Angular displacement is usually express)jj1 ,ici 19uu6p(h( esvb zbd in units of

  Angular velocity is exprem /tjlr6t6hzo-i b,fn ()(sqnssed in units of

  Angular acceleration is e yx*y.2)pcq/gylbovr+5n+ jks4 li( oxpressed in units of

  A boy and a girl are riding on a merry-go-round wh nit pb33eknb5nlj( b*f(r8+qich is turning at a constant rate. The boy is near the outel5 8bnt qfn3k( * 3(brbj+ipner 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 yg ll 6lv;xj 1m-w/jpy7o)lk+9b /xtbwhich 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 angularkv-lxj/yt;+9)om 6bb wyplg/j l l1x7 speed?

  A boy and a girl are rid34oendhn y 3ghn9g9bo t(42wo0 7ffqaing on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl ish 3o3f79 f y(qgwo4bt9n04 ngna hod2e 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 con +cu,m*;dkry1f4 z g5su4jmmustant rate. The boy is near the outer ed4fds45uu, zcj;m kry m1*g+muge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merr jm8x53; el ovueqbncz45rx+4;k1umdvv0f0yy-go-round which is turning at a constant rate. The boy is near the outer edge, while the ej5fv 01zuu;3448oxnbxvel qmcr5v md;0 +kygirl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the 4c4el64 hqrgmfollowing is an accurate statg 4lc4hme q6r4ement?

  Rolling without slipping depends ql.9litd/d hym96x/m on

  Two equal forces are applied to a door. The first frbho9lsdh/bjp+.;t z,xhk19orce is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied per,hr lh1zb9 h/djs.potk b;9+xpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a dooraz2 lrfjzv; .h+;s*rj at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane z sjr;h2;*f r+ljvza.of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to5xxx94ukmv8jm 9enz9 the door. The first force is twice as large as theumm k9zx5j849 nxvx9e 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 resistanbe /3 k2c1yrfuce to changes in rotation/2 3 krubyec1f?

  Consider two uniform solid sphet n9avr9tqv qkj-,n1c.;q) wd res where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of dr .9q;nq ,va-1k q)c ntjwv9tinertia to that of the smaller moment of inertia is

  Two uniform solid spheres ha81t pw yi) k,pev64b;l)soskr ve the same mass, but one has twice the radius of the other. The ratio of the b kpo tkire,48l s;y)6)wsvp1larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and t6 fm73gda cm(:g4vkft wice the diameter of 7ggt3:mvmc(f dakf 6 4the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius Rk nfqqz b;vei;5og8(+ . If these are increased to 2M and 3R, what happens to the s5k (;vfe;gqq+z 8i bonphere's moment of inertia about a central axis?

  If a constant net torque is applied*4:(a ,g9qdo*o*k icssv pejd to an object, that object will

  The moment of inertia of a solid cylinder about its axis is give 5/yccvbnj;-j,iqx 7yn by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its trai,cyy /j ;7c-5vjxn bqnslational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a masss. x)9rm dq0bx;:o uhc of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of xx9r0h;osm.cuqb:d) 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 radius R rolls wi,geh): eoanmd *io j6+ph2oii1grw+ 6thout slipping down an inclined plane starting froo,iewpn eoimhg+2i)hr166d+ o* g ja: m rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without sx vch4z.i4 e(q-tzgy:lipping down an inclined plane starting from rest. The ang :gy4cz. hix(z4 evq-tular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when8hdvxo.c1zw w5t4n1 x a net external force acts on the system." Th to1zxwhwvnc5dx.148is statement is

  In what circumstances can the angular velocity of zfv/ wxc e1(1ysystem of particles change without any change in the system's angular momentu zcwfv(e/ 11yxm?

  The Earth orbits the Sun in an elliptical orbit. Ignore any x x+ (-r xky*mr;svph4friction which may be present. What happens over time to the Earth's angular momym xk;s- rp +rxh4*(xventum about the Sun?

  The Earth moves about ta x58ac )z4vb,23unco xvndi h3/3naihe Sun in an elliptical orbit. As the Earth moves close to the S3ixa)o a8vcun34hb n5i,3n v2 zd/caxun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrsad rn*qd ;s/8lea6hw:2k- djetched arms close to his body. What happens to his angular momentum about the axis of rota srnq - h/a;wk:sd2e*al6jdd8tion?

