Angular displacement is usually expresia +io/7it1 pp3wq4 ocs in units of

  Angular velocity is expressed i1, umdx5hj7zahs8 t43rdnt m/ n units of

  Angular acceleration is expr k olp gi)u4v*6-a jm5p:epq6xessed in units of

  A boy and a girl are riding on a merryil9tvuya(o340*c xa14q ty zd -go-round which is turning at a constant rate. The boy is near the outer edge, and tut0 9 t 3l*yda4x1(vczayqoi4 he girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a 4( jwy2n sz(ahmerry-go-round which is turning at a constant rate. The boy is near the jz(2 swhy(a4n 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 turning at a constan4tkzill6*idda 0 f *s;t rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater line fdi*it;0 d l*klsz4a6ar speed?

  A boy and a girl are riding a merry-go-round which is turning at a conskr20gz2 d/9ebr b5szqtant rate. The b rrb g2zz5kbedq902 /soy 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 u+ 5xfrm7l6 rja constant rate. The boy is near the outer edge, while thelj ux56+ fm7rr girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accy pvtjq+yo27k 1z bd;.urate statement?71k;p2yd.z+qo tj vby

  Rolling without slipping de5 1yaw3c.oalt5k5veym1q rb 9pends on

  Two equal forces are applied to a door. The first force is applied at the mt,todqaja+ )e 4:zn 5zjl02obidpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicujead5qt jlo: t)2 0ab,+4znozlar to the door. Which force exerts the greater torque?

  Two equal forces are applpucn7cvi*/cz y+0:pi ied to a door at the doorknob. The first force is applied perpendicular to the door; the second forceizc pp vi 7u/n*0ccy:+ is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendiccm0tb9sod4 ml dn 71*hn,n /moular to the door. The first force is twice as large as the second force. The ratio of the torque o7m4 nlc9,/o tdm* on0 hm1dnsbf the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in-g(/k:fma3sob sa2 lv rotativ k :g/fso(3a- ml2sabon?

  Consider two uniform solid spheres wm9 u8mnanp p;d: 8 g9gpt:l5rvhere 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 smaller v mdp:g:5 8pn8 mp9u galr9tn;moment of inertia is

  Two uniform solid spheres have the p-w xhdm384mzc2/jjh same mass, but one has twice the radius of the other. The ratio d-c82wp mj/3 xzhhm4j of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one kkg 9k+l 2ion)has twice the mass and twice the diameter of the other. The ratio of the larger moment of9 g k2+ni)olkk inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these ayf )xa )t4a2.v) fg azl7(bpktre increased to 2M and)kp.lfz4 a ag byv)t2a(f7x )t 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that obpxgz8s. xb-1e +*tx+ yi :oypqject will

  The moment of inertia of a soj0cldr e 9gl7zg+:w 1alid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translw9a:0glczj l erdg +71ational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass ofaw1r adp;tov+so : 0pthu c+z/4u+sv2 10 kg and a radius of 30 cm. o: t++;t+va0wph 1/dpsov 2rza ucus4What is the ratio of the rotational kinetic energy 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 radius R rolls without slipping down an qpx/bc4k 1 y,fy,p3kn inclined plane startingpnkyx4fp,qc / 31bk,y from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radi4- k ptjj6x-ys0hgw.dus R rolls without slipping down an inclined plane starting from 6wk 0d4-g p.jtxy-j shrest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net externalmo44j,s: 0k ano cj9n26k9lza e q*u z,k7igdl force acts on the sy:en20c4a d m 4zzg6qsokl nklui*,j9ojk 79, astem." This statement is

  In what circumstances can the angular velocity of system of p/c88odt 6 /uixd pr,vy1tcl8tarticles change without any change in the system's anr8l i6vt,ttcoy 1dxu8d/ /8 pcgular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which l8lb);9wbu s 3pmhnr-may be present. What happens over time to the Earth'sb8 nl bmsp9rl; -)w3uh angular momentum about the Sun?

