Angular displacement is usually express ghix )y.+7vm-sclu u.in units of

  Angular velocity is eup+3pzap wgb-u((h q2 xpressed in units of

  Angular acceleration is e ct0ggl4itz) v0l/1qmxpressed in units of

  A boy and a girl are riding on a merry-go-tel8 3sw ;1o9terpc-hround which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who p;8wochr -e9tsl t3e1 has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round whmhqf09:4+ytsttse *hich is turning at a constant rat +mhtse 0*:94ytfqtshe. The boy is near 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 whiztjn72 (j, cush- pyv/uup 6l9ch 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 l j6upuj pychvt-u 9(/2, nl7szinear speed?

  A boy and a girl are *arhj ) w9z.9xguby-a .p6 ru.uf9gu ot cgi):riding a merry-go-round which is turning at a constant rate. The bo.hbaucu a:t.iwj9yzxor)6 9)9 grg *gf.p -uuy is near the outer 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 at a conswsm l jq ywfq6o:c.k;d0 k5c 1j3:,vostant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleratks mwk :3dwjy,of56q 1 v 0:.ol;cscqjion?

  Consider a rigid body that is rotating. Which of the followlh3vb,j;gl ( iing is an accurate statement? j,hi ;g(l3lbv

  Rolling without slipping depe j9fue j25/ ykbzsnj(8 +m-rpznds on

  Two equal forces are applied to a docf6 6wtc1m0 zhor. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces a61hc0tzfw 6cmre applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are apy -l24g -fqtlyplied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts th- lg ytlfqy4-2e greater torque?

  Two forces are applied to a4 og n-5eco 5hrvpkq:9 doorknob, perpendicular to the door. The first force is twice as 5hg- :5roeq 9cp4v onklarge as the 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 changes ingq ubt ,g)li07- p. cjnc3/pvm rotationgg0m/lp j,cn utp q-i .c)37bv?

  Consider two uniform solid spheres where both have the same diameter, but e5cxh vhui**r a,; vs8one has twice the mass of the other. The ratio of the larger moment of inertia to that of the small8 suhcx;,*evhiv *5ra er moment of inertia is

  Two uniform solid spheres have the same mass, but one has twic5m(4nqh0 kkg ae the radius of the other. The ratio of the larger sphere's moment of inertia to that 0gk k 45amn(qhof the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the di dq+(whrp /p c;+rsm2tameter of the other. The ratio of the larger momenthcr/mrt ;pqw(ps+2d + of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M anhl , i)o20tfl*z jjbq:d radius R. If these are increased to 2M and 3R, wha,fz: oji2hl*0q b) tjlt happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that objaaaos8 + s7nyr4h21j aect will

  The moment of inertinxrudq p1ncb;oy:j4,*f/c c/a of a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls wij q p *x4bc onc;cn/1,fyu:rd/thout slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle ofwr: 1 estcfvd)) ppu;, 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 energy of the wheels to the total translational kinetic energy of the bike?dwcpep fv)st:1 ; r),u Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without sojc qt4io f03lyjn98(tyrn aui6 ;k:;lipping down an inclined plane starting from rest. The lri(jo8j6 fa:4 c3i ot;y qyl9tk0 nu;ninear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radi3pin)f19 m,y)bjn- kabgf x z8us R rolls without slipping down an inclined plane starting frop)f-j x1ng 8ay)i z mbf39bnk,m rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles channo yvze8n6un l6nu t9k5i7fp5 g8dner3zl7; 1 ges when a net external force acts on the se zu1rt5py 5dln9 vun7ngno ;n8 f76k8lize63ystem." This statement is

  In what circumstances can the angular velocity-*bc5m+l0)ga jbpl he of system of particles change without any change in thep 0)c-aegbmj +l 5lhb* system's angular momentum?

