Angular displacement is usually express in units o88 0pxvoedb9pj uvct -)ac4,cf

  Angular velocity is expressed +d 93nphaik),e1pw ju3cx, wbin units of

  Angular acceleration is expressed e30 kjnzlj: ,h nhu )zeg3)c*zin units of

  A boy and a girl are riding on a merry-go-rouxjsg5 :47jklx lt64w6dr+ ql-:m qkxb nd 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 aqjj b6-+: 75 xk64lldg xr4xw tslmq:kngular displacement?

  A boy and a girl are ridind8d6d snp )g+0ad 1gikg on 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 angular spe)6ia+dndspggkd1 d 0 8ed?

  A boy and a girl are riding on a merry-go-round which is turning at a c2ij 28uw5p wwo io 9;(ijlzw8mg 2de(xonstant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linea(o8 mw z5ow ;pw2j2dgi iji (xu8l2e9wr speed?

  A boy and a girl are riding a merry-go-round which is turning at a constak5 pd:ly/ qs1wnt rate. The boy is near the outer edge:p/ws1lyk5 dq, 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 p6u z2h(c:p z 3l*kbq/g8abztis turning at a constant rate. The boy is near the outer edg*3z p 8t2z kbpbg/luh6 a(cqz:e, while the 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 j)s(+ neell qj0*dy, jaccurate sls(,)0qeyj+nj e j*l dtatement?

  Rolling without slipping ubv2oshj zs ie i9.;*0depends on

  Two equal forces are applied to a door. The first force isa5v36i pomyea7uv .) ;5fa gbi applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to 5)a3 6p.yf57aibegv oau;i mv the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorrq:y-l yqc2qsgrrt--8oc - p-knob. The first force is applied perpendicular to the door; the second fory y : ct-q8lsroqcrp---gqr2-ce 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 9 qos9 :h:h 1n l)jv4p+:krbubmva) nedoor. The first force is twice as large as the second force. The ratio of the torque of the first pbh4s r):ej+9n)hua: 1:lbvqom nv k 9to the torque of the second is

  What is the quantity used to;wn/*ag k (vv-.ap 1 hkyy8vif measure an object's resistance to changes in rotatio*yghv8a f;-( pk vka/w 1vy.inn?

  Consider two uniform solid spheres where both ha)be1wz+i l0fv mzu-9xve 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 mo +0xubzwmv l e)1fz9-iment of inertia is

  Two uniform solid spheres have the same mass, but one hasz0p ft* i.mlm0 twice the radius of the other. The ratio of the larger sphere's moment of inertia t p t.0*fi0lzmmo that of the smaller sphere is

  Consider two uniform solid spheres where one has qg -g *q tdl n9l5hprda-3ag*8twice the mass and twice the diame l-q*3tg8dp-gr 9 nlgaqd5*ah ter of the 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 rulpp3mfbc(r x6 hqa4ib( 84; sadius R. If these are increased to 2M and 3R, what happens to the sphere's m8a(u64(fph4c; spri 3qb lmbxoment of inertia about a central axis?

  If a constant net torqu gq)z j zh7w,.nj7jyt0e is applied to an object, that object will

  The moment of inertia of a soli6:z 3c3b-bvnnx d osc/d cylinder about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of ww,z 0kc;qeam xd ah(:146e wlnhich has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotatim,6e1a:qdz 0n 4we xk ;acwl(honal 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 aprq-n(4u10 pzoqr-ns; r+hudn inclnp 1 zq(;prr4q+nsro huud-0-ined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radiusepsdym q*v q/4jkb1 i4x-/dw8 R rolls without slipping down an inclined plane starting pw di yqdmx/*ej/4k 8q1b-v4s from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles ovrs6/(b 5yjjrkvt-. q)z9 fqchanges when a net external force actt) .qr95 6jbv yjkvf /sz(qor-s on the system." This statement is

