Angular displacement is usually *+atn+mnmzo 8 x1d 0uyh ke9m0express in units of

  Angular velocity is expresn2w5 +ks /p r8,euulzhsed in units of

  Angular acceleration xrv*s -nmn+g8-dgabb,( +sni is expressed in units of

  A boy and a girl are riding on a merry-go-rvsnh-s qd i 8b-3mcwi89)cli8ound 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 displacemen8s3l9)d-i hwm csi-v8b8c qint?

  A boy and a girl are riding on a (4 3m 7sxjx mn94 i;urg.kpajamerry-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 angup;uj ja (ngs4xa7i3rx 4 m.9kmlar speed?

  A boy and a girl are riding on l 1(l0fb9)q8yt gv c qkt,7jey fay:)la 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 greaq9) l7,y0f t8l) yetc1vkyglb(:j aqf ter linear speed?

  A boy and a girl are riding a merry-go-round which is turning at i*;4).xh jmke/tiz 2kg, 2i8zptlu z ma constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetalz4z/tgu )i.jh,8ki tmzp* ; m kx2lie2 acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constantsl+k) ufuu/dew5g q) .f2ft w/ rate. The boy is near the outer edge, while the girl is closer to the center. Who has t5/ku .s )wtgqlw+ffe )/d2ufuhe greater tangential acceleration?

  Consider a rigid body that is rotatin1-w iab ik1( 2ft dymb 3+(4djsv-vinqg. Which of the following is an accurate statements-i d1 b+4n ajv(b-(qyidm2vt1wfk3i ?

  Rolling without slipping depene/ hy5o m 2mqjz/+cu7pds on

  Two equal forces are applied to a door. The firb.n*k+h vgfw 0/4mp jxst force is applied at the midpoint of the doorv+w.4jh pmf/0x g* kbn; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. Th5:pcpz1d epf*ph8c/ ze first force is applied perpf ppzdpe z5/:h8c1 *cpendicular to the door; 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 door. Thehza84q*la+:hyybj4- s8f rw a first force is twice as large as the second*-jhswr8 4yq a afhl:8a+4ybz 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 in rotatikt 5+g vl)v5vron?v)+5v tklgv r5

  Consider two uniform solid spheres where both have the samtk4 clf5+ +,o gj3 2dhqjcfn*de diameter, but one has twice the mass of the other. The ratio of the largerkc t2qdd,3l+n*4 hojf5c fgj+ moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the rc(yrcimu 3c2)eip ,m2adius of the other. The ratio of the larger emm )ccyp( c2,ui2ri3 sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass oj,*r;og64naodiu v;(2ea r gand twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inerr,(2dieo ;u onoa6 4a;rgvjg *tia is

  A uniform solid sphere has mass M and radius R. If thes k2g(vvhn-dcnh3 7mo +; cf w+rp00woie are increased to 2M and 3R, what happens to the sphere's moment of inertia about a cv + m 03gh02wnc7 dc vo+wrkf(phoi;n-entral axis?

  If a constant net torque is applied to an object, thve6: z9rvb r8eb4-ia nat object will

  The moment of inertia of a solid cylinder about its axis is given by6jwe, -lwt5uvq8c* mp $\frac{1}{2} MR^2$. 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 which has a mass xrsr7/q h77 x4anm (p(w /ddebof 10 kg and a radius of 30 cm. What is the ratio of the rota(eh4nra /m7dr7d (wsx 7/qxpbtional 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 5u5nj3icxc tif 0 jv;qa* :bxrnuv,.)slipping down an inclined plane starting from rest. The linear velocity of the sphere at the b)xba nc5i.3 *:0n rj,ivf5tqc v;xj uuottom of the incline depends on

  Suppose a solid sphere of mass M and radius R ).fblhs:e kqbg-e8sh:.zx 4l-ctwj )de .- h qrolls without slipping down an inclined plane starting from rest. The angular velocity of the s8 lec:b xghteqs.d )we.lhk z-f4bq)-jh-. s :phere at the bottom of the incline depends on

  "The total angular moao)os.b4 j0 x 4bxp,xj*v6f iymentum of a system of particles changes when a net external force acts on the system." This stat0ij4vb4 sao.xx j 6yf) bxop*,ement is