  The Earth orbits the Sun in q+qld2clozlvu cj;n.70 6xj0zx 4f s 1an elliptical orbit. Ignore any friction which may be present. What happens over time to t; 0oxl f+jzc0s v1 zjcd.46qq ln7u2xlhe Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As t pphq .n)eqlk)m3.dv 5he Earth moves close to the Sun, then which ofkq. h3p)q me5)l.vd pn the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirou51py/if wk bq;ette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum ab q /;wkfpyb15iout the axis of rotation?

  An ice skater performs a pirouew62,se krc.z oxqd ..jtte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kineticj.kczd .se.6r w2o,q x energy about the axis of rotation?

  An ice skater performs a pirouette (q8mw vnv1*8wga fast spin) by pulling in his outstretched arms close to his body. What h q8w1v*v wgmn8appens to his moment of inertia about the axis of rotation?

State the law of conservation of tr4a2 p55fffx w tf*8uangular momentum.

  What arc length does the Earth travel in a three month period in its nearly,v hca6 ozmpvq 67-ol4 circular orbit about the Sun with a radius4pl ov676ao,-vcmqzh of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a len08/ s/9g3asc dzo-tuc jbmo 6ggth of 0.30 m. What distance does the tip of the second hand sweep through in 3 mimc jog -as3sz8oc/0g6tu d9/ bnutes and 45 seconds?

  How many rad/s is 25 revolutio(a l y esaic3.cpvp(lz39:n p6rlgq;5ns per minute equivalent to?

  A bicycle wheel rotates unhh5 9l g6e :ybklu8xe)iformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rlg5h6ukx 8:lybe9 )ehotation?

  A pulsar (a rotating neutron star) emits pulses d7 c)ft,yf iafz+ vm,-at a frequency of 0.40 kHz. The perioi +mf, c-dfvt,zf y)a7d of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it tul(hozgaf 7 43z:iv 8sbrn in 0.20 s?so: 8vibfah3z4 gl(7z

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poi ;4rcfi v5sj3xnt on the outer rim move in 2.1 s? 4f5cjx;sri3v

  A bicycle wheel rotates uniformly through 2.0 revolutio)zmpsn:fih)p7 1xhz 2p) 9yuv ns in 4.0 s. What is the average ang ) )pnhz1fs zphupy7vmi)92: xular speed of the wheel?

  A bicycle wheel rotates uniformly th,p2 gcdds.k .,d .fw999surjlm ep/cwrough 2.0 revolutions in 4.0 s. What is the lij, 9ws , k9eg c/2s.d9cp.ddfru.wmp lnear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of fc)r0/xrshp66.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Ac/s 0 rfp6h)xrssuming 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 constant angular speed ccurd),5 yu6v7pnoi0of 2.0 rad/s. u)pdc,rn6v yoic 570u What is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m :b+w uw;t ng*pmp,jqv)m ,am 7in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of th7+mpg )tn *uq,m :j;,vb pwwmae end of the cord?

  A wheel of radius 1.0 m is rotbigrpu p*2kxx3y a;: 7ating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point ux3arp2xgy; 7: pi*bkon the wheel's rim?

