A bicycle odometer (which measures distance tw8xj4(oyeyr- raveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicyy8x(oj4e-y wrcle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poihw:98a ,kz xkbnt on the rim have radial and/o bhx,89a:zkkwr 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 component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velocity png /zv3 h2fxkq9obei.3u b *2$\omega$ Explain.

Can a small force ever exej*o5p1nurhd .cs09x q1zw/f art 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 a sit-up with your hands behind youv( yb(e+md ci(r head than when your arms are stretched out in front of you? A diagram may help you to answer bvi(+(( deycmthis.

A 21-speed bicycle has seven sprockets at the rearp.ik7c:n ee5qlr3) x9meli9 p wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large5e3eimn7:c qk9pxllri) p.e9 rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fle2wr1/5 lzw df1jgs2 knsh and muscle concentrated high, close to the bod5fkdl2s/j1rw1g 2 wzny (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkersl1q dev/8 4hl-xr6zlh (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torq1 ,nfw73rwb bk44 h3 :hfcqhqsue also zero? If the net torqukwf b4h17s,w cq4hh3bq :nr3fe on a system is zero, is the net force zero?

Two inclines have the same height but make different angles w*xb l/q olkcq9muh3y861j h47yhj x (vith the horizontal. The same steel ball islch lhq7x16k xm j8(/b9*34oy vuhyjq rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start-15 ag ss oo (qolqwe9b8ka89m 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 first 9w8sao1k(qo85e- sbl a9 mgoq? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinc n;t3+f xw:/pq.gdey i;s7yhder have the same radius and the same mass. They start from rest 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 greate: tq. x;py3nsdw c/iey+g7hf; r rotational KE?

We claim that momentum and angular momentum bj+ ,xr .4;lhsao ,mgbare conserved. Yet most moving or rotating objects eventually slow down and stop. Explajsb hbg4xo+ ,rl, a;m.in.

If there were a great migration of people toward the Earth’s equ 4gq;8c7sf b+.hmw eaeator, how would this affect the length .wbeq+g8fem ah4 7s; cof the day?

Can the diver of Fig. 8–29 do a somersault without having jasi0w-n15 haany initial rotation wwha 0-jia15snhen she leaves the board?

The moment of inertia of a rotating solid disk abouu p527yu /j7tvae*tzb t an axis through its center p77yt j*ve/5utbua2z of mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool; m 4qqg)f-zkx holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? ;) fxkq4 z-qmgExplain.

Two spheres look identical and have the same mass.dq 8kn, nfz5doi03m kz 0ggy5*dyl t28 However, one is hollow and the other is solid. De,yl8f50 knm0 qn g8ykd3 5zd*i 2dgoztscribe an experiment to determine which is which.

The angular velocity o/(pps;idro;bx w f*:6sb ko4 hf a wheel rotating 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, describe the tangential linear acceleration o:irdb(b;ophs o;p x46 /f*s kwf this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing fjq:i dc,mc hz+osl4ex /r 397on the edge of a large freely rotating turntable. What hapce hlc ,3dx9/fq:z 7m4i +srjopens if you walk toward the center?

A shortstop may leap 7(q,t:fut9 .te wsjxg into the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in fe, 9j:( w.uxqtt7sgtthe opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, v1*8mfsuw ao:cc 6)c u+jvqh:discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the hev a1 8sj6c c:h:wovuu*fc) q+mlicopter stable.

  Express the following angles in radians: (a) ldie be)e3) :yusbx); zd )hx/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 Earth2fb+ixm4 5tdf :1ujnc because of an amazing coincidence. Calculate, using the information insid u+cfjb2mdin f 54x:1te the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam didvquczxb3ivepktmq, +oh9: . .,3ag-verges at an anc ixdab.e.+v 3okhv3q,g p:u,mt-z9qgle $\theta$ (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 t aueag 1t7+n7is turned off during operation, the blades slow to rest in 3.0 +ntg1 7a7teau 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 chi- /ngsfpcji pi 9j1nx-.vaqi :-f/c1wld. If the ball makes 15.0 revolutions, what is its diamete ci fxiwji11a / p-ncvspn.j-q9- f/:gr?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km.b+io* 5z+a7y2owpph j How many revolutions do the 5opz a wj b+7y+ihp2o*wheels make?    $rev$

  (a) A grinding wheel 0fx5- m xvgayk8+ /ehx7.35 m in diameter rotates at 2500 rpm. Calculate its angular v5xag7/8 fyehk v-mxx+elocity 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 revolution i d0,rkcr)8. zib1n ys8*ip0w)iwgzd sn 4.0 s (Fig. 8–38). (a)* ird.yksscr 1dz))08 8p i 0bw,zwngi What is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around th 5fk;ji cf2x imo62pg7e Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poin)6.yo9e(i g vcbov7hit
(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 partkd p,o c1*mh-q2sx j(aicle 7.0 cm from the axis of rq1 p s*(,jox mcha-dk2otation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniform smc kwr4/*pf)ly about its center from 130 rpm to 280w *k)msrf4 /cp 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 radiuseb-jqdnolfi9 .5p(3g $R_1$ 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 space5 /funsnxhemx; jl01(23jjxd craft 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 thought of as a cylinder with a diameter of 8.5 m. Dete/3; jxfsn2 em1j5j (xd0uhln xrmine
(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: 3bgpra7m68 , ysh rim3w,xtk rpm in 220 s. Through how many revolutions ms8bim3,6khwpry ag:7 r,3x t did it turn in this time?    $rev$

