A bicycle odometer (whichh:k*i,,fb43c n 7wr b;* thsz -lajcvw measures distance traveled) is attached near the wheel h j lwt3i bnh*zkb sr,4c:7avf-*hw;, cub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Do2hbhq/4e x4z1m;t,yl6j dxst2 f c+kaes a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increamfckyxj/x;4z t t6s4b+1 qd2ale, h2hses 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 3zoi.rgpmo :;a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater )mgr2c qk kq2j-58h-wnfrbg. torque than a larger force? Explain.

If a force $\overrightarrow{F}$ 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 q rek, 8kye/il f4frmtpn (9(0with your hands behind your head than when 8iktrmky, q((/l9 0refn4f peyour arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at tx89u 5y fy(/v+n8verg jd bq-fjvj50vhe 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 harvg9f5 rj8+j0vdyj/n5vvbe(- u 8y xfqder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on bs:ai0f:.49. rpih; mv .rs* bpdkthaheing able to 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, explain why this diph .hbs 4if r a:p;:*d.9tsvhim.0 karstribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) can; hprnym, t5 -)slyf4rry a long, narrow beam?

If the net force on a system is zero, is th6.jr tudz z4jtm*c 4f0,az *nye net torque also zero? If the net torque on a system is zero, i0*dc 6yzjmz*jr,4 u.t afz4nts the net force zero?

Two inclines have the same height but make different anjgrk + *wc9/c /5uq5)7qpx7djckvarz gles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greatzrk 5/j+d gu 7/jp crw)q7x9akc*5cv qer? Explain.

Two solid spheres simultaneously start rohr 7o bmq0.a*tlling (from rest) down an incline. One sphere has twice the radius and twice the mass70brqohmta .* of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They sirv *7 6nd,n .hvjsaid,t h+;ytart 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 toa; d. y,,dnn r+h*ivs htj67vital kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angul7 ixu+hv4gy 3l)o+ usdar momentum are conserved. Yet most moving or rotating lgs o 7di4)h++u xu3vyobjects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equaton8 zs iyuq:lv7:v/bd(r, how would this affect the length o/byqz:l7sivdv u( n8 :f the day?

Can the diver of Fig. 8–29 do a somersault withlud+5m62zyr b out having any initial rotation w6zuyl+b52 mr dhen she leaves the board?

The moment of inertia of a rotao7 w )*x (r7amqjp-xqcting solid disk about an axis through its center of mass x(q7x-pma )wq7cjo r *is $\frac{1}{2}W{R}^2$ (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 rotaf0ti u:bz-mw /ting stool holding a 2-kg mass in each outstretched hanfz :u -wit/mb0d. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and t kwuw)(w;ixhr69)+el *y pyoc he other is solid. Describe an experiment to determine (ur+yoww *eh;ik)ylxw c6) p9which is which.

The angular velocity of a wheel rotating on a horizontal axle points weg;k, oo fqse)p4+qvk/ st. In what direction is the linear velocity o/ s+o4 qv)g ;qopefk,kf a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the ek.uup,s9+f fhu m 0:hadge of a large freely rotating turntable. What happens if. ,kusfph0mfu: a9h+u you walk toward the center?

A shortstop may leap into the air to catch a rx/ wmxv7 trk( k.nd,adn*85q(y:( baoajd2xball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you loo jrnkad r,ok:/7xxd5q(a8v(ybta. wd mn2*x(k 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, disci03d;wnzl 6n: g,fsjc uerp-9uss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operat:p-lcg,efj i3 w sn6;nr09zdue to keep the helicopter stable.

