Angular displacement is usually exgf 5-iv,+5 ceod)jn apgp ,su2press in units of

  Angular velocity is expressed in unit34o v:jx54ks jf-i, olu wk3imdhmu40 s of

  Angular acceleration is 6r q q -a-mw5aoec,xl,expressed in units of

  A boy and a girl are riding on a merry-go-rousz4z 5bac*2vw;; +oqaq g+lgknd which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacemecqb* zsaw gal kgz+;+42q5;vont?

  A boy and a girl are riding on a merry-go-round which is turning 3z dkd.m r04jpw0iob6at a constant rate. The boy is near the outer edge, and the girlzp0 dr46ijk3.md0w ob is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on*:vvmumuf8fwfd;b l (:i3 7hh a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linearu:3fvh v:dw; 8m li(7b*fm ufh speed?

  A boy and a girl are riding a o8dikv2mzed--z /qnqz0 /t0r merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal accedzi 2z/0dz 0-nv/mte q-kr8 qoleration?

  A boy and a girl are7mhrja1 xdovcn +,7u x i(wt0a3v )6rv riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center.7 x, inx3 7d6a+ctru0a(w1vj)h vromv Who has the greater tangential acceleration?

  Consider a rigid body that is re s oyrt./,6reotating. Which of the following is an accurate statemeeyo.6rsr/ et, nt?

  Rolling without slippg sz**30khzabing depends on

  Two equal forces are applied to a door. The first force is apptm ibxnq 4fnxrcx:9vw y/3,:3lied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Whicnr3qvn/::mxwtx3, by c x 4fi9h force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first for0jz4- uaz prb8ce is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts thr-40 zjz8baup e greater torque?

  Two forces are applied to a doorknob, perpendicular to the o9s+cz qr:i** u8ot gkdoor. The first force is twice as large as the seco *c :s9io+qrutg 8*ozknd force. The ratio of the torque of the first to the torque of the second is

  What is the quantity/mn+sh2n,,gijhncod:w i:n1 used to measure an object's resistance to changes in rotationsni:o h+ 1w hnd2n n/ijmgc,:,?

  Consider two uniform solid spheres where both have thegz 5,y denz*w/ same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that e/n *,5zgwdyz of the smaller moment of inertia is

  Two uniform solid spheres have the same masspm 3g4 t4+qwuo37ua gv, but one has twice the radius of th4t 7+4aw m3 up3goqguve other. 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 twice the mass and twice tdd9 fw1ikrg 9(he diameter of the other. The ratio of the larger moment of inertia to that of the smaller mdf 91dk 9(wrigoment of inertia is

  A uniform solid sphere has mass M and radius R. If theqf-6og2deun( /c r6i bse are increased to 2M and 3R, what happens to the sphere's momenq eo2d6(gur/-c n i6fbt of inertia about a central axis?

  If a constant net torque is applied to an object, that object iv6v kjw. 3gz:will

  The moment of inertia of a solid cylinder about i,c ,hi ev i ; pdmuen:nk-*dims-c3c:5ts axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy th 3s*e kmpcei;-nccdu,:,vi - di5mn :o its translational kinetic energy is

  Consider a motorcycle os(g; wnwo p)u,f mass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic enewsw nu,()pg;orgy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radi be-i;,h- czhzf-5kr vus R rolls without slipping down an inclined plane starting from rest. The linear velocity of the spher-eh5;-hkf c z -rbivz,e at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down 1ax(tb1 ip93fghl9oy an inclined plane starting fromfhot x l b9p9(g1y3ia1 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 rjdg hxe vwc8s7p:a /n:( sa k5(6wy,3rw.gv dwhen a net external force actaw,nd7 (gay5vj(rvp3 kh e w.:8xg6srwdc s/:s on the system." This statement is

  In what circumstances can the angular velocity of system t8 rbox+ y.w fjfm3sj0+6 5fjdof particles change without any change in the syste 8b m3tfs5 fwjojx6++yf. djr0m's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any9gk 13p.7y*1how4ll-0t kfpp vco eee friction which may be present. What happens over time to the Earth's angular momentum about tge tp-h ef9owvl7 k11lep40 k*cp3yo.he Sun?

