A bicycle odometer (whiegj.) )0m0njhg jfa/fch measures distance traveled) is attached near the wheel hub and is designed f0jj)f mjggn/0hea) . 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. Does a point onex4v 80r .vhvs the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tanv0revs x .8h4vgential 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 velocitype/5y 4 :hwfub(vv+ yp $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? df99o2l isc3v u1lj :q; n1hllExplain.

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 your head tha h zav(ii-ct*+n when yourai i*z-(h +vtc arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at t uuvn)g6kuojap., /g;uv xg1;he rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or avugnkx)u1; p./ agguvj o,6;u large 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 ( rew2oph0u s,a:3cf y,tvoa:flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution ofh,0eyc( opstuaw3a:2,:vfo r mass is advantageous.

Why do tightrope walkers (Fig. 8mb, 5vspk;td8ky o+2 w–35) carry a long, narrow beam?

If the net force on a system is fbs1hp 5 fmg67zero, is the net torque also zero? If the net tor7hfps1m 6gb5fque on a system is zero, is the net force zero?

Two inclines have the same hef 5*feswul*6llf32c ga,n1 0rslwd3z ight but make different angles with the horizontal. The same steel ball is rolled down each inclin f3e sa* z5nllwcu,llgd0r* 63fw21fse. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultanexela s6 4xt;k:ously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kineticl;s6:4ax etx k energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. i6l9af;m q.pbgu, 0pg They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bom;b igl9 u0a,q gp6f.pttom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conse 3-vdijie)4rk rved. Yet most moving or rotating objects eventually slow down and sto 3eri-)kdvi4 jp. Explain.

If there were a great miq9 x1 tsmnup g00tc(, z9k6 ybsby+vm1gration of people toward the Earth’s equator, how would this a,vzbptx1y60 + y(b0qg9mc 9k unst 1msffect the length of the day?

Can the diver of Fig. 8–29 do a somersault without havi4a ;gql6,y tsi2xjf0tng any initial rotation when sxt4 yqf,st2j 60gla i;he leaves the board?

The moment of inertia of a rotating solid disk about an axis through its c04zaeyj3z5ezsh vyqi6- 86khenter of mass y6- vqzzskz64 ha5ehie8 yj03is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in eacrh)( d4wrfhs1 h outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the sashrfdr4)1w(h me? Explain.

Two spheres look identical and ha7w,nzpn97:ep t1ai pw,,hvg mve the same mass. However, one is hollow and the other is solid. Describe an experiment to deh,tepw1np m a9v:p,w,g i77z ntermine which is which.

The angular velocity o4n1ym1uvhj4st4)v em f 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 of this point at the top of the wheel. Is the angular speed incre 1v)uvj 14my nhmst4e4asing or decreasing?

Suppose you are standi kaz1k*: f9pt4g :xjdkng on the edge of a large freely rotating turntable. What *:k pk1gtfkxj 9az d:4happens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw ica4 ,rpomnt92 y6y+x bt quickly. As he throws the ball, the upper part of hi rao,tp2 xb4cm9y6+y ns 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 ow3 wp2 j,so2nkf conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propsnpk3 j2wo, w2eller can operate to keep the helicopter stable.