  The Earth moves about the Sun in an ellipticbn:s3 rtiz1w8 i4h 9jsxk8rk9-g s0yw-+rahi al orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun0s8y n9 r+iwhzah- jg rkss-w: 4btxi39i18 kr?

  An ice skater performs a pirouette (a fast spin) by pulling in hi 2i oj0ifb7 d3f4im7i+ne7p4 ra;txuis outstretched arms close to his body. What happens to his antfb+m i7r270o3j; x47p4e dniifauii gular momentum about the axis of rotation?

  An ice skater performs a pia ,ecjl o5 f+w2tzc90qrouette (a fast spin) by pulling in his outstretched arms close to his body. What happens ae9 lc25c qwjftoz+ 0,to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (b p;zc 3bimab:1w*p8ea fast spin) by pulling in his outstretched arms close to his body. What h z mi8pe bw:1c;*3abpbappens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momenv+ )e;grl:dt ztum.

  What arc length does the Earth travel in a three month period op8m8 ydna1,s2knyfe-y h9 m,in its nearly circular orbit aboumdy, yf8 9poy n,me8sh-ka2 1nt the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length kc)akr5)udype: uej4u-lwk1xxi 6n0 i9n y5: of 0.30 m. What distance does the tip of the second hand sxy:160ce upx) knue) aui:ky r45nj-klw9i d5weep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent to?u 7eo9v+pjn,pa2rdm0

  A bicycle wheel rotates uniformly through 2.0 revolutil z.dhrp 0h+0ions in 4.0 s. What is the frequency of tz0hh0.+p rdil he wheel's rotation?

  A pulsar (a rotating neutron star) emits pulseslgi;gwz (8u) z at a frequency of 0.40 kHz. The period of;8 igu(zwzl) g its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it tu54,ybcge9h izz 4,ku)l.ups n(9z2tfhj bns2 rn in 0.20 5 zu i,2gh)f kzzuen9s4b(.942, jbptnlhcsys?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will ak+5hpdr*0 dv fem-8rqz zp/n. point on the outer ri. m erp+rfvdzn/0p85 *kd-hqzm move in 2.1 s?

  A bicycle wheel rotates uniformly thrtb6um 3hq h1(cough 2.0 revolutions in 4.0 s. What is the average bc hq6(1ut3hm angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whh sa18aorrxkrvu* ve9) v/m,3 at is the linear speed of a point 0.10 m from the center of the wheehxs)/vr1v rv*m, re9o3a ak8ul?

  A cable car at a ski resort carries skiers avhqbc7ggpz2 cwih.; xh /p-9/ distance 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 must the pulley rotate for the cable car to make 9h7c cgx pw;.hvizg- /h/bp2qthe trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of ,ir,r2 e .qmtpigki202.0 rad/s. What is the linear speed ofkri.i i,r 2qtmg2 0,pe a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m b z5igqxsb; p 7;uc/t(in length. If the motor rotates a5 bs;7q;ut/b (zig cpxt 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 b5aj- .x, nkdsa constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the whee,sabd - .5xjknl's rim?