  In what circumstances caii zfxee*ka3yd( 7ez4k4-n5 g n the angular velocity of system of particles change without a5in3digazzky*e-e 4k e7(f 4 xny change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orp/*4i g *l0.p b5wog mlppr.vebit. Ignore any friction which may be present. What happens over time to the Earth's angulpig4pv ow/0m*l.l5ppb*r eg.ar momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves closf:e s tam: i/pi.+y/zde to the Sun, then which of the following best describes the orbiting speed of the Eart:di py/s/f :tazim. +eh about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulliw9nqfppm(u ih7y/ 97cng in his outstretched arms close to his body. What happens to his anguc py pi77wfhu9(q9 nm/lar momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pdj)d 4a7(giepulling in his outstretched arms close to his body. What happens to his rotational kiepg jdi ()d4a7netic energy about the axis of rotation?

  An ice skater performs a pirpw v-48 azxkb8ouette (a fast spin) by pulling in his outstretched a 8xpb8azw-v k4rms close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum c pm9:5a 2o1hflixmx(5ot: ok.

  What arc length does the Earth travel in a three mk-g(xk7 jv mlvm fqh+)h 72tb/onth period in its nearly circular orbit about the Sun withbvl)77k g-m vj(f 2h/k xtm+qh a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of tdx)n d4-fx gyo zl19-0.30 m. What distance does the tip of the second hand sweep through in 3 m fl-d1tdx)yg4 oz9nx-inutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equival+arkr*re.gav h)8 0vx ent to?

  A bicycle wheel rotates uniformly through 2.0 revolutig5b6xfrf 1f)e :mrq )pons in 4.0 s. What is the frequency of r )gef5fb)rpxq1: 6fmthe wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of yc ulihido66pfr, 2))0.40 kHz. The period of its rotation 2fi6l,r)pyiuo h)c6 dis

  A phonograph record rotates at 45 rpm. Thrt qft8.h4-bgd ough what angle does it turn in 0.20 8df-.hb4gttqs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point:;9b sn8+ m5 8wwfbbkzgkl 2zn on the outer rim move in 2.1 s?bwn;89b2 kl: g8zn5fms zwbk+

  A bicycle wheel rotates uniformly through 2.0 revqin)r+oop1 hq 3d6 y)golutions in 4.0 s. What is the average angular speed of the whee)gh1+q6 ir oy)d3on qpl?

  A bicycle wheel rotates unif4 +zv ,mwmb5m5em8zppormly through 2.0 revolutions in 4.0 s. What is the linear sz,m b4m +em5zv5mpp8w peed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distugghts4)4 9j bance 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 mustbhjsg) 9u4tg4 the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotah2 8) 9+:sjlyjyv igjfu)zlsc,myg50ting with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on jsc)hy )jgufvi, : 9ljg02+y5lyzs8mthe wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length:z16ee ml:l .2ch 8e/tmmu9yxvlvur6 . If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the corx: u6ehyrce teuv.6v 9ml:1z8/l2lmm d?

  A wheel of radius 1.0 yq4k ok) c*v1wm is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration o*vkc 4q)wy1 kof a point on the wheel's rim?

  What is the centripetal acceleration or:zyry( 5szuvms)9 /z f a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m/szrsmyy9vzz :u5r(/)s ?