  What is the centripetal acceleration ofu +hzlpuu tn2 ,5on/p ahj+h(0 a point on the perimeter of a bicycle wheel of diameter 70.0 cm when a2n+5ut uplnh (hzj/+, ouh0pthe bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station qgk2l8 wfr qg8):ssp ls*+mbk.u4* wi(r = 1000 m) rotate to produce an artifici)gk+gqurif * qms 8b:l2pl8 sk*4sw.wal gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed g4o9vj+ q *zb kxr:wb(of 20 m/s. The maximum centripetal force (providejvkg(b ro9bqw:x z+*4d 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 of0 glnmu1 x,jk6rtnf mom 33y+kr43h9k 20 m/s. The maximum centripetal force (provided by static y91nkr4ummnxj3ht0 m6 3gk r3ok, l+ffriction) 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 str h8zqk (tucvg7z6 ; jzs/:b5zjing, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what k:7ubt vq jshz8 z5;cj(z/g6zmaximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and rav /7 *c izkc(e(bp.um+ssmar4 dius 9.0 cm rolls without slipping 10 m down a lane at 4.3 mkv(m.cemais zcb( ur/ps 47*+/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 acceleratiod x,9d))k oyip t;yh2hn 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 ka99 0auwh7+xnl/c- ouek na) 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 after starrwu6utjw) imrm4pku/n-,e *0 ting from rest and accelerating at a constant angular acceleration ouk0wwm)-,ej/r 4u t6rp*u nm if $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratcea29f.sa 5r* n y)n)bp5mmbzion 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 const jgk6nyaj 7 n(*c6hsx4ant angular acceleration j6knyc aj67 xhsn (g4*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 tu,trdv62 .m cm2wu9wnh rning through 2.0 revolutions. What is the av,dcrw 6t2.wvum 2 h9mnerage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformlya1yhdlczt j9v1 o7t: ,b4 l/qh)eu6yq from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming t 9q1tb o6z1q4juah/)7lc,dth :ve yy lo rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 / k :as1bejs3;ybf) qpm/s to rest over a distance of 115 m. What is the angular a:3k1 bs/ys) bfqe j;pacceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8vuc8*heh(c4g s-; wo j.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come tojecocs;(h - 8*vuwg4h the stop?

  A centrifuge in a medical laboray)55tdru-qbt7qeoo*9m pw/ ktory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular ac)-b7 ykq t 5 *wod/q9ormu5tepceleration 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 torque of 88cc v37a n-wj- ftqrxsb5y y090 Nm. If a 30 cm long wrench is used, what is the magnitude of the force y8j-50tqfc8cw3 nb v- rsxya7required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque ofur;/vj( 2uzja xfi zqx4*9bs -,rhu,y 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force applied -sh9qbrf;vz2u,i (jx,azy 4xj/* uru at $53^{\circ}$ to the wrench?

  A wheel with moment of in iw.ql/l0zh 5zertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule i u,3dj;,qdm;vfn(w kw s modeled as follows: mass m is at the origin, mass 2m is at x = a, and, masswdmq;n3u(j ,k, fv;dw 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted aboumds3999/ ku19ix nt pgdz2oert 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 radius R2 = 0.9rm 9dxi99du3sne21 /zto kpg50 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 +.c:+e,- srrnxw7d fymt ,gcoe 9fj5b 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around rg5c7oc+fn e:y d.- e 9t+sx,r ,bwfjmthe 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 init4qt+82hv( t rdhjsg.aially 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 of inertia of a ha2+4d ( .hgvjsq8ttr rod about one end is ML2/3.)

  Consider a bicycle wh)p rsx, t l7n/b-ngec)eel to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprockeel psb r7g)x/n),-nct t. 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 wra6gwd i02z r1 a+qol(nr9d8unopped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angud9w rnzn1q6o0g8i(2ul r d+o alar acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulleygv :n xg:9)-y2yzv kzu of mass 7.07 kg and radius 66.0 cm. What is the azg ygux) kvy::v- 92zncceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to :ma b,vb d2kbzulx89 3store $1.00 \times 10^{6} \; J$ 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 of8,uj2)xw7x ki,e 6 zlyw2d oos $5.00 \; kgm^{2}$ 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 kxs 9is7wx-; *c hmn)hdco0dj:g and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches m70 hcd:-9dci jxo)x s;sw*hnthe bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed ovq; 33j3enrqs( b s 0msza16wxf 10 m/s. How high up an inclined plane can it cv1 sa3 3rej( wsn6;0mz 3xbsqqlimb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released f+3/sp4mj* jlslez* og rom rest and allowed to roll * lsoj43g+zp/*ejsl m down an inclined 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 witho o.oq4.vd2hmzut slipping down a 35e incline that is 7.0 m long. Assume it stoo4h d.2zmqv.arted 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 milj: b; yjwx/8hosh c )(9qpz4omentum 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 mo;)p 3x+pxiu h;/dca oument of inertia 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 p2t4+eq fo1.ql / ajtga moment of inertia of.1qaqeo2tg/ l+ tp4 jf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?