Angular displacement is usuall-i looxq/4wx lcdg6f * .cc,5py express in units of

  Angular velocity is expressed in unitu*x c d.yx94dys of

  Angular acceleration hh( iri37atdf nv5*ba* (j ho(is expressed in units of

  A boy and a girl are riding on a merry-go-round which is v55vdxfd,b b- 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 di5f - v,dd5bvbxsplacement?

  A boy and a girl are riding on a wp vez wb6pwh;ft(:13merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the ce3 b1( ep;tfwzv:6pwwh nter. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round whk gk8 q*ca m*z3:o;jjuich 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 linear spc* qgo8:uj zk*ak; 3jmeed?

  A boy and a girl are riding a merry-go-round whicl0- b67yp)xyv) fvyb vh is turning at a constant rate. The boy is near the outer edge, while the girl is closer to th)p) y0yyv6 xl7vfv- bbe center. Who has the greater centripetal acceleration?

  A boy and a girl are ri460s/rs;uq.8v jld4fkmrj8 pb4ggfpding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleratiof; 6fd84qk8umpgrj/sgs.0bl r p 44jvn?

  Consider a rigid body that is rotating. Which of (4i/gtyc12yk (x gza+p :yooythe following is an accurate sta 41to k gp(/zy +a2:yocgy(yixtement?

  Rolling without slipping ug;e .bmx9*b jdepends on

  Two equal forces are applied to a ;to,3 onnd77*djr0 p imnk1w vdoor. The first force is applied at the midpoint of the door; the second for0 3op*viomnrd,7d 1kt7njn w ;ce 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 door1d6wrn)2ijb )6fx rhp knob. The first force is applied perpendicular to the door; the second fpn)r ) i62drhxfj b61worce is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular vh82- b o2hpydf/qdu 2to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the uf h8ddb p-yv2oq22/hsecond is

  What is the quantity used to measure an object's resistance to changes in rotatibeyhnh a/q9e h r(yr kn;4:w8.kna8h (h9:hqben wr/y e r;4y.on?

  Consider two uniform solid spx;om51tk,)sngia+f vheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia t o g1,x5;st)+kfnm avio that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the rajq-bf. .qvo .cdius of theb oj.fv-q. cq. other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twifobijozstd /,* ;*8aln,u 0tcfy6yq6ce the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia i qjlto,t ya6cbz ,6d* f8si0*; /yufons

  A uniform solid sphere has mass M and radypxm;b v4d/:k ius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inkxp:dm 4vby/;ertia about a central axis?

  If a constant net torque is applied to an objv(u 2 o*atsva.ect, that object will

  The moment of inertia of a solid cylinder about its axis jz)sfh ) wb4b04aboo 3is given by 0.5 MR2. If this cylinder rolls without slippinh b a 4o)bof34zjwsb)0g, 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 of 10 kg a(eigh0sx*uyz06gr, pj8km-v nd a radius of 30 cm. What is the xjki - rp*uv e0,g0hmz8 (g6ysratio 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 doh(yw)ks7q bf )knl)dsx86w-*k9 oeq nwn an inclined plane starting from rest. The linear velocity of the sphere at the bottom o-d*nq kk s yklx )w)sbewho7n)qf896(f the incline depends on

  Suppose a solid sphere of mass M and ran 3h.kdpn9 bq-)cq;og/ h-y wwdius R rolls without slipping down an inclined plane starting from rest. The angula hqbp -n-dqc).y39/kh wnowg; r velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a n7yz1tdudi pf * (. 3mkeg zz063xp1jypet external force acts 1ey 0pytgzz(k 673d d13*zmixp.f jp uon the system." This statement is

  In what circumstances can the angular velocler6d gpemt: *f1y1/7zp8 dum8kbhx 3ity of system of particles change without anyzmek88 p3fhdb1gxry t:7dm/ep *u6l1 change in the system's angular momentum?

  The Earth orbits the Sun in an (vk o1 hgukb pd5n,9rm17n7p96sywdy elliptical orbit. Ignore any friction which may be present. Ws ,vgy kk995opn7r(u ympdh1dwb 1n67hat happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbvvbnuohhtqin7 c:4*9-1dw + cit. As the Earth moves close to the Sun, then which of the following best describes the ort9 7 hq-w1+4cbnuncih:vod* v biting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spiztb a6hw(t,- mn) by pulling in his outstretched arms cloz(m -,aw tthb6se to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (4)y(dtwmq5 /ap;a v lfa fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy aboutl(mw5pv tfdq; )4aya/ the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling gk-b/ 6y-vx zyin his outstretched arms close to his body. W-x /kygvy zb-6hat happens to his moment of inertia about the axis of rotation?

State the law of conservation of aaexfrqh,qvh,xa k.g 22k79 h8ngular momentum.

  What arc length does the Earth travel in a three month pt :t0bsdxayp.cmrri,zzvg281.r 7 3teriod in its nearly circular orbit ayr1prv tzg. 7:dt z3. ia8ctsrm2 b0,xbout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.3rts:*1gpkloo: p5+ eo0 m. What distance does the tip of the seconds :opgt*1+:5rkeo o pl hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalentjjeo/ erraii /)-d:)sl hrp:cosj7 /: to?

