egn3bkfh 1h *frw+8ak-:o :) tc91xtes uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Deterfnre*giq)hcxk3r9hb+f-o8w j1n: a k1at :3k mine
(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 radiudpfyw 08l)nhq8 1(8rrrw xn 0ls $R_1$ 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 spac- g9d- -dm,ecs tzu9bbecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start odtgb-z -u,m 9ced 9sb-f 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 restj 6l. v*; b bqt;m.qmvt;8-g3bwimfju to 15,000 rpm in 220 s. Through how many revol.86*3m-ml;;wt .b vb f u jqtbvjqig;mutions did it turn in this time?    $rev$

  An automobile engine slows down froy6,9cbtx(7vm9cey x km 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 highspejwo4+d 20edrehppw; a c4,frkfe:0m , ed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachi0 mehe2 dfo:p4ckr,p ;4rj+,w awdf0eng 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 accelerates uniformly froctk:z/+* 39t 5c0lmjtds gexaa6ue()jc nr+em 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in ttld t59 xg + c)rzae /jjas cene(6+uk:0m3ct*his time?    m

  A cooling fan is turned off h.rktl 6 0a:wowhen it is running at 850rev/min It turns 1500 revolutions bwa: 0r6k tl.ohefore 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 tml(t yxey8z9 c5nl1 sjam:e7jq;*xnaz+ 93 skhe car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0jmytjs: *38sem l1k 7cq;(9a n 5zl nxe9+yxza.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 s:g*k8 nyd36:d7aeb zvb i;kgvpeed uniformly frbb;ikd8e kv7dya*:n6v3:gz gom 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 eacbcnk2ygcs , yl9n4-y.s2 u vw5h pedal when climbing a hill. The pedals s4kulcy2nbnv w9.cs-,y52 gyrotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wvfevxe8rao 03yh7f dk*e7i +2ide. What is the magni0 h*v8x 7a f kioe2deevf3y+r7tude of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel show h7q()ew59qxn4ljj zoz whb2 d.9z:mcn in Fig. 8–39. Assume that a friction tzeh2qxlnw:97 o4 jhj( zbq5. w)mcdz9orque 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 whik.) -476qzo.w0rhq1uxgc f yw/dnvs gch pivots as shown in Fig. 8–40. Initially the .w us/oz 4qchnr6 ) yqk.-x71vdf g0gwrod 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 cylindf 4 di+kzdg/6ui mc*6a4l(rv ter head of an engine require tightening to a torque of 38 6cl/(4ta zk4fm rid vgi+6d*u$m \cdot N$ 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 jw.ry -ljk+vl zxdz4sgdha)0 63y z35of a 10.8-kg sphere of radius 0.648 m when the axk+wy0.4 lx 3zh jaz-r3ygj5v6 zdsld )is of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter8q tlzw*)fa+puxh4y3n twh 0)gs-p h.. The rim and t 3n)0hpf-s)px t qlah *+yuww.8tz4 hgire have a combined 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 rod is rotated in a horizonu ynh 9ai0/5x:w ng3b5vlo oc:tal cir/ on55v hi3c x:nl9y ua:0gwobcle 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 angun-(zvwzdg fx zvrrv ; 6mf:qfui-:4 8)lar speed(8 :fv-gvr-4z;qf nwx dz6zfu v):rm i (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 ar d64)azief h 5l)mwkw jeh* l.oj+34vhray of point objects shown in Fig. 8–43 aboumel+khj 4fa ohw*)4 36dvl 5hiwe)jz .t
(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 twoh-7 , z5fmwlks 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 satellite spinning at the correct rate, engi 3 / 9h9 lb2-posvey73jie3tijbb v*pmneers 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 tev3sb9l 793mb3epo y/j * ivijhb-t2phe 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 radlavgr*1f0/gj:t2h; -kfza nk ius of 8.50 cm and a mass of 0.580 /jk;g rvafng2h -0alz1ft:k *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, accelera; +a3jgabwb6 l(/ruxr7swav0 ting it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-dfts-t0ja g4,b riven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (eac-,bttjg0 f4sah 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 sh ,i1:cu hu19 jzo2iabzut off and is eventually brought uniformly to rest by a fh1buiajiuo9 ,:z 2z1crictional 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 aicut4lnt v,kr:u ,kbe-6d0 x7ccelerates 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 the action of the forearmjqa68+7(baey fs+k jg, which rotates about the elbow joint under the action of the triceps muscle, Fig qfy(jaegs+a 7 b6k+j8. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be conside x5+.luigx+oj red a long thin rod, as shown in Fig. 8–4 xuj i5xo.lg++6.
(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 consish /)mjc -ik(8 0nvun/ok kimv4ts 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 accelerates2c:qr6 dz ,hdhhrn1tle-n2, t the hammer from rest within four full turns (revolutions) and releases it at a speed of 28tq:,1hh26z r hr- ,le2cntndd $m/s$ 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 m*ovh8 v2,i/vj f/z-: f sfek;gh mwa2doment 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 j28zhswx5tf1torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass w p:j.)vq tp6e7.3 kg and radius 9.0 cm rolls without slipping down a lane qv:)t6ewppj. at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sunpz:4yb , pt nbqjt :t65ph/-vbwdv6f. as the sum of two tp ,b/dpvjb:thzy.-ntf6qb4 v56p:tw erms,