  The Earth moves about the Sun in an c0yp.q.u .s zhelliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth q pc.husy.0z.about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulx x;s2-u :a/9ivh j n0svne5flling in his outstretched arms close to his bodyu 9f2hv lnxie5n0;va:/js-xs. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fva4m /pba-qr,ast spin) by pulling in his outstretched arms close to his b ara-p/ 4vm,qbody. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outkv, 0x0+ 5alm6dx :6xhexbge h5l*lbjstretched arms close to his body. What happens to his moment of inejxkmxl*x ,abx b e56dlvlhh0:5+e60grtia about the axis of rotation?

State the law of conservation of kd6e lph;7h jp tfvc7yh-x/x9 44vx.eangular momentum.

  What arc length does the Earth travel in a th f3qo90p3j q0wjv7l heree month period in its nearly circular orbit about the Sun with a radijhf09303qwlq pov7 ej us of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance d,w /hp jqt-2usgxztou .q- (5yoes the tip of the second hand sweep through in 3 mg/qqoh- p5uu. - t2xzj,tw(y sinutes and 45 seconds?

  How many rad/s is 25 revolutions tz1em6qo8ve7 - i adg8per minute equivalent to?

  A bicycle wheel rotates uniformly thr3lh/.wa tp x8eough 2.0 revolutions in 4.0 s. What is the frequency of t 3 .p8aexlh/twhe wheel's rotation?

  A pulsar (a rotating ne ( rctaa)czve.ehyn.k5r 7s592pdu4q utron star) emits pulses at a frequency of 0.40 kHz. The period of its rotakh)5.2 p75r(ae z9n yvuscr.ac4 eqdt tion is

  A phonograph record r6hw6z*bjqh ; aotates at 45 rpm. Through what angle does it turn in 0.20 66wj *hb ;hzaqs?

  A wheel of diameter 26 cm turns at 1500 wl9.n s4mu(.fj4 lktqkhltj o-:) x7zrpm. How far will a point on the outer rim move 4 l9z(juf to qxhl.nl:)k4.kj-mts 7win 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ir unw05xi; 5phs the average angular speed of the ;0piuh r55 xnwwheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4( bcp(u1ghis1fpv v08z *n;ji .0 s. What is the n jgpbuv hipc1;180((*vfsiz linear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers 7wed wg3 /6lfla distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming n/e f wg637wldlo 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 wit1/xszs- itw 7 k7um(gih a constant angular speed of 2.0 rad/s. What is the linear speed of a point on 1xu7gtm/ 7 s(i- izskwthe wheel's rim?

  The cutting cord on a gas-powered weed cutterby:,rba+eq6 i is 0.16 m in length. If the motor rotates br 6,iybq+:ea at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular 8).lv )humu 3 9fadv:oljtl3+,zgd kxy1k+bkspeed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's rdoy9b1h l8x)) gz kf d:tal.+u33lvkj+uvk,m im?

  What is the centripetal acceleration of a point on the perimeter of a bicycletvilzyc+4zco0w 2 i63 wheel of diameter 70.0 cm when the bike is moving 8. z4ctwl32vzioicy+60 00 m/s?