  Express the following angles in radians:ay8uz . tfix*rs8u1qj -(,vhk (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 amazxb)+ywnb x 8aaf/f) .bing coincidence. Calculate, using the information inside the Front Co/f8 wxb)b+af y).ax bnver, 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 i/f bf2tcklg g8 5acqo ,arpby+130y(beam diverges at an angl 80/gc+3,bcy1 kfpl rab y(togq5af2ie $\theta$ (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 4fe3i4 2att go5n 5(jjewaa3+i bxz3k the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular ac3tzaa5i g j2w 3oixek+(4e j4f5ant3bceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a 1vh7g l4uafe /d5hz 8klevel floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is ie47k u hz dahflvg185/ts diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Howxtylc- ;)d qi*loh4 -k many revolutions do t-x -iyl)odq*hck4lt;he wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates asq + rs18,e;nzqrgc(xt 2500 rpm. Calculate its angular velociqg s(1cr zq +s8x,;nerty 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 oo u d/)w rgwi-f3b17eane complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of -dw)3/1webr7aif guo 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 the vi ,pz+gd yq0;Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spe+2 wz)bpgb37s l-0w6rzdx9rd7yzzlaed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from (cgehra9(fzan( a,(i the axis of rotaa,fna9z(rieh ((agc( tion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniform /y /vza,ygyqan;s +4zly about its center from 130 rpm to 280 rpm in 4.0 s. Dete/s/qy+vz4; ay gan,zyrmine
(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 radiutzw jbrw;,qtt9.b 52jr6-k ( -wwzf1fhbnq, ls $R_1$ 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 spacecxz,y a)r*(;/rguar u 4ed nek2raft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the ster / aen24r u,x*u;aygz()rdkart 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. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. dh.i iu ,s 7jf3t:a)ty-8td odThrough how many rdti7y: 3o.istf,au8-h) dj dtevolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. 7(b5c) b zp3nt l1f2vd 5kccwdCalculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed d.la j,bbux7v(m:dmdt;, j f(jets in a whirling “human centrifuge,” which takemdfa: j ;mt(d ,.d jb(x7bvu,ls 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 u)am nhfcn c okw+q2c9/;v;9r:c5pff240 rpm to 360 rpm in 6.5 s. How/2;h9wf 5rmf )+pncncq fav;:cuoc 9k far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revoltvkcj-5d 22jwzf x*:uutions before it comes to a stop.2j c d*:vjt5zkf-x2wu
(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 cbn8zouu)6n8o okr*t;ya s/ ( war reduces its speed uniformly from 95km/h to 45km/h The tires have a diamorso 8*(zoa u t6w/n8 ny)kub;eter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uuifg 4sg:8 :bjaj .jz1niformly from 95km/h to 45km/h The tires have a diame8izbg jjsjg: a f4.:u1ter 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 pnt* zqqq0f qiv e(w+mi/;0 )wsedal when climbing a hill. The pedals rotate in a z0vetqis0(m/w* q qwq;f i)n+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 Nh9b 1lp5u7 u ,: wiy)cwpjt5 m5qls/iq on the end of a door 74 cm wide. What is the magnitude of the torque if the bp5suqw/q wti,l 51ih mcy )u7lj5:9pforce 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 t8t 8/gnrd 0(gyf d 2lrcot1l2hhe axle of the wheel shown in Fig. 8–39. Assume that afyrh(18/tn d 2og28l l0dc rgt friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attache3cmo+8 xkqv6k ykwv3dt-w p48d to the ends of a massless rod which pivots as shown in Fig. 4+x c vtkq3wpmov y8 -k3w8d6k8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tirq:5uayfa. :;kbtfv9t lzuemr)f97 7 ghtening to a torque of 38 t9aqmae )fr;ru7::zkub5. 9yv 7 lfft$m \cdot N$ 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 hsp + w)kwt,*(wpk 1hasphere of radius 0.648 m when the axis of rotation is t tw*a,w(h)+wpk1kshp hrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of ;k peblb- uk476u/dhmyuyw8 - a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass b ;l--p6h/eyd8ykw k mu47 ubuof 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 iue:h*,b 72vmw.amnwe s rotated in a horizontal circle of radius 1.2 muwbee 2a n.wmvm7: ,h*. 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 /3 u4dz 1wt2ndd/hvwerotating at constant angular speed (Fig. 8–42). The friction force between her hands 2dw34h e/vn1dtuzw/ dand the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig. 8–(mfjqf6g5( ig/q-dop 43 abop5fmq-fqi g/6 gj( d(out
(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 consist;ii hf d*0tz/ pah ei2rh-2ew-s of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spine3txvjz1ia mh8d3h3 4ning at the correct rate, engineers fire four tangential rockets as shownxejad3hhzi tv38341m 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 cyl k:8k. oj)ro.bug;xm ie.)qgee2qb 8zinder with a radius of 8.50 cm and a mass of 0.580 kg:imb e)8 keukjqo 8orgxgb2)..;ezq. . 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, accc whj(je9-9bwvj;1 u )ad vmt*elerating 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-driven merry mt -k zkc/m./qvb)*lt-go-round and is able to accelerate it from rest to a frequency of 15 rpm ) tvkt *blzqk/m/.-mc 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, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually c y xm/2ktf-p7brought uniformly to rest by a frictional torx27 f/mp c-yktque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball atfm28zdchxvb *)+x p 2m 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 baw)gm2 fl g:(kdll is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unifor (:fg 2wdklm)gmly 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 considered a long thin rod, as 8rkn-f px;o9p shown in Fig. 8–46.r -;k f8xon9pp
(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 conq/6 veg..hs et2sm;vnsists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the ha/xg(hr(hp td 7w* kdfclmx:q8-o l51c mmer from rest within four full turns (revolutions) and releasesd7t( /x( l og*xchp mh-8lk5r:fwcdq 1 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 24; wotdj7j erof inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of v9l ) q)(vsvkh280 $m \cdot N$ 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 rollsip(cex huw 4oo8;wt-1 without slipping down a lanpo;i ct ux4(w1o-wh8ee at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of4kj;gmge 6q:b two terms,; mk 6e:q4jggb
(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 /nz9arhupgaz j0dctmk x*vo82doj, 9 q; 5 2/imass of 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 1.00 revolution per 8.00 s? Assume it is a solid domk, ; ojci ada0j5h/p92r 9vx tg z/2unqz8*cylinder.    J