  What is the centripetal acceleration of a poitc mx05 dvxfszm89;v3 nt on the perimeter of a bicycle wh t 5 cdf;x0mv8smz93vxeel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (dpp hffw5fr,6 xc h6t +,x9c ud;m0k1+mwc1ftrpm) must a circular, rotating space station (r = 1000 m) rotate to produce p6wruchfp10cdtk,xt6;d5fm +x,w+9 hf1 f cman artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular ceo 5ezn :*grtqa2u ti 9k4(tg(urve of radius 50 m with a speed of 20 m/s9qaue4g 5te knogt( : t2(irz*. The maximum centripetal 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 cuj)a1z;orw 8 tv 4tv5ns7i tbdi j.,wsq1t9 f)qrve of radius 50 m with a speed of 20 m/s. The maximuz.j irn)7t)fv tdws v1 ;,bits9 aqtqo5 j4w18m centripetal force (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 whirlrgmym 6f+ tc*)ed around in a smooth level table. If the maximum tension that the strinr6*)mtgmy c +fg 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 kg and radius 9.0 cm rolls without slipping 1oa3xkfq/-i9p 0 m down a lane afk pxq9 3o/i-at 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 angular accel m ziqf0+)s00jqafdn xkc2: zq xd /vs/,9yn)heration 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 codc gdlfb 0:m83nstant angular acceleration 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 afteg 6 jp:j o8 +pdfuyua/1*zxxe)r starting from rest and accelerating at a con8)/x*f xp:e6jdaug+y oz1upj stant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular awq2x*03c xebyiz9se.u8y; kxcceleration 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 anguos -3q7vrh1ta 9rj(sllar acceleration ol h v s73stojar(qr-91f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 ra8jjdm-g5s s(*v d3mfmd/s while turning through 2.0 revolutions. What is-sm 5vj 3m*8d(jdgf ms the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly fre nl4qo5rbi*-23 fha/t q.beu om 8.40 m/s to rest over a distance of 115 m. .32 nr*lie f4t b/qhu-aqbe5o What is 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(q,hl 9hikm arh.om,gujh)nc6/.v 7 m to rest over a distance of 115 m. What is the urh9,.m n)./l a, c(hi hkvjqmo ghm67angular acceleration?

  A wheel of diameter of 68.0 cm m(ob,3,a cfqs j)x ,syslows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long do,,c(fmos ,by3 as)jqxes it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotab;tt (2 y1mtewl/ jyt ub3*qw uw)a1,otes at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 t2b)eu w myly (1w13;w,uqbtt/*oa ttjimes 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 w;1t cxo2v.nv db:q i)rwu/m- jheel require tightening to a torque of 90 Nm. If a 30 cm long wrench is un/jo;bxvr. v2)wmt- d:1qc iu sed, what 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 0m5 bj8bb 7+vmx:y 7jf(viz egtorque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when thzvm ( +j vbfmbg 7b:yixj0785ee force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia hx+wv 1m:z:trx 7 3hzst-d j2v$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic moleculeedl;w4- yq xe1 is modeled as follows: mass m is at the origin, mass 2m is at x = a, anl- yexw4q;1e dd, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is piv3ajpsbm cn -u4y,t:vlho8bt: 4; j1sqoted about a frictionless axis thought the center O. A rope wrappetlcnt h;4o 3vby:bmquja:4s8j 1sp, -d 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 axissqa7 gued vl )*bbz brt) j-q(*/x4s:g 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 oz-v4 d jtussgb* gr:qq7ax)be(/lb )*f 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 7 +a/kjl+ fnkhrod is initially held in the horizontal position, an+ kfj7k/h +nald 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 rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 chc fs.63ftlrl q*bdfz16 , vp)m 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 4.1 s, what linear speed does the wheel achieve, assuming it rovb3sphcz, 6)dr .f f1ql*l6f tlls without slipping?

  A 1.53-kg mass hangs on qkee: 3ygxtatpg 1frt/ 5i3(/e pq*4l a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelq*g/ qft3p1(/et yi4p r35: exekgatleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mas +lk9qq3hy5pb s 7qqybh+k53p 9 l.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to st 4qvwz*9ch :gxore $1.00 \times 10^{6} \; J$ 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 inerltq34, ) htdbl2mw,kyc):yrktia 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 masjm 0fk z+ny2:rd2mebn50yh z5 s 1.0 kg 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 s+2n0z yek5mr j5ynz d0:m 2fbhphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls wi7xdi 6 vkyzn,xt-+9ka th a speed of 10 m/s. How high up an inclined plane can it climb bef a9i-+,n6yk kz7txvd xore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from re.smfn / fl4v/0irt deu6v+x c(st and allowed to roll down an inclined plane. trcdl xnf.(e vui f+m/ /60sv4 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 slji;zs -(c1.xd d3ikirco;fr ,ipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inerijx, -dr. rfsz3 odik;(;1i cctia 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 chkt1y p mvk 3uljn7u8,8anges 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,6pwgbkcaen d1 /st( * 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 of inerf+t 3ep0v-rofw0a .w jtia ewo-at fp0 vrf0j.+3wof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?