  Express the following angles in radiansscnqvap gvfg/l w- ib+ 20;w2:: (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 am,t +sscxn83dn azing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, acnn +, xs3dt8ss seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The bel bipq xv6 57bz6h . cbv2d6ox6mv.z,kam diverges atkb,b.qv p.mc66b x6 vzz h2li6vox7 d5 an angle $\theta$ (Fig. 8–37) of $1.4\times {10}^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When thekrx ge1:he4ya2 sx1-up4 :pvl motor is turned off pa11ve2::4hs-yxxp uler gk4 during 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 the ball makes h)e(h xh3z x2 yg/pvd-15.0 revolutionspx2dh/yhez3 g)vhx(- , what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do t t(8eo0s5a s gi(sk(vxv,ius2 he usks (x,t0ig(ss e5 8vi2v(a owheels make?    $rev$

  (a) A grinding wheel 0.35 m in diaml25vtu 39ui qf snez2v)ejp6ip * /i:zeter rotates at 2500 rpm. Calculate its angular v2iz/5p6lqi*2 zui9up:3f n vje)et vselocity 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 comp+ tj z ep)ej7p.paglc;* ucoj 9b)5eo2lete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seat5pjlb7j e a +g*eje u2.)co);zcppot9ed 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 E-nyf8sat/i1 ; w*h7xxs+n ov marth (a) in its orbit around the Sun    $\times {10}^{-7}$ $rad/s$
(b) about its axis.    $\times {10}^{-5}$ $rad/s$

  What is the linear speed of a point zai* y .t w1eubu ;d8-h2ljpf/beev( //x0 euz
(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 pzc ue no7x,4/- tnpdo4m(i vgf;u rp35article 7.0 cm from the axis of rotation is to expei(5 vxp3nz/ e4m;7rd nf 4upo-otc,ugrience an acceleration of 100,000 $g^{\prime }s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpmy //g*k :ri*-au.gqqb 7gdtfz,2 bd 1uan,jo x to 280 rpm in 4.0 s.zbgaq2*,g/ f *bkgoqjx-tydu7i n1ur:.da,/ Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius))bwht y ,9lxtxw t5y, $R_1$ 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 themselve gm2,/yjjc gb)s into a slow rotation ym 2/,jgcbj)g 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. 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. $a_{tan}$ =    $\times {10}^{-4}$ $m/s^2$ $a_{rad}$ =    $\times {10}^{-3}$ $m/s^2$

  A centrifuge accelerates uniformli;0npm/ / ip2 wij(j:qccx c6cy from rest to 15,000 rpm in 220 s. Through how many revolutions did i6:c/pqi/p2xm jc(cwj0cn ;i it turn in this time?    $rev$

  An automobile engine slows down from 4500 c -re-noh.yd ecd5x 7jf/)/0cephlt +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 forr se-) dwmbmsum9( xhg48ho +( the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching it ebm +(w4 g-s8r9hh(om)mdsxu s final speed.
(a) What was its angular acceleration (assumed constant),    $rev/mi{n}^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240c +itno1;: n;s jd;zii rpm to 360 rpm in 6.5 s. How far will a point on the eds+d 1tzii;i;onjc ;: nge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/mb5,vvfezhfr 7 /n+ s2iin It turns 1500 revolutions before it com + iz2rf b5vefvsn/7,hes 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 the car reduces itrtd8 2es gxk4-s speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.rekgd 2s4x -8t80 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 makej ,n g,l/lb12,*od tjbvq7u zv 65 revolutions as the car reduces its speed uniformly fr*tl 7n ,,u 2zb,jgldqo1vv/j bom 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 each pedal when climbing a u7cn4 lk ;d/rmhill. The pedals rotate in a circle of radd/; 4mlc knu7rius 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 obc1mj) mka yg1.rrfs 431*l5yxsrym+ n the end of a door 74 cm wide. What is the magnitudem5*m b.)ag11frs 3ycj1 rysl m+ykrx 4 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 shown in Fig. 8–39. Assume/l6z (l 9pd08d g;nybjd*xkag that a frict xzg09nkl d y*dp86 (;djalgb/ion torque of 0.4 $m\cdot N$ opposes the motion.    $m\cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod which psfuyo v5/kf;j+ * rn3vivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate tsv3n/fo*jky5; + f urvhe magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a tor5r9f ulcl p.9zque of 38 .9pfulzc5l9 r$m\cdot N$ 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 inebpwklo6) b27urtia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its center. o)bul6b 27wpk    $kg\cdot m^2$