  A sphere of radius 20.0 cm and she 2v;+r4b lcdffc,+mass 1.80 kg starts from rest and rolls without slipping fh++;c ,b v4cr dle2fsdown 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 v h b.1uf1h5:xjqcz8ka6c7ld /bdpw2 h ertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the gz7d c1h:hj6 / 2cukb x.qdw1hb f5p8alround? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210 6vcaxqy5fw-;j rdc 7)-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angulay-q; da6r j5)7xvwf ccr speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylcg v3h0cc4( rcindrical grinding wheel of radius 18 cm when rotating at 1 (4rcg3c cvh0c500 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 pl.lf*f;46ladb zq b9a3y shkkpnd:u 09atform 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 rotatfadz 6lnq ub0hp9 .4sf:k;y*k 93dlabion 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 mv9hfo4s)5y f +wk8jp/o7o6 zo:ic nphoment 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 innhoc94sfw/5pzi7 8:pfo jyho 6vo+k) 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of58rnr );swlbpt vs b*9 1.0 rev every 2.0 s to a final rate of 3 rtpb*) s9v;8 r5 lwnbs$rev/s$ 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 arou;tc m gsyb18 p 90elh gsms0qo;/ /nhyn6-cx6wnd 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 ag;6 nyscge s/mmo06s8 q1xt-9nhbw y ch0l/ ;ps 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 ,ugomvj+r64cjwlb 3g ea l091 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 t;( wyk-pm lxmx/wxdip,1 z51ghe 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 Ilk6t fcmcr*p9f09g f9 is dropped onto an identica*pl 9ccr9ff 6gkf 9mt0l disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a t;+hdi(r-,whdn (b iht 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 roqrc /jr n3)m5ctating merry-go-round platform of radius 3.0 m and moment of inertcn5 /cr3qrm)jia 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 frpd1mywfv4wv - -79qlfeely with an angular velocity of 0.8qpv-- m79ww4 fvy1l df $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half ig .mmn 3d:xct7ts mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming xm7tc3. d :ngmthe 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?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 1292jknif lf:f h0r+h );f-nwb r0 $km/h$ 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 hgcfbhvq(-t s4z 8 2j-$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freez.b 2kp2ubn9 *.hdb:w1z plgi ly without friction. The moment of inertia of the person plus the platform isiz .b1*p2g2puh d 9 w:z.blkbn $I_P$ 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-go-3b0u a7;yx cc*3unfyhround turntable that is mounted on frictionless bearings and has a moment of inerti*a7c3 ;y cy ufn3ub0hxa 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 ooi2; ,5y53yc znttxxu +da98*df:j+g wbla yo f 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 lengthd ubgfwitc yya95+8a;z*lny x2:3 o5djo tx ,+ 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 mm7k sspsh0g,r.g 8f )dbh2 l-id/bi5 faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about id/ hhs,f.msi sb 2dm g-prgklb)70i58ts 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 a tft-ow f;q)a q,q-es3rate 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 m acqchg;q(ca;ly c ;gv5u 2x ajb:m 37uo6puires a rotational rate of from rest over a 6.0-s interval at constant ac ;6xc: qp lg3 5uc;bamg(2o ;uv7ahyjngular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrica 8j;0puh+mtcg3:je yff *c d:cl disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid 0j c*yffmge td+c3p8: jch:u; 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 ie( (hruzh aozb uj5:23s the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but wf+xjb/ hek7fb s(,3q i qn9d8kith mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 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 momentufxbh/78qedqn sfk93j , ki(b+m.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile iyusj g mk*65 zo+zri73*2zaans for it to 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 flywhej2u7yskzz 6img *ao a*3+n r5zel “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 ,s/wl9 yqefu-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 /2j7jh*jg: spg 8fijjspeed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can piygur /,7 kme+fesh08 zvot 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 release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that8e hguykrezm7f+, /0s 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 vertically on the floor, ane+a0mqw +k;as 38fgg1k hdh9pd 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 hagea0k sqkd;8+fhag 9w1+ 3hpms height h, where h

  A bicyclist traveling with spy52e wld7vj0w3 h2j, no ll1kpeed v=4.2m/s on a flat road is making a turn with a radius The forces acting on thh23ey,p 2o5wwlj1kl 7 nv djl0e 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 rock9.sv r+*it5h*zdcbw e into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above zch*ri9*d vewbs+ .t5his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thi8xi.cmww ,oml(gu 4j3jz8b z1k;gv5.ow drh-n rods, making reasonable estimates for the dimensions. Then calculate3;zw.jjz8bku,l m ow8wg( mchd1 v5g -oirx.4 the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consistm.3m8tr9s0 mwqq3-83ol ahcqdx1ayeuq c 69 os of two cylindrical plates, of t ow6mc 3q8lm.-9m0e qr 1yd3 aos8q c3hau9qxmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 they4j jb8. ei2nr looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume i.428eby rnj j$r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but(j: p3t+ i jhci7hdt 7ro.r)j:b1dfvs do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spes32v3v8k qc;nhik; zted uniformly from 90km/h to 60km/h The s3 it2kv 8 ;z;ckhqv3ntires 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