Angular displacement is g/ kthweal,)t(y8 r rkzn/40nusually express in units of

  Angular velocity is exprsll(en az 3*iwi+2x f( fw4 j(cor-*yzessed in units of

  Angular acceleration is expressed in units of ez8ptyu5am8 )

  A boy and a girl are riding on a merry-go-round which is tiqbvxrhu1 /-9 urning at a constant rate. The boy is near the x1buvr9q h- /iouter edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is tu1hmk .tgke el*yo70 k8rning at a constant rate. The boy is near the outer edge, and the gi0 el*k1.egktyk h8mo7rl 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 turning at a constant rnngs77wy-+. z d;ujqtw kq.0h ate. The boy is near the outer edge, and the girl is closer to the center. Who has tg h7y zn.-j.k+q qw0;w ndt7suhe greater linear speed?

  A boy and a girl are riding a merry-go-roehha63q w 5nm*und 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 centriw6a h eqnmh5*3petal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a coqt:v +g + 3dvpepwzbw;-1x7f- s+wfrxnstant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tav71+xvd-ps fg+tww :q-r;3+ewpxzbf ngential acceleration?

  Consider a rigid body that is rotating. Which of the following ie(hf a )j :9n-d0k,c+ wqiqjsts an accurate sta h+w(-sn0ic 9): q,djfet akjqtement?

  Rolling without slipping depends) 4napks3fb15cqlwjju0l 5t7 on

  Two equal forces are applied to a dooraf xk/,yv(q- s. 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. fay, /-kq(vsxWhich force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is app25* +s 8bxay4ktu7xnkrq5wcmtq 7at:lied perpendicular to the door;c+ut5q 7k5ra4m b t2kqs nx8:*yxt7 aw the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the d79z g;*n emb wxzx2du5oor. The first force is7mbdz e2;9zxu n5w*gx twice as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used lh 6gf7d;ce71g sexr) to measure an object's resistance to changes in rotatio gfhs)61 l7d7gcrx;ee n?

  Consider two uniform solid spheres wherevmoa xk8b: kz8,fo+c* both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that okk mafx+*8boz8:v co,f the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but onexr+ j.9f 91hz9d1eogp pm emsio2(vecxn59 8t has twice the radius of the other. The ratio of the larger p1 .1ejxe ef vg(98ind9oxshzp9+o mc r5t 29msphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid sg53 j o-ii(boypheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller 3jg i(i-y 5oobmoment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to1gktp5 rn9:yf 2M and 3R, whrn5fg1ky9pt : at happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is o9 /7 f+h5nxvd4y ayfsapplied to an object, that object will

  The moment of inertia of a solid cylinder abou t s-cygelk u5 3kuist0/:7k6bt its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translatys 3luk5 g k-t:s0et7b/ku6ciional kinetic energy is

  Consider a motorcycle of maspg/thd ,p8yj e-p30qe s:j3ijs 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 energy of the wheels to the total translational kinetic energy ofjy0p/3djt8 qgi:p ,hj3 eps-e the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere ot 1 o*ia80d+. aa (zfssfrklt8f mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear veloc aidaasz fsr*l8 k.t1 o(08f+tity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an peu *8skdr/.grl8kh 5inclined plane starting from/ .kpksdgruer h88l*5 rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentudv +rdulzc8o4 6a4, gpx)7l q7g:yrkcm of a system of particles changes when a net external )c4vgckqr:7 4 udpazdgyl687,lor +x force acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles cha;j 94* ocfeh pj1 hcj9cjo9-d-48ox-rl muwlt nge without any change in the ;j8h wpruc1e*l9h mdj-oljo9f4c4 j-c xt9-o system's angular momentum?

