Angular displacement is usually express in uz30mfp :fd.v8 yw2pg rk h))punits of

  Angular velocity is expressed in mwh( ,/tsgnn2vk m p:uvb y d+*x)ga6/units of

  Angular acceleration is expo7wsh1 +bi,tx z* txu6hrs g2/ressed in units of

  A boy and a girl are riding on a merry-go-round which is tsyzuo6j3 c w ,1.xaeof ;qf35iurning at a constant rate. The boy is near the outer edge, and the girl is os6j,5q1; 3.wzfyu fxeo 3 aiccloser to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a mergn)//b4azpx ):b hsr n5lr f8qry-go-round which is turning at a constant rate. The boy is ne8)qx)hb5/s: nfg 4 zrlpbnar/ar the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turh9 .c lfu6h2qtning at a constant rate. The boy is near6 2qhucfl.h9t the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant r./vc 2fac 2jtm7pkz 3rate. The boy is near the outt2/pcz2v.7cfmr k3jaer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning ugxy)7k 61 oovat a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has tvok )xu6g oy71he greater tangential acceleration?

  Consider a rigid body thajv mzcei)htvfqu4lu:j7 4 w)jj74n2 -t is rotating. Which of the following is an accurate sthu u 4nlq) j ew7v2vc7f4jj-mzj:i) 4tatement?

  Rolling without slip6kqq(b24-, yz m / pl;mlt:ljx vbw-ebping depends on

  Two equal forces are applied to a doorbt q4ujbc2:ne1v)l pjqv()7ak/0fc+hy i7 py. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force ec4jky20qeh1)/f( lbp ju ta7 i pybvv+7)n:qcxerts the greater torque?

  Two equal forces are applied to a door at the doorknoevsr9c fftd. izb2m cv/8 g.89b. The first force is applied perpendicular to the door; the second force is applrgimfv zd c /9ve2tb8fc9..s8ied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perp(ugblw p 23:deendicular to the door. The first force is twice as large as the2edwu l3bgp: ( second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to 9m8mqa ns4a9x 6dm4 tw8yn89ad ezu.fchanges in rotatiow4aa8mt9 9zm.n8 9qya f6 nmu8dsdx e4n?

  Consider two uniform solid spheres wio 5;agfwtgqq(7 ; u0shere both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaw0;t7ugaif(sqgq; 5o ller moment of inertia is

  Two uniform solid spheres have tpz r3wlb7vbw kb4r9+5he same mass, but one has twice the radius of the oth b r9p3+zvlbrw7kb 4w5er. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twi 5*v/ * g2jw qi27hwpy qcc-rwqq5,oazlua*k2ce the mass and twice the diameter of the other. The ratio of the largyi2a *2*o,kq 5hcvp/cz725* j uwralqqwqw-ger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If gfipb4-ff6zy 9vk f12these are increased to 2M and 3R, what happens to the sphere's moment of inerti64pfif 9kfyv z1 2bgf-a about a central axis?

  If a constant net torqu7,/ccziw 33wn tyxc-re is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. Isf sy*,qdm) p7f this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translatqymdp *7)ssf, ional kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has6j:-us.bk;5x6xd e ,aq auzu a a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total transla du aa:uksu-x5x,.;6z abq6ejtional kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down ar5egmb3-(5 mrl uw /-sekx2in)v p-m wn inclined plane starting from rest. The linear velocity of the e 2-mbs5 3u-r5(melm pig-wwrx)k vn /sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M andh8f. sv v/vl;0j/dgg h radius R rolls without slipping down an inclined plang;vhg.0/d j8v/ fvs hle starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes wx:jixnf56n avdingvh: (+n6 1hen a net external force acts on the system." This stf1(h5dgax6vn:x v6:n jii +n natement is

  In what circumstances can the angular velocity mxk+i)q/wv 3s of system of particles change without any change in m)wsx k+iq3/vthe system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore youzh0/pr h xm)btemd9e m173c86n1fany friction which may be present. What happens ove1y78 3tceru1 n bexmm)h0p o6fz/dh m9r time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As ts /469r0i /bdrdiwjxthe Earth moves close to the Sun, then which of the6drd wb/x jr4i09tis/ following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a e3b w-8-5bpmt 3rvxngfast spin) by pulling in his outstretched arms close to his body. What happens to his ang b 3nwmr5g-3tbe-vxp8 ular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullin9k4. qqa92hq9upb 2f c n mm2ms4lxg:xg in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis ofm.m lhqb92kux9c4q2 m 9 pgx4f2a :snq rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstr( o9qufqjuuf d ;:vy;0etched arms close to his body. What happen( 0 qquf: jovy9f;u;uds to his moment of inertia about the axis of rotation?