  An automobile engine slows down f +xskq5v kn8w 60a4yukrom 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 stress :rib r4z7m+pies of flying highspeed jets in a whirling “human centrifuge,” which taki4pm+ 7ri:rbz es 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 accelerates uniformly from 240 rpm v+jqeq hfa,a+,re-6v to 360 rpm in 6.5 s. How far will a point on the edge ofh aj6-e q qravvf,+,e+ the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850r: *qtx7 -3nzkbumjnp *ev/min It turns 1500 revolutions before it comes t*-quztxnk3j 7mb p:*no a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed univ +8cp 64ygzd(g6fcjy00 u sas )l7cozformly from 95km/h to 45km/h The tires have a u00 cfdg+lc ygsz 8 o)zcjs7(vpya664 diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car re)x w hm/0fnc(qo,bvwz5uf 6 b8duces its speed uniformly from 95km/h to 45km/6(fb mb0 vu5,wx nq)zcw8hf o/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 b6w/vv e+ jyw41 *scu(bleua w1ike puts all her weight on each pedal when climbing a hill. The pedals rotate in a* v uws/1u(wvj e46c1y+webla 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 widezt 7.;c18d cbqogip2a1g zbk4 . What is the magnitudd1zag7t;gk1oq 4ibb zc8c2. p e 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 s7 9n6 od y)0citzdcr13lcdk(pc1 s;ethe wheel shown in Fig. 8–39. Assume that a ()6c c;dpyzl37ocdks 1 tdce ni10rs9friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to tis5v ai/rkteyy(2c s 0*o- cf6he ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rodvi kit*r o 6/s(25cfy0cae -sy 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 torqu.cz xg2v0y+qhp(40nfhqba )v e of 38px. h+g hzy0 0nqq4fbv( )acv2 $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when thedqg41ohe f1x - axis of rotation is through its cent -gofx de41qh1er.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.: x4lux..ir at7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass ofaitx ul:x..r4 the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end+ix90xkbig+d qvm14mvm. v 5 y of a thin, light rod is rotated in a horizontal midqvx+vm+ ikyv4m x.0 g591b circle 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 potj85bydn / 5z;h74ex iaw x9akdter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay isaad i9z5 yj;ekbdh84wx5x /n7 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 i2 tsv)-lc r9 *qw6ef 3umpp0lobjects shown in Fig. 8–43 abor-6*lesq wm 2 cpit03)u9vflp ut
(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 twrf8 vwz3jed 3r6 1pzr,i i/qh+o 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 satellidbehjh7l6l7f *c*l u5 te spinning at the correct rate, engineers fire four tangential rockets as sho5* u f7cld6h hbl*jel7wn 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 satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder wi*lb/ufa a)g-1cn a i-lth a radius of 8.50 cm and a mass of 0.58/)-aal i1funbga l *c-0 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 bahm7of k--4a let, 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 a small hand-drivu j wka2v.c +,1z:heu/z3utyovw) 4fgen 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, h t)2+j/va3 c4u :zfw1ezgkv, uy.ou wand 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 andvgl+2 zp ,.pug ,tkgo; is eventually brought uniformly to ,2tlgpu. g,voz +g;kp 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. 8–45 accelerx9ou yiptd(7:g2t*axa i1t /7z0dj bmates 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 mnf:opw(s61* hw 0iq,:p+ zaqdn ml zcl6;zs(thrown solely by the action of the forearm, which rotates about the elbow joint under thz ni +p( m* (lz1qd0w6waolcs,s mqhz;p:nf:6e 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 c2zgsgl0z9 l9 can be considered a long thin rod, as shown in Fig. 8–46zg g9 l9lzc2s0.
(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 of two mass-m;4imflsts4pj gu1(7w u6sles, $m_1$ 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 four full turns (revogs5:ae+qi ee)f:x1 h nl1se ne:+ )eqgfi5a:hx utions) and releases 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 moment of inertia ocln iwmyxrdm em)0x/i:9 .s+.f $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque 8pt64x6trahxcp;7e*x dddo 0of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without s h.f :7mwxtg.wlipping down a lane at :t.w mxw7 .hfg3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to t(gn+ 3wongc)z 6 *tmkmhe Sun as the sum of two t6cnmo+tw)mz( g3kn*g 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 of 1640 kg cpqgf 6a,s9ow0fgg /;and a radius of 7.50 m. How much net work is required to accelerate it from resgqp/ c0;as wgo96 fg,ft 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 b ,qv0 y r*4zc4:znykqfrom rest and rolls without slippingq4kz0vqyzy n*4 ,cr :b down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall zo. fpr+m,vy0 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? [Hint: Use confv. +zo0m,yp rservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin sggj-.d+zge)+cn , us ztring in a circle of radius 1.10 m at an angular s z-cgng++d ,.u jz)sgepeed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinpu-,y(dbn u 1, ;n:ogncy-b whding wheel of :ynnycuh- p;w(o1-u n b,b,gd radius 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 plat ,awi (ueqde 7.t4*frnform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotatio7we tn4r(a*qfd.e ui, n 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 Figp)fxq,a.y4jt izow *3 . 8–29) can reduce her moment of inertia by a factof).a3yjopq *xzi 4 t,wr of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can incre:/ hx* e+a7qeplirm(oase her spin rotation rate from an initial rate of 1.0 rev every 2.0m*7/ee (aqip+ rlx: oh s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotatinu5gl b 5pb .bb4f8ut-1je9ewpg around a vertical 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 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 i jwbegb uf98-5b5pb. 1ul4t pet?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning ypd;rz5,i vx4ji2z 2nat 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 )( p;n+svz qeithe Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an. 8+hqk4ssypv identical disk ro +k 4vhq8p.ysstating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 *acz n.7rud 2:gnuvzss;s7e,$rev/s$ 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;-u e*y l sm:(ms(vxwc the center of a rotating merry-go-round platform of radius 3.0 m and mos lsc*; (-wuvym: xme(ment 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 merr.pw:vihas,+37 f 7q hgm-wzq wy-go-round is rotating freely with an angular velocity of 0.8 . z:m-f qwwi ,a+q3h 7psvwg7h$rad/s$ 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 hu-. 8 u2ptrfh-rlmiv) alf its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost ma2mp. r if)rv-u hul8-tss carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in exces*m.2t,p c:9t-qyf kmca z:qvjs 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 f+s9d /6gxq hc$ 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, xg: ntn+euyr4wr ,o3: that can rotate freely without friction. The moment of inertia of the person plus t wrutx y,:nr:eo +3n4ghe 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 du: a2mv)7evr viameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of ve)r7vmv ua :2inertia 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 grv*i 4cs.wj0pf4/w zvfr6( ,zed(fgxb3v ua4 xound 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 from the spool? How far does thezbjsr w4z4,w4xg0 cvxpduv*evi ( a/ (6f.ff3 spool’s center of mass move?