  The Earth orbits the Sun in an elliptzn u8eocbl5m 3-q1hw+ical orbit. Ignore any friction which may be present. What e5oz- ucl q+w3 mhnb81happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Su0 x5dmx mi )// 5/h:hns t2hngohj0tfcn in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about c/5d 025 xohxj/mf)hh s g/tthnin:0mthe Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his oud,i*4gim : v xms6rs(utstretched arms close to hisg d6iv :rx,i(mms*4su body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling inx fn1ry-x.hl a 7:z6xl.i(zjh his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotr.z x.7f zj1ali: lyh6 -xxh(nation?

  An ice skater performs a piroun3cl ohhq( kkj)8; :s.1(sjygjx;gpd ette (a fast spin) by pulling in his outstretched arms close to his bodj;o syn kg8 )pjhl dj(sh3:x;g.(qc 1ky. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momenthi mqwre.l3cu0 6c1n0 um.

  What arc length does the Earth travel in a three monu yj5o- -dy ldwexzu. ;yw63e5th period in its nearly circular orbit about the Sun with ;jo5 wlzyyy eue3--.dxu5w6d a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a leng lm0gd284 nqmrth of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and lq02rgdn4m8 m 45 seconds?

  How many rad/s is 25 revolutions9f/ b5i*xv(4u7vt mbeg: wd yz per minute equivalent to?

  A bicycle wheel rotates uniformly thn n .,ct czgn,6(pja/-jbn1 9 gwbbz2yrough 2.0 revolutions in 4.0 s. What is the frequency of the wheel9/, cgtb nz bjcjzbnn,nya-2(6.w 1pg's rotation?

  A pulsar (a rotating neutro4.ot z(irl( zfn star) emits pulses at a frequency of 0.40 kHz. The period of itsro.(l 4z(ift z rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.2t/yq4 j6 t;pxl0 s ;py6/txl jt4q?

  A wheel of diameter 26 cm turns at 1500j .o( taxc )6i)unugir7fm z-2 rpm. How far will a point on the outer rim move ingo2-x6ui7z.cia( ))rn t fm uj 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is 05 jl b7xird5z2 xce)pf 4+cr.hqmihl57ck 1jthe average angular s .jzr1 cbk5 7c0idi+emr4jllxpc 5q7 h2x5f) hpeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions 9m 5qs/y8 hx/ya+d zgoin 4.0 s. What is the lio// gaqy s +xzd85m9hynear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distancsac0 h*t 1dm9fe of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast mcf 01*satd9hmust 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 constant angular spee4gix oomcjlaw.ze(g(5, p 3h5d of 2.0 rad/s. What iswejo(z,(.o 5x5ag3 4gpml ich the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-. pvsq:sts,y1 g+.h b mkxd3)xpowered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of ty 1sh)tqxmp3sdgvs :+ .k, .bxhe end of the cord?

  A wheel of radius 1.0 m is rotating with a constant ang95vhuj r: 6i 4m twiz.n+ 1 msut6lwp3bqzz9j+ular speed of 2.0 rad/s. What is the centrip+ .pzm n3lzi sjm +:bw6utqrhij419695vtz uwetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perq/r hb)a-t58il.m daj ylt1; rimeter of a bicycle wheel of diameter 70.0 cm when the ht r85 /qmaa.i1t;jly dl) -brbike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space statiok6c6 + ncl *.yqm6ikx1vrwp: xn (r = 1000 m) rotate to produce an artificial gravirw6k+ cl.m:*yn1cx6qp xvk6 ity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve ofs:em ,5c.ygvv+dv9o f radius 50 m with a speed of 20 m/s. The maximum centri:o9g e.vdfvvysm, c+ 5petal 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 radir0eb7i0 u eg0 gl78d 5-elfeefus 50 m with a speed of 20 m/s. The maximum centripetal ffdei0le77b 5e0r e8 0elfg-ugorce (provided 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 string, is whirled arounop3sihk.e 0lq-jsx+6(tw 3o u d in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what m - pes6to +s0h.lqwxukj( 3oi3aximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cmwkctp)l: 9dv+ rolls without slipping 10 m down a lane at 4.w k+lv:p9tcd)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 constant angular acceleratio7os ou *k zo. i2/2yd).qjtkhrn 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 acceleration okm1b: y eh3ivsog4-e,v wo * tc8qjv,(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 aut 4ha1o63u/ 0u zuct;m.ltwqya omobile tire rotate after starting from rest and accelerating at a constant angular acceleration uztm6ha u1ot la4y;3w/0qc. uof $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration fhxp z7 6tca37n:)qxt 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 constan1 jbu4o8; xq(qst xdx6t angular acceleration o16tsu dxbxqq8o(;4 xjf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/.(0+n8 tbjee tmfi r(ss while turning through 2.0 revolutions. What is the average angular accelefe0brt(( inme .s+t 8jration of the wheel?