  How many revolutions per minza/rx n3v1tdol;2 *t;tx j8n 2qy9q ewute (rpm) must a circular, rotating space station (r = 1ye2r /nqzt9 2ql dj8xvxo3aw; *n1t;t 000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating akad:p8tn p,82f . arnp flat circular curve of radius 50 m with a speed of 20 m/s. The maximum tkapa: n. np8p8dr f,2centripetal 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 o3/ sxydsrkab n5+4 prm8t,o 986rhd dsf radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided t hs/,9m ord58a4sn rs+yb 83rxdpkd6 by static 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 ;hm7yphj7.*snqb (kwz *t7a g x0wm.dstring, is whirled around in a smooth level table. If the maximum tension th7j0 mp (wmtahs7*d.b;hk y qn.*zwx7gat the string can withstand is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kq5 kz4lat,wgym.g )7bg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3qzbgtkl7y5wmg4, ). a 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 constant angular acceleration of7h4w.wb ms ri(rxrv0 2 $4.5 rad/s^2$. 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 acceleration odcxbu/e4 y84. q:afdu f $4.5 rad/s^2$. 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 autom/k o*:f px.fomobile tire rotate after starting from rest and accele fmo.o*/xpkf: rating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration /b 81lj)x fcs-dqk)pc 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 constant angulaodiox0+2;-v a7 ygdm ga28dyur accelerat02xgydm2aigd;8 +vo ou ya7 d-ion 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 ,:c(,x4y-zgfawot4mh;b5 g xjm:jq s while turning through 2.0 revolutions. What is the average angular acceleration of ,4o4c (a:zxqmyfbwg;-msjjhgt5x:,the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s e m (r7/mmkiy*to rest over a distance of 115 m. What i*ke (mri /mm7ys the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovi: o1r.a /arirer a distance of 115 m. What iri r:/aao i1r.s the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to r+fy;6mu b pn/7xt,m xum,yu* oest over a distance of 115 m. How long does it take for the wheel to come 6ty ;, my/mu,ufuxb mopx+n7* to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev ehn 0a0cke-s6/min. When switched off, it rotates 50.0 times at a constant angunk-e6 ah0sec0 lar acceleration 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 whj fe.lki c:y*)eel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is:c*e i.jk f)yl the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque om syu,5xrul hduds/in nu6:3hq3d:9 8f 90 Nm. If a 30 cm long wreunh3dsyul6ur s u 5nmi ,hx:/d893 :qdnch is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment nc5ju5 scvx//jc ;m1t of inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: ma:4 dknw2,lbm/rlg9q, mx zi/y ss m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is td92riqw,g/:bk mx4lnz,l m/ yhe moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought h86cshm br6jxvy ;)k 0ea,1as the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 ;sm0y,a) h68 xjs1r6ckba ev hN 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 about a frictionless axis thoughtty/ieti0.kedgxyce3 * 7q( .e the center Ok/ .tdete*i70 cqgxy ei.ey3( . 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 radius 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 is initially heldd) *e*,geq(yvv70h tr yu1upw in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The moment of inertia of a* ey(*pduvqyw,)v7ue tg 0 1hr rod about one end is ML2/3.)

  Consider a bicycle whee6jkfj)(stc t1lvj 76ol to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the a7oj6t)s f c(ktv1 j6ljxle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped a ,e2getqbqbyru,;y f-sgrp/0k/ xv8,wml:. bround a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerat/ 28u wtb ggx, srf/kr:m-qqv,l,ybb;y. ee0pion of the pulley?

  A 1.53-kg mass hangs onj8hzjjtmdl+0:t u8m , a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acch 8+ jmj08jzd,utlmt:eleration of the mass?

  A rotating flywheel can be used to store energy. If ioc53bb.crn 88tkj,x ut is required 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 inert-sl)dtc g-x g22- gogvia 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 andvj . vz 25bpa,ds*s1c+ i5secf radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed , 55pcs. c+vz1 vaebissj*d2 fof the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10om*k 8r0/lt j 39-spev58sljk dg(lp e m/s. How high up an inclined 8k*oke/8lg -3dtp (srl levjp09s5 mjplane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and alapp.:v1 h uoj)k65n iwlowed to roll down an inclined plane. How fast is it moving after dropping a vop5:h) u1 ai.nkpvw6jertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slip w **qt+ gxtg1stxnq4*ping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia qtg x1tt gq*+w*ns4x*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 momentuad a0n8:(z pnhu3f3qcy* ljv/m 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 i:rdq b5/-chwjnertia of $5.0 \; kgm^{2}$ 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 moment hqo c g)k)f iur9 ,rp7uybm5d**qnn ;nea r121of inertia ong idq,cn u) 9b)m1 r*nky2* rfeo7rhp ;1a5quf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?