  An ice skater performs a pirouette0rkp1dp 4t m ,j)urf7p (a fast spin) by pulling in his outstretched arms close to his body. Wha ut 1rm47p r0j)pfdkp,t happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin)/m6tys wp261dzod w* v by pulling in his outstretched arms close to his body. Wm6yvsw p*o2dtw1 /6 zdhat happens to his moment of inertia about the axis of rotation?

State the law of conservatk r4swp1nbu4-zka- s9d5 -etxion of angular momentum.

  What arc length does the Earth travel in ax 4*km1,k ,jte/wri2 bzyr0yd three month period in its nearly circular orbit ab,y d *,/ekr4ybz0txmk 21j iwrout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the tug: v (wwm**lha+z pb2ip of the second hand sweep through in 3 minutes and 45 (:b*+zhpl gwuaw*v2m seconds?

  How many rad/s is 25 revolutions per minute equi:lq78qk,syq(xg biq p 3f:3ngvalent to?

  A bicycle wheel rotates uniformly through yq sea+5b.jlk(rqk2 /2.0 revolutions in 4.0 s. What is the frequency of t 2 . lq(b5+/ykkserqajhe wheel's rotation?

  A pulsar (a rotating neutron stan (pm /kt mmu*rvbif. 8p:0s.;lg i/lrr) emits pulses at a frequency of 0.40 kHz. The period of iv .k si8m:pulinm/;/ t m*. p0glr(rbfts rotation is

  A phonograph record rotates at 45 rpm. Through what angle does/4p5 1ahr ch 1hmr.kyl it turn in 0.20 s?1 cmr k/4hh5pr.a 1lyh

  A wheel of diameter j r43n3jfaa)z26 cm turns at 1500 rpm. How far will a point on the outer rim move inznaj 3f) ajr43 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 resa4fp(h/ 7d h6mxkw3ivolutions in 4.0 s. What is the average angular shdmw pshx367/( i4k fapeed of the wheel?

  A bicycle wheel rotates unifwbzql(6ud / y8gm ;5ddormly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from t/; lzddy5dwg(b8 qum6 he center of the wheel?

  A cable car at a ski resort carries skiers a distance of ih, :pk0noo ,(orkvdj1 0x(wv6.8 km. The cable which moves the car is driven by a pulley with diamet0jpo1w0dvh(,:(k ikn xvor,o er 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 constant angulapcdsapjdm2r o;w +8*.r speed of 2.0 rad/s. mjs*r w od +c;8pad.p2What 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 in length. If ther-wuuwmkpwwv2l5iv7 g66 -x8 motor rotates at the rate of 20 rev/s, what is the approximate linear vmrk5-iwx vu6u- 627 wpw w8glspeed of the end of the cord?

  A wheel of radius 1.0 m 1n iwgb8;iko 1is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's og 1iwk8n b;i1rim?

  What is the centripetal acceleration of a pez so(:b xgi)bo- /ih7r 2o8itoint on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moo(thibs8i/ er : i)o7ob2x-g zving 8.00 m/s?

  How many revolutions per minute (rpm) must z7dj z73a vub1*vh x2c ,*updca circular, rotating space station (r = 1000 m1d*d2*vchzubpac3,u 7 vx 7jz) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m crinh7e-b m9rpw1f +:2k vlp .with a speed of 20 m/s. The maximum centripetal force (provide hv mw2be .1:7l- r9+krinppfcd 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 oy dqh-+lfo4-1yqs s ;rf 20 m/s. The maximum centripetal force (provided by static frictisq+ - srd-yo;fq4l 1yhon) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attaa34(c4z+1 lvyh5f gtu wn3u acched to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can w3fz 4 4g3tvw uyau+h5a ln1cc(ithstand 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 kg and radius 9.0 p./uzcqykyu1, ; t3hucm rolls without slipping 10 m down a lane atu/ tk h 1yy,uuc;.qzp3 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 constant anga( p .7jxws9at ophbszh.zv-qc/*j 7; ular 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 accelaggrwd(x3r dj ztv7 yg3 6vvbf019j8 1eration 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 tir od5ej/ ms+ dxh1ao8 lkkd)pw*j;p/ b(e rotate after starting from rest and a1 jpkjpbdsk 5h8ma*wlood +d//)x( ;eccelerating 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 anguv6 ooil6s69veqk)0bb ojm3l 1lar acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s dece5td9gl/ x tlu,lerates with a constant angular acceleration of xg9tu ,dtl5l/$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an antq19bki5h- xqgular speed of 6.0 rad/s while turning through 2.0 revolutio tqkxqi1-5h9b ns. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 4sakh j/135li0msxod 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rota h/smk ax0jo4sl 53d1ites in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/ yrm21zwi a ibk-;/f4ks to rest over a distance of 115 m. What is tm ziwrkbyi4;f-k1a2/ he angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly fr: rv;hwo u9o6gom 8.40 m/s to rest over a distance of 115 m. How louog ov9h: w;r6ng does it take for the wheel to come to the stop?