  Calculate the moment of inertia of a bicycle whpo9.ji+muuka(09 h vseel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The p sv9a 9ij.ohm+ uk0(umass of the hub can be ignored (why?).    $kg\cdot m^2$

  A small 650-gram ball .at sd)ehq n)u2ifjff- v11rr94+ded on the end of a thin, light rod is rotated in a horizontal ciqe1)1rdd 4 nu.9fdf2)+v ah rsi-tfjercle 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 a.u hytzr( jsp 597qfh7ngular speed (Fig. 8–42). zfhu7y phs(5.9r7q t jThe friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m\cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg\cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fiwd.pb.yxjia 5 l/)+ zsg. 8–43 ab..asyxlz+5id p w) j/bout
(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 twzfy 9lh(;q u;8u5epxhek0v3 mo oxygen atoms whose total mass is $5.3\times {10}^{-26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $1.9\times {10}^{-46}$ $kg\cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times {10}^{-10}$ m

  To get a flat, uniform cylindricazw lhb1 0,um-c4l m+(htia2 isl satellite 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 hcazibmtl -w1h0ml s,(2u4+i 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 cylindert2 -mk qf2u dimm(89zq with a radius of 8.50 cm and a mass of 0.580 kg. Cqmd mum2ftiq(89z 2-k alculate
(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, axcjcov.7 4h6n5 7ged tccelerating 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 hanakdm+ . :a)f cja//5nl* ndttid-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of 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, neglectingd 5tn+lf ia.:/aat nk *dc)/mj frictional torque. $\approx$   $m\cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually brought2w5z:n dbibi - uniformly to rest by a fricb:zwbdn-i2 5itional 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. 8–45fw4 m- bp,y,g/:wf4j z l:wjlw 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-k;9pxo imbq -(yh2qn;l g ball is thrown solely by the action of the forearm, which rotates about the elbow joint 9yqx2pnb hm-;(;li qo under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considerelb) m hbn4q +5ge gg750xcx(wzd a long thin rod, as shown in Fig. 8–46.)bq 0ggecx mx ng5b(4+5hl wz7
(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 masses,(dlgp )6/z iw:crxs7a $m_1$ 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 hamok9po0gh (vr 6mer from rest within four full turns (revolutions) and releases it atpo rhgo(k9v60 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 inkzmts0r))( h aertia of $3.75\times {10}^{-2}$ $kg\cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqus4qy5p is: p+o q-1wxve of 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 slipping do( fd2tlc0mym4xk03h ywn a lane at 0(tcxyy04 hf dm 2km3l3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to(t (yd 8ldtoxiz9*vi9 the Sun as the sum of tw(dy(t99t zd8i xl*voio terms,
(a) that due to its daily rotation about its axis,$K{E}_{daily}$=    $\times {10}^{29}$ J
(b) that due to its yearly revolution about the Sun. $K{E}_{yearly}$+    $\times {10}^{33}$ J [Assume the Earth is a uniform sphere with $6\times {10}^{24}$ kg and $6.4\times {10}^6$ m and is $1.5\times {10}^8$ km from the Sun.]$K{E}_{daily}$ + $K{E}_{yearly}$ =    $\times {10}^{33}$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. a) mo h:ubjn b;gy9t4kye67(4dncp (jHow much net workdahpgb j4(y 9nkc4ob; t:m)u n(jy7 6e is required to accelerate 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 star..m9iya nu5.;xw gutgts from rest and rolls without slipping down a way..u n 9.5 ixgmtug;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 ve2:en42uwzo qartically on its tip. It starts to fall and its lower end does not slip. What will beo:4 2 qznewu2a the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotatinga(zybfktx rg 4n9i 27s6;ww)u on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10k9) f2 6;b nu wx4rzait7(gyws.4 $rad/s$?    $kg\cdot m^2$

  (a) What is the angular momentum of a 2/sq /tfpvl 1*3ii- hlm.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 150qi 1p*t/mih-l fvs/l30 rpm?    $kg\cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m\cdot N$