  In what circumstances can the angular velocity of system of particles c tt .v*0ko6o45 kgwwtyhange without any change in the system's angular momentum?4 kkg5ttw 6o.ov*ywt0

  The Earth orbits the Sun in an elliptical orbi-pjr)4 :o5+ m0vmy a /mvkzihat. Ignore any friction which may be present. What happens over tik+am-o5jy mv/4vh ir mz0 )p:ame to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbizrmv)wkn7+ +yu9b qh *my /r)my+t2 agt. As the Earth moves close to the Sun, then which of the following b+w +zr y97r)h+gmymtqbkam*)n vyu2/ est describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pi6e 1 qdxwjs(5yrouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentudjw1q y5s(6x em about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullil25dg 8yh hq) bpvp0oq*2gx )qng in his outstretched arms close to his body. What happens to his rotational kinetic energy about the d80)hqp2vqpog5h 2* bq lx )gyaxis of rotation?

  An ice skater performs a pirouette (a fast duiv y3,f xl2nbgj0rcu)4iv,1(2 rix spin) by pulling in his outstretched arms close to his body. What happens to hisg,ri2 l1 i)3,rfnvxu x v40ubj cy2(id moment of inertia about the axis of rotation?

State the law of conservation h.wa-5 7 .nf9 lhwggp7rt gji 5op5k2aof angular momentum.

  What arc length does the Eqrwu**i jm 10;oj)i dharth travel in a three month period in its nearly circular orbit abmq;*d0 )horj1*ii w juout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clstxdbnutc 9h+a/ji :25* isw.ock has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes w d9/s5tu2h+xj.i *bcnti: sa and 45 seconds?

  How many rad/s is 25 revolutions per minute equ6 q);;li5jupk:dfex0 z pv nn2ivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ij0x2825ftr;af i xxbms the frequency of the wheel's rotatimi5;2x2fj ab8t0r xfx on?

  A pulsar (a rotating neutron star) gxdi.4+ hrn9-ypfl(r emits pulses at a frequency of 0.40 kHz. The period of its rolhdrf p49 +gi(nyrx.- tation is

  A phonograph record rotates at 45 rpm. Through what angle does it tu:uw) par5po j,-ygq x7rn in 0.20 sxoj )pr5 up -7:ywagq,?

  A wheel of diameter 26 cm turns at 1500 rb zbebm,q;d6cykl6 u pv6 a;e6sv5q(0pm. How far will a point on the outer rim moveq ,sp6(6bbvaeuq0;ml5 de k;z b6y6vc in 2.1 s?

  A bicycle wheel rotates unifom :khff. g/gl-z ;kj1vrmly through 2.0 revolutions in 4.0 s. What is the average angular speed of the wheffk1.kvjhm:lz /g ;-gel?

  A bicycle wheel rotates uniformly through 2.0 revolutionsfl/ os*r9;mv u in 4.0 s. What is the line/rm;9ufls*vo ar 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 6.8 km. , w/zr*zsi:aaayvh ;9The cable which mov/zaw; :,ahry i vazs*9es 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 the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speedvqxlzh,4(du/ 3 am :bz of 2.0 rad/s. What is dl: ub vz/ a3(xhqzm,4the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lenki is wjn:k-00gth. If the motor rotates at the rate of 20s-0w kin k0j:i rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed op yq k4csh9cs:k5me4d 7, uf+yf 2.0 rad/s. What is the yhe9 q4y smkc+puf57 4:ksc,dcentripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bic kj q)x19wb/tl ,cv6, vs-aknxycle wheel of diameter 70.0 cm when the bike is moving 8./ bxq16 cj)wn k,9vkvl,-axs t00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space juk:p+ f; tb*-ea e23h l.mdjrstation (r = 1000 m) rotate to produce an artificial u mft3;rkl-e:+hjdp.b a 2*ejgravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a spee458. 9 uip)ck7 lwymce4dpczzd of 20 m/s. The maximum 5pz)ezimdclc8u 7 .9kp4w 4cy 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 withp* r1jn fb(kf: a speed of 20 m/s. The maximum centripb1fjkr*:p( nfetal 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 o6m. qo jv26rx) jz umb wsmx56-2+v0fxlk u(zto the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string2uf -6u.) xsjmz562lm roq+kwvxbov m(x 0j z6 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 ra (npvq2yfe o qfp9+/,adius 9.0 cm rolls without slipping 10 m down a lane at2 evfonp( fa/qq, p+9y 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 ang l4ndbv y((4vdular 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 accy4 sm5btk/ii+ ;-jzeyq*bm) meleration 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 afpk9hv bgzu c )t3kz:4y2 w72gater starting from restgau9z3 wgtkc7p)zhk2bvy :2 4 and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and0 0*eg195hilch 3 c u2rxyppo4u7fbu i has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 btj f0wq)/ dcgacpd-c -3sz:7rad/s decelerates with a constant angular acceleration -/cdwaq dj3-p)s7ccfg b:tz0of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from re /7g-vzn idvg hf59gh0st and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration gg0v z7ih-/dfng5 hv9of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly /nd-+f /bxgg) 7(wjb0rlko qnfrom 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions oxwl n r/j+7fbk-bn(0qgd g)/the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 ,ja.r(bz q mkr9 k8h8 vuq.d9zm/s to rest over a distance of 115 m. What is the angular accelerationu qbmkzk9qj..z da9,(vhr 8r8?