State the law of conservatiox:w 6 :y-hwhyvw zq(0 zmxu34bn of angular momentum.

  What arc length does the Earth travel in a thrk ;1bmkl,d9vpee month period in its nearly circular orbit about the Sun wit; 1k9d,v bmkplh a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 .xb2zhc*y/j :dt- jdem. What distance does the tip of the second hand sweep through in 3 minutes and bz2d.djjtec y/h :*x- 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent o5z w;m b,rg(oh*d;jof*r f;xto?

  A bicycle wheel rotates uniformly through 2.0 a(u h9w0qpib:7n8y ; .z dignarevolutions in 4.0 s. What is the frequency ofzp aw (:yd;9bu.n i7qni8a0h g the wheel's rotation?

  A pulsar (a rotating neutron star) emits pu8 bz*a.at, xvklses at a frequency of 0.40 kHz. The period of its rotation zat 8 *ak,xv.bis

  A phonograph record rotates at 45 rpm. Through what4qa4ho 4w3fs n angle does it turn in 0.20 sfo4s3n4aw h q4?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outeh/em+ii o(t4ye+ w-iimt f8o: r rim move in 2+yt 4t:hi o+(i8m-mi/o feiwe.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions ifg6) yemen9gxr5qa/4bc5(re7wq , a yn 4.0 s. What is the average angular speed of the wheel x q5g4(rb9rf,ceaymnweg/ 65 ) a7eyq?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0w5gyyteb+5*ljf 0 nj 4 s. What is the linear speed of a point 0.10 m from the center of the w*y lw5bj0fynej5 g +t4heel?

  A cable car at a ski resort. m-x4gr)jyzlyj/xkqo, :3dt carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pullemzl-qx 4rxd.,yt k /j:jyo3g) y with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a c)z m-q02vrbx: x.7ihqm/vbkeonstant angular speed of 2.0 rad/s. What is the linear spe mqi m2.bxq x)-0hz/7vv e:rkbed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in ls9a i-o+u-pgp1szwl 8u f.s ;ysc t4);i+hd zzength. If the motor rotates at the rate of 20 rev/s, what is the appro;9+ itosazu;4)h1zpcpy -+ssu wl8.f -gszdiximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 :gl4g e*l q3irrad/s. What is the centripetal acceleration of a point on the wheel's riq 4* lrli:e3ggm?

  What is the centripetal acceleration of a point on tfw7d4fvw 6)yvhe perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8. v)7f vfwy4w6d00 m/s?

  How many revolutions per minu+7zm mjbm85-fge1n 1 l3qxa aate (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce a3a+qjamefz 5amx1m- gn7l 81b n artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flby iw t6hki6x h2hfu 0:u.c7)tat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripef6t)k 7hc :26tw. ux0hyu hbiital force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/ysdrsxm7ym8o c6e 464 s. The maximum centripetal force (provided by s e8sy466 rxmom4dyc7static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, is whi,e;ri1;g q-b wugwy )erled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if the string is not to bre)1u;gw rqy b egew;,i-ak?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipw rmj5h-l) fc(ping 10 m down a lane at m hr j()wlcf5-4.3 m/s.
(a) Calculate the angular displacement of the bowling ball.   rad ( fill in numbers only)
(b) Calculate the angular velocity of the bowling ball   rad/s ( fill in numbers only)
(c) Calculate the radial acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)
(d) Calculate the tangential acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)

  A wheel accelerates with a cq+ 6;rrinq2h4vq v o 3venj.9wonstant angular acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angle the wheel rotates through in 2.0 s?

  A wheel accelerates with a constant angular acce (cv-v a.rbty.16jth eleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does a 0.300-m radius automobile tire rotate.me6gcr 3 w g,eqoo36h after starting from rest and accelerating at a constantqg6e ,3 gm3c.orh oew6 angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratioo8o ga(8.dn a: kzybu6n of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a co ;+.bdk*bcol vnstant angular acceleratloc*b .+ k;bdvion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while*,jggkn1bs6 .qf5r i0o n1ldf turning through 2.0 revolutions. What is the average angular acceleration ogsf fk,.1b0*qi nd6 n1ljr5gof the wheel?