A person stands, hands at his side, on a platform that is rotati bc.n (xm-zkz8ng at a rate of 1.3rev/s If he raises his arms zcb xn-k (8zm.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 momeno:8z;zklz/jdzbi; 0hj.8i r qt of inertia by a factor of az0q;/r bi.:dji zhz8olzj ;8 kbout 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 incr9j 4wyugdrcy nh7/e y0xvc9 5-ease her spin rotation rate from an initial rate of 1.0 rev e4 wxj07rc y/yd9 hcgen-vy5u9very 2.0 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 rotating around a vertical axiseqtbtsy0 )q 1-n,kuxd*:x bed.v4 sa; through its center at a frequency of 1.5redytkn- eu 1vb;seb:x x,.t0*sqaq) 4dv/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 it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning7)7feb(a6 zmx/1ao zofy4 ivt 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 ofgn+.ka thk +q6nvo ,e) the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times {10}^{33}kg\cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6\times {10}^{24}kg$ and radius $6.4\times {10}^{6}m$ and is $1.5\times {10}^{8}km$ from the Sun.    $\times {10}^{40}kg\cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an ide:o4c8ximm w2,,fwat gq737z8jiwvzz6 lkgm+ ntical disk rotating amwfwq3xzz j8wg ov2:l , 84,kmiai6tc zgm7+7t angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns anmnr9ll -h, q d(iw3e0t 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-roun(6d*ga1leuzuei hz 6t)me,8:ynka0 ud platform of radius n8z ayu,km giz0 a6(1eheelu6tu)d:*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.$K{E}_i$ =    J $K{E}_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating frebe 9o ,0 xb0gh0n cfhlvr26l pxico213ely with an angular velocity of 0.8 i1 ph,hlxl 9o2o0f bc nbc3xv0r62e0g$rad/s$ 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 dw zjw;. c5+mgbrarf, losing about half its mass in the proce;rb 5cgmw+ .zjss, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest 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?$K{E}_f$=    $K{E}_i$

  Hurricanes can involve ;i rdyk.*/tkqvj8nm; winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $\times {10}^{16}$ 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.    $\times {10}^{20}$ $kg\cdot m^2$

  An asteroid of mass j-akzt,i33,jf a. zff $1.0\times {10}^5$ 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.    $\times {10}^{-16}$ %

A person stands on a platform, initq)a.q, prcybx,cy. e9ially at rest, that can rotate freely without friction. The mom.aq x qyb.e9,y)cr, pcent of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity ${\omega }_W$ What will be the angular velocity ${\omega }_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will ${\omega }_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-gq85ob 71 viodgo-round turntable that is mounted on frictionless bearingov8g5q7 dobi 1s 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 endrq em7z sqttruo(j*cw-- )j6/ of the rope lying on the top edge of the spool. zqc( uqjt6r *m-e-tsrwo 7/ )jA 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 Earth such that the same side always faces the Earth.z,2w 168uvg1gfu xjv *nufzm1 Determine the ravzv1,z6x1f fg82jw1 ugnmuu* tio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times {10}^{-6}$

  A cyclist accelerates from *c xc)zh *dk6bx/fj ss1 ,axy7rest 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 2xz3)wvl ex 8c; ke ocbrly:d6* 0ril*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 by :d*6xl c2lcw 3 xorelv8rk0;e)* bziythe motor.    $m\cdot N$

  (a) A yo-yo is made of two solid cylindrical disks,f+e 8k31( dm wzohsvn. each of mass 0.050 kg and diameter 0dzf 3e (s8mhkv1+n w.o.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if 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 r+r:,b 9s) o wv8a6xg5lyozhr gear 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 mass 8.0 times *twk3d;k 0-qwny 9c2zt3+ *jh bqyrxwas 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 -y 9h2dww*kq wzyq0t*b3jxtr+cnk; 3 star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times {10}^9$ $rev/day$

  One possibility for a low-pollution automobile is for it to u;(qst(e .gdbl se 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 flywheel “spinup.” b.(q(et; dsg l
(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 $1.7\times {10}^8$J.    $\times {10}^8$ 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