  A wheel of diameter of 68.0 cm slows down uniformly from 8:or-rkw ( 0*hct(tuzx.40 m/s to rest over a distance o-wxuorz h*c0(ttkr : (f 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed o m,h7.) layy2 uq0wueof 3600 rev/min. When switched off, it rotates 50.0 times at a constau,a2.7 y 0oqmheuyw) lnt 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 tightenb7161ehzfp qoydv*5 n py )v(ving to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendfdbp7y ohy(5p v) 11zqv nv*e6icular to the wrench?

  The bolts on a car wheel require tighteninc5(3u9qw :eqhj m1/p f zig4:p4kjnmcg to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the forp4j:mcnq gzpi 1 (934cuq/ehmwk:f j5 ce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i,vv5)c*rq ,vf it u(:rcsy 3zdnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: l2m5z:jn3sdemass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. 25nzdmsl j3: e What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis tox7xir* aj p9-43depfhought the center O. A rope wrapped around the outer jexd 7ai* rp-fp 9o4x3radius $R_1$ = 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 frictimp/4 muux98 cduaay,-onless axis thought the center O. A rope/u y m m-xcp8a,ua9du4 wrapped around 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 i v-6n5ofobmm4 nitially held in the horizontal position, and then released as t- mf65v 4obmonhe 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 rapsat)0 0a9 su3b6l nrsd c-;jzdius 30 cm 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 thetj6sz l ud0nb0ar 93ss)ap-c; wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless xhslj2e*,k1n a; e) mmdisk pulley of mass 7.07 kg and radius 66.0 amnjkm es) *,l2 ;1xehcm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless pobe t,v- g asy8d)5c3p 2-smlu as+0xdisk pulley of mass 7.07 kg and radius 66.0 cm. Whaysm5uc 0vsts3obad,p x eag82l)+p-- t is the acceleration of the mass?

  A rotating flywheel can be useddz35 ilg k4spptmrf2qx36je6 i4k)m9 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 ink5 r.yw3f ijf5 jh, li6exr-b.ertia 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 mass 1.0 kg and radius 0.010 m sd j6(gu7ec+mxzl0+myb n :l m/2za ec/tarts from rest and rolls without slipping down a 1.0m+(une:a 0z 2ybx g6+lml cd ej/7/czm-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 5ygd;jenhvahm7 + uqn/v;4w 30sspo +m rolls with a speed of 10 m/s. How high up an ovmq+snnsy4w;vpg 0+;jd/ h7 a5 3uheinclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from res1(5 wa sv,ry9t6waimtt and allowed to roll down an inclined plane. How fastw sam y9 wta(1,iv5t6r is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 jmvsq yb 68* 62spujw0qza9q;cm rolls without slipping down a 35e incline that is 7.0 m l8yq02 ajuw6jm6q9 vbpzs;s q*ong. 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 momenjb4b6p ,hp 5gqtum 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 ofq rm+dm7l-mt8db) abzn*i )7u $5.0 \; kgm^{2}$ 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 5.0p9l-so6 mx/4,fih .suza7jo q0 rad/s with arms extended has a moment of inertia of.s pifmux a9/ooj4-z,6 hl q7s
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?