  The Moon orbits the Earth such that the same side i )nt0e w:/m )u0vg)dwtm5htxalways faces the Earth. Determine the ratio of the Moon’s spin angular momd 5u t) )htvit0:m0x) /gnewwmentum (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 accelerates6n2 1 qj fkpkx3*.;*rgiqlrgd from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 mqnz:w62 ay ran :k(zps 3 bu)cpw6lqzi:4+ pj. acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque azl 46pu:)wj : :abzpywq .+ n3zikpsn cr62q(delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of twhbj m,-* gwf*)4j c7dw q2jbiuo solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin s db wq,ifcjmw)h-ugjb4 j7*2*olid 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 sp f.i tr *s:ng1ng/oumw; ai3;reed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with masz .u8 *qiub-ots 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all timeito-b.uu8z q* s, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it tqx4pfhfy5r4/fqk5 4k-el 4.vqa:d pko use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheeyffl qfqe4 5r-qkx4:5.4dp k /pv4kh al “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 an 1k2rafnk 7ui2- zfg(u$H_2O$ 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(0x a*lq,f.x3jyxovv 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 and2x335 j0hxygc.gei izw:sb4m length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of releayxi:ije 5.xwz 2g h330mc gs4bse, 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 radiuc rohmt(eqr*x4.i5 h0el s0z (s R. It is standing vertically on the floor, and we want 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 heighis (h0tch e0o*q54(rrex mlz.t h, where h

  A bicyclist traveling with speed v=4.2m/7r4 zcnyn f,cdd m0iz r+n8j015lj;- :btzevhs on a flat road is making a turn with a rh+8tj lrdcbv f j:e1d,0zi nnycm7 rnzz-045;adius The 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 o6k3e q6s znqb5f length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and whereq5kzqen6 3 6bs does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as t7hg7v9jie p f(hin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with ( g7hep7j v9fioutstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, o :zrfbb19 zh/:gmyw1 +;1 vowwmuh2 cnffzugm9z;1 1howvhw:r m/2:1+ y w nbbc mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 track of Fig. 8l*o zpu9r0qb o*:3yjoosrg+5 :j+ b6 urulw4 f–58. What is the minimum value of the veu0j:6:og+9olqb4l yo* *5 rrzu+3 uf sbrwpjortical 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 cy:b //ye*yvp)ejb,ido not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifokgt05)wx 6:2kstd( v wgvl.srrmly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was thk6.wd 2vxtsgl) v0( 5tkg:swr e 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