(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 ofczp q-kp29ede6 vuoez * (f7*b 1640 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.uf9- koq*p *cevzbp26dz e (7e00 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 rollsn8 9a.hgqfxh ):1z cnd without slipping doa9zd1 nhqgx.) nf :h8cwn a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fas-wkj*ca0 -d uq2k-lrll and its lower end does not slip. What will be the speed of the upper end of the pole just qd wr*kku0ls-jc-2a- before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a xu j7 llm2* uhn;6s3dm0.210-kg ball rotating on the end of a thin string in a circle of radinl 3sh jxud6m; u*m27lus 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 whee84qlgw- :1vwoxtdpyi nii8*3 l of radius 18 cm when rotating at 15n4 1wd i:xp g3wy8ilt qovi8-*00 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 h8vd ytziwt3ed/3g*8 side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a 8zd3/*tehdy 8twgi3v 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 mlq;(n 3q;y vngf5f c0in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s whenqf;n;cvyln (qfm3g5 0 in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her sxlrho4qcg6rv n x -;0;pin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final r;g ;cr6l no04vxxhq r-ate 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 cente oxhhu :c2 .li80nm x.oksc ;7tsiwe6,r 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, ontwoi 8mh.,u 6ex;2xc:o7nch ts lk0i.s o 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 figureo (jxfr1j g1orad8x:1 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 nvr; ,q-. pwywq 3*famEarth
(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 is dropped onto 0gnubkhe;6k u*y: gdha 914ys an identical disk rotatin uau *eh1k s;ky964dbgyh0gn:g at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atj wxq97ro/s* dxht:gnpjn77 ) 5n qr(y 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round 9tm 2s7c xvvi/j4ub;kplatform of radius 3. bs 2m49;ckjxt7vv /ui0 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 angux;r:rj ( i3pk43qwr vslar velocity of 0.8 w:33k xrs;q4pjrv i(r $rad/s$ 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 dwarwxv y jeh.c/ ub.n03l5f, 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 m0vy u.nl3w 5ecjx/b .homentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve win)t/:omwu kny9 ds 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 +d tgj2qkpj/2zg-rl; 2m. vlm$ 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 rotate0abvjkdsyciz7 mdv8. h7/km; r * q0 kil7j;4z freely without friction. The moment of inertia of the person plus the platf dm;v8 cj;j70smiy7ldkvihk 7a0bk /r.* 4zq zorm 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 tpepla2heudd onlj 1r2/ y 2fm*0wt;:8he edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a momendn/jyl oa8 p2rpe1f ;u:dmlt0h22we *t 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 s h3jomtd2y9tny:g ((dk s 1f(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 sm1y(tjfg kh 23( tysso9:dnd(lipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earthf gz9sh2m)j ja2baqa*-o ep4/ such that the same side always faces the Earth. Determine the ratio of the Moo92gea/a2bo*-hjmafz q4p)s jn’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 at a43cpoh r7begwss10 * r 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 shape8* o me fqwg4azg ev,5 .are2)pqdon,: of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered wea eof,g2)ogravm 4ze8pd :*q5 n.,qby the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0j8*p s:a,u.csrl 4lq r.050 kg and diameter 0.075 m, joined by a (concenlaqs r:l*s,.8jrc p4utric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of thnoe8he7an7ci6 rn bh6;n)9sie rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mosh. 7t,uq7 luass 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 7 thqo uu.sl,7radius 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 use energy stored af y(; 7h+hcp:2rnykl in a heavy rotating flywheel.(l+ hnk;yahf7cp:2y r Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates9 7( ysxpicyhks*44f )k9aglx ub13w t 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=38e r cb1i:iob)vlr;8u.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore friction)fb-jpxwk7 q :aj *1(rz about a hingkz7prx:a- f1j*bj( wqe attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vejjx 0np.pk* (z3f a5qqrtically on the floor, and we want to exert a horizonta3.nq5fx(k *pa0z q pjjl 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 u5gpuwtaas())6 i ;fswith speed v=4.2m/s on a flat road is making a turn with a radius Th6 ); tiuu5asaw f()gpse forces 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 lengthj: )3giyvz 1ej 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 t3e:zjvg yji 1)his feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylindher3de51 n v05g fi.zjer 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 ti.jd vefe513 0 igznrh5ghtly against her body.   

  You are designing a clutch assembly which consists of tm.um mj ./hw3hwo cylindrical plates, of ma3 h/hmm.. mjuwss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 tr- nc9d9/emyrback of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to rey nrbcm-e 9/d9ach 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 hquohb+mk:4kkb y5 g a6sj+1+assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions at+(z7m -1d6l mnnrwtvs the car reduces its speed uniformly from 90km/h to 60km/h Thev(1n m zrd7n6tl+- mwt 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