  A wheel of diameter of 68.0i0v +d 6v2nnh5wyk2 oy cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is yn+ih6y5v nw v2d20okthe 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 m4w:zrqm:,*oau 6 k muj/s to rest over a distance of:wku* uom jazqm6,4:r 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows doozynlbg7v23 4 s7 9u:syhtcn*wn uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to g btlovs y*7h3nz 2c:ns974yuthe stop?

  A centrifuge in a medical laboratory rotates at a rotatios6 zx*ty;s:uiyn; r: e0kv- qrnal speed of 3600 rev/m tssyi6x * yqzur;vnk0: ;:re-in. When switched off, it rotates 50.0 times at a constant angular 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 wheel require tightening to a -b4( wu:oanul5w a yxf(.reb107u zfstorque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular bu 5ffwayo(ul.sab :0xr z-(1u w 74neto the wrench?

  The bolts on a car wheel require tightening to a tobdd tz-a,qsx7 3 e2i*zuc+sdjn 81e8krque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude ofxe 8dd-ij2s*7sd,kc e83+anuztzq1b the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertigw zfz30 w 9as9x-yy)xa $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled ayo3kp5 -bioe 9s follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about te9b35po oi-kyhe origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought theo7x9xepnf g4; g:jcr 7 center :r9 ;xg7 n4fxoc jg7peO. 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. (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 tt h(fc(orzsztusk( /j 1 +:;z,ykwod.hought 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 wr/1u;o,r tc.(y:fs o(dz(h+zwk ztsjkapped 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 initiallf -4. uuvopocnv e )-asa3u3nl8--cmry held 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 se3ufo -nu vru 3v-n).mca-lpoc8 -4a of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel t9f0w*fc dn;qho be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass o;f0n9hfq *w dcf the axle 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 around a frictionle+by34m cz tb0shp4*d vo;0av lss disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pul4340dh +cp;molv *bs bvzt0 yaley?

  A 1.53-kg mass hangs on a rope wra0 ys.kd48ozxs-fzq-*( q b oo*bp/owvpped around a frictionless disk pulley of mass 7.07 kg and -*0-soo4kbv*q/y.fop 8(d xb o q szwzradius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is reqw tc86 n.y.ieehd9yp6uired 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 inertia ofl( 9jhne1 ztc2lv 1k7q $5.00 \; kgm^{2}$ 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 radius 0.010 m starts from rest and r *1,2a)qxihj- lk achrolls without slipping down a 1.0-m high inclined plane. What is x a2kr ha1jqc)*-h i,lthe speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of masej5,oaug8;0mw: sf5frr1b b es 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane caj:1f omwe f;58rr,bs0 u ebg5an it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is rndyky55*d 5 a90 cmtnk2o en0rdhr+*peleased from rest and allowed to roll down an incl 0n5*mddayd 2r*h kkncor9 et+p50 n5yined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slicq 6 ln)sj)uw+ ;.uj.q9 wikrzpping down a 35e incline that is 7.0 m long. Assume it star6) jzuq;kwu isrw qj.n9)l.c+ted 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 momentum dmx;gpfb +pd.,g0b r8 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 r+wx. +,urm;q xh+ 5vju o2zw-icemy)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 58: 8dzvylx- qp.00 rad/s with arms extended has a moment of inertia ofzvd y p8l8:-qx
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?