  How many revolutions per minute (rpm) must a c 6 io )1dgu3k7fcx6wmy+p v8hrircular, rotating space station (r = 1000 m) rotai8 )o fgc1u6rw+xpvm dy367khte to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve ofm63gdl;b. ;o50e nk rc mljs-m radius 50 m with a speed of 20 m/s. The maxi mm mbj. l0;g;d65es-clorn3kmum 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 curve of radius 50 m with a speed of 20 mv1b v7 lb4p8jm/s. The maximjpm 81 b7vv4lbum 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 sl3wx7ud*:un the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand iud:3*lsuxw7 n s 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 10 m dow(*yhn:erfh1qzcv ,c8 n a lr: fcvhz*1, qy8 cn(heane 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 :z pg 22em-g,2l6udm targw,jangular 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 0 6r4z(m wfmcoa constant 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 after sf(*sdhn . sm)nq* sgb*tarting from rest and accelerating at a constant angular a h* gs(*d.fmsq) nsn*bcceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and hdd r,r (xhsz(.as an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20uj,o0c74* (xl sbah ie 8)sc;irg 4uhx rad/s decelerates with a constant angular acceleration of g847su(c xi4 i*l;h ajrhcu0xes ,o)b$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reachesn:r ewts,0a /i;-lvmrfw( k 1g/ 5cbfx an angular speed of 6.0 rad/s while turning through 2.0 revol(; c- 0xwgwt:ar5evnrf/ lf1 kbsmi,/utions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm w(i (dee x.v*7rrak 4rr2p6igslows down uniformly from 8.40 m/s to rest over a distance of (rpv ix*w 726ir4.rr kg(deea115 m. 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 l3 m)edw86hwe from 8.40 m/s to rest over a distance of 115 m. What is the angular a3ed )8wml whe6cceleration?

  A wheel of diameter of 68.0 c7sl)pm: m:ie 0 hpwoq /b2g2xcm slows down uniformly from 8.40 m/s to rest over a disgmpqs mw oe p2:l:/bx0)7c2hitance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratolwscme+*ej r7 +;0 cspry rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration befo +ees+cwm;jr psl0 *c7re 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 90 Nm. If ojbdq-ru+zf-h , 2sc:a 30 cm long wrench is used, what is the magnitude of the force require -:,j2rus-+qzdhof c bd when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. Ihg g8. /w :cvh6-6 -xtlytftmbf a 30 cm long wrench is used, what is the magnitude of the force required w-cfy xh:tg gh6. 8bv/-tmt6w lhen the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o5k-igcc 68uz4fe ec y;f 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: mass m is at the origin, mass y jd- l6pfyz*gd2l8+b2m is at x = a, and, mass 3m is at x = 2a. What is the mom j*zbd2 yd8+6lg-fplyent of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought thegdf,8oreq1 q: 5l8f vv center O. A rope wrapped around the outer rad,g qr5v8v1q f8:ofled ius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoughtw pmp la7;cz94 the center O. A rope wrapped aroucma94 w;zpp l7nd the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 held in the h + i*p6dp9texrorizontal position, and then released as the i6+x rpedp9*t 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 wheelecspj.txz2,y5inp 5p qm*z g).ay;q; to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. j5 )zsz.api2q5ptx;;, eypqygc*.mn 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 w6sxd *rj--sw;:q8. mkce q roy4-inwa rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceler-rkq4 .wye8-r wq -x c*6smwson; id:jation of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulleyve xy ge x*/:3vv13dqbshz 9h( of mass 7.07 kg and radius 66.0 cm. W qh 1 e 3d93v*h(/vsgbx:zvyxehat is the acceleration of the mass?

  A rotating flywheel cnh0y.5yxv lz: pa.;cbeeb73p an be used 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 of /. uy5o(o: i4tiqttna $5.00 \; kgm^{2}$ 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 fij+8djflu28 ahrckp13z .z wqt)p3 0arom rest and rolls without slipping down a 1.0-m high inclined plane. What is the speu.pa)jc83 0p hlz+2j3 kft8zwr 1 aiqded 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 speikt,yxst+( n6tgms 6 no7 xh80ed of 10 m/s. How high up an inclined plane can it climb before coming 0ts6(nnmth+ 7s, xxit6k8ogy to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from k*hy-x:k jur 8oh:yrx6xnw(4xk9 v;crest and allowed to roll down an inclined plane. How faskxyx8rkn:-h6:o;uj4rxyh 9( kxw*cv t 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 slipping down a 3*d es-mq:dkt) 5e incline that is 7.0 m long. Assume it started from rest. The moment of iner qtsdd:-ke* )mtia 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 momnfg 0i yb7b-f inq5r*-entum 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+ ge:c8hj.ve: wdwy(j 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 a moment s5- rqajb:tu0of inertia ursbt a:5jq- 0of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?