  A centrifuge in a medical laoy- z 1kuqzwmd r0-c,yd e7g:nqo; ,:gboratory rotates at a rotational speed of 3600 rev/min. When switched off, it c - n y:u7ogqgmkq,wze1d,:0 -yo;rzdrotates 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 requirs0 r h;/jpau5fl. lbb7(x)j a8vcjl:fe tightening to a torque of 90 Nm. If a 30 cm long wrench is used, whata rvj l h)c( uf;xj708bbpsja:/5f.ll is 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 of 90 ,r4hpg cva2m .Nm. If a 30 cm long wrench is used, what is the magnitude of the force required w,2gc prmh av4.hen the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i3h db0e/f5 i.uz )obfbeki(q2nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows:l-, nodvg.u j8 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 jo-8un, d.lvgabout the origin?

  A solid cylinder of mass 10 kg is pivotn*a:agf6 :31 mfihuzwb l/1h hed about 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 ral/1n1fh*m3af::a i h6zhgubw dius 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 thought th14vpdh5 0y8smipu4 i te center O. A ropus iv4d m80ip5t41pyhe 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 inititfdgx3:r/4hgmww5f cq. h: t(kw u e0(n2rlr( ally held in the horizontal position, and then w/d(: 2w(rwh.4xeu:3mf k r lc(hg0ft rn5gqtreleased as the free end is allowed to fall. What is the angular acceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. Neglect u7jqrl4 4kkp4the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cm for 4.1 jklr 44p 4qu7ks, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs c b9bly c8uga r;q qzw5(q6/0non a rope wrapped around a frictionless disk pulley of mass 70 bn; cc5 qyuqw(6bag8l zq9/r.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fricteo +dmj*+ f8gnw3m ewxwft,x a6815opionless disk pulley of mass 7.07 kg+wxmw o6,ft5wg*8 dn81aje+pf3 xemo and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be us:,bgh,vsr*xs+vsr nf)7c2j; )i/oecc pr v 6 bed to store energy. If it 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 inertia r:dht (: tmorhc9 *:fbof $5.00 \; kgm^{2}$ 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 radi ,yh7ch7a) :btq6jt3ibsuf frwc031t us 0.010 m starts from rest and rolls without slipping a) ytuwqcfc bb:16,i7tft0 j337hsrhdown a 1.0-m high inclined plane. What is the speed of 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 xdo k9y el 8bi0z:x3ps3c17cs10 m/s. How high up an inclined plane can it climb before com pyz 3ko 9il38 csbe:7cd1sx0xing to rest?

  A hoop of radius 0.50 m and a mass of4 gmk +/ tigew9frnrh71ao* 2o 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it o iwa*ef1og+2rm/t 49h7nrgkmoving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping drmhioiid7 (bqpi 2 rv1h ,,-9oc6dwt+own a 35e inclino- om9h ( it+iicd, qrri2h7,p6dw1vbe 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 momentum chas)h vu6 qb)/6vtgh 4mu1,sbq a):x agqnges 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 ofhq4 qtdu5u8h ( 5ib-yxk8r-cn1p0va d $5.0 \; kgm^{2}$ 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 rab yp dvv74bx./d/s with arms extended has a moment of inertia o/pbx vdb.yv47 f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?