  A wheel of diameter of 68.0 cm slows down unif -j 56bp3-gcm3oaojdiormly from 8.40 m/s to rest over a distance of 115 m. What is the total number of od3b mia 3jjg- 6c5-porevolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/sry4/;kvqkkn9 ef0 pm; b4ks6f to rest over a distance of 115 m. What invs4p4 06k ;qyb/9k kefmrk f;s the angular acceleration?

  A wheel of diameter of 68.0 cm sn.cn v7 vb9 l9,h k.4sjfkg6fulows down uniformly from 8.40 m/s to rest over a distance of 1 b9vkuf .h n97fjl.4sg6cn,kv15 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/i z,. b*say6mgmin. When switched off, it rotates 50.0 times at a constant angular ac,6ga. bzsy*imceleration before coming to rest.
(a) Determine the initial angular speed of the centrifuge.    $rad/s$
(b) Determine the angle (in radians) through which the centrifuge rotates before coming to rest.    $rad$
(c) Calculate the constant angular acceleration of the centrifuge.    $rad/s^2$
(d) Calculate the time necessary for the centrifuge to come to rest.    $s$

  The bolts on a car wheel require td 3x asqpm 4k9qd95,mkightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendic qsx dam k45mp399dqk,ular to the wrench?

  The bolts on a car wheel rco6o bg4 noe4;i*j3p xequire tightening to a torque of 90 Nm. If a 30 cm long wrench;4exoibon6pj 43c g*o is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in .pnru3e:pe8k ertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as fo -1vy1m 7f 8xtk /sdyfldyu.u9llows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. 8-fy9m.dukf/xytyd lu 1v1s7 What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought txst(t cmh ;+)g1 tf)myhe center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F ;tg1)ch+t ms)tf (mxy1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted abl5 9 rp0(wavn/obm/fk out a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radin0 /r /am(olbkv9wf 5pus R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod ocghz(/a cp7jhl0d5k 9dc s+o(ru0n:is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it/dsrcdnl(oj 0hg 7k9oc(ch: z0pu+5a is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radiu25hgideq/b nq2/z:yr s 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cm for 4nid/qy2h r5 :/zqbge 2.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk u;e qwn xnj+ 4x,6:kwa.ce0svpulley of mass 7.07 kg and rw4uj w,xeqnc+ ak 6;vs0e:.n xadius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrajtk wgvws:u8/-lv9 43 5ji-xcn rx2 jxpped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cmj-tx rsc34nxk9j25 j-x :wv8w igluv/. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requifs 93yurbzm 29n:z8;2r zel .ybu*sbwred to store $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment of ine b1wj we b9wwx7.0c72 wrcmh45qh my5xrtia of $5.00 \; kgm^{2}$ starts from rest and accelerates under a constant torque of 3.00 Nm for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?

  A solid sphere of mass 1.0 kg and ra7:og lr)rsab 3 :rj.evku6knvb03 .kkdius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the 70bgk ov.la ne3kvb3: sk)r6 kjru:.rspeed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and rau1; md2j 4znmfx9j,vlc7d6c t dius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming tzmcn2x; mdjfjuc 9v,4 7 16dlto rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and-piwo ,-q;g r )eijbk6 allowed to roll down an inclined plane. How fast is it moving after dropping a verticib-rgkji ;e6)w -po, qal distance of 3.0 m?

A solid sphere of mas si/)aq)brwll.kwi .+ ;7vuw fs 1.5 kg and radius 15 cm rolls without slipping down a 35e ir; is l uw.fqv)w/b7lik)+w a.ncline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given by $I = (2/5)MR^2$.
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

  An object's angular momentlt:u-ijw)n+ le0(9hp,lef ai c( dt2s um changes by $20 \; kgm^{2}/s$ in 4.0 s. What magnitude average torque acted on this object?

  A proton of mass $1.67 \times 10^{-27} \; kg$ rotates with an angular speed of 2 x 106 rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton?

  An ice skater has a moment of inertia of otkmc.bbui dyg(8-( 9 ly.8ch $5.0 \; kgm^{2}$ when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to $2.0 \; kgm^{2}$, how fast will she be spinning?

  A figure skater rotating at 5.00 rad/s with arms extended has a mx 9ag9po a2zs.oment of inertia pza2x9 a.ogs9 of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?