  A bicycle wheel rotates unhk xis4-8l ub1iformly through 2.0 revolutions in 4.0 s. What is the frequency of thehl4 bu ki8x1-s wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequenci22k+cib t9ozd/,. +kguana uy of 0.40 kHz. The period of its+2u 9b/zdgnk .ao, + at2iciuk rotation is

  A phonograph record rotates at 45 rpm. Through what angle devpu wtg t7d43( ;wvwrt q78-coes it turn in 0.20 sc(t-g vepur;4w7 8dq ttwv3 w7?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a po3yv*+omua*qx n s44x sp8 b0acint on the outer rim mvyb**48+uqxaaxos3mpn c0 4s ove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revgry //czo4u9f jf3 r6holutions in 4.0 s. What is the average angular s fjy3fo/r/rgzh64c u9 peed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revoluxbr,87gydt d73yanbw:g( e9wy,q x(ctions in 4.0 s. What is the linear speed of a point 0.10 m frb ,e(xy gy3,bx:( dny7r d7qg at9wc8wom the center of the wheel?

  A cable car at a ski resort carries skiers a d2kg v)n4 :,m7 h (chdtnw0kzxyistance 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 thenx2gh:m ,0 nvdct )k w(47yzkh 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 of 2.0 r1uina:bc8f+vc(,4 zgat yb 12ins1 nnad/s. What+inu18a1a ,f ( cz cybnn2n4its1:b vg 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 lenek*uo14pbh*+xg gxk3 gth. If the motor rotates at the rate of 20 roke*khg4 +u3 g* b1xpxev/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 angulac4il2/ ru)boznntg: . e m+nq/r speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel'oc z2: rm /neqngl4.)+untb/is rim?

  What is the centripetal acceleration ozbnqj(e*;e1r;2 i jdf jm;g7 :h9pgyaf a point on the perimeter of a bicycle wheel of diameter 70.j ; 9fe:;hjzg y(21ngb qdir; a7p*mej0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a cin 6m0oe9l9xla rcular, rotating space station (r = 1000 m)e mlxn96la 90o rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curdge d1lkp t;(9di-l*4p bo )tave of radius 50 m with a speed of 20 m/s. The maximu*4d1kd)pib9t; (lte-dl pg aom 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 with2h*v.)s+ 6ea7a84xbbt ,yy ;efdub zqi8jdpq a speed of 20 m/s. The maximum centripet+d;ajq d.27 e8a8ey 46hfy *i qsp)ztb, bubxval 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 whirled around in agplcd9zp :73z smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if the string is not 3z g:z7dlpcp9to break?

  A bowling ball of mass 7.5 kg and radius 9.bt1/+;ez+*-i 0c frjp*uzq( ykf lojx0 cm rolls without slipping 10 m down a lane at 4.3xtq/l+;kijy rf-f* e+1up(* bczzo j 0 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 accelerat-qskz;a9;0-vj8 dmizmlqme-t)z( h mion 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 :wix)e *iq ep3i11k7gx prd*x a 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 starting fi8pw0wkdu ; i7f/7c3mwu8u ecrom rest and accelerating afwuu3i 7mc 07i8d8e k/pc;wwu t a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and hasef 5f9o;qt 6aw2 yr63sfubc0rzv0a 9j an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/sgcd/7yz0 y t9q decelerates with a constant angular accelerat/79dczq0 yty gion 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 speedid 8jpo y ;t-3) ybl3*26rpyhulq.mxkncg87 a of 6.0 rad/s while turning through 2.0 revoluti3y- akq3;l du7rmibjg c .8tp)hpn8xylyo 62 *ons. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovce;zrh hf ,-xm*e :y9a7ffdg1er a distance of 115 m. What is thefmfg 9x ze1*h;h,fe yac:d7 r- 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 to rxiyg1 gqiug d+ u5:2y/est over a distance of xdyiig:qu/g2g+yu 15 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over o(o-h.lunk9 a a distance of (a-.9okn hl uo115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatio*;osghzu8 :-rq. xgiknal speed of 3600 rev/min. When switched off, itghg izo-q8rs: *u. xk; rotates 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 require 2tj2g,;udp yp tightening to a torque of 90 Nm. If a 30 cm long wrench is yg,;pdp2ut2jused, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening;ia8 vwxx6w r9 to a torque of 90 Nm. If a 30 cm long wrench is used, i9axw68;r vwxwhat is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of x9-r7dm ez ;mhinertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as (9 gzvmgj8pfs.+6b a4b ru y1rfollows: mass m is at the origin, mass 2m is at x = a, and, mass 3m 1j(zf9yau4rv +r s8gbp m6b.gis at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is 8 w hl h/0x*ozoeo:: 2eadc0eppivoted 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 wrapp:w pdo*ezx2he/ l0:haeco8o0ed 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 axis thought qez1x y*gmhp /3jo. e*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 radogmp3 yz j.*xeh/ *e1qius 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 iub -,cbp4zvv5 s initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleratio4, cz-uv5bbpvn 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 je,on 8+dws)-u3lmxq,rcax)/ b:wetcm 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 u8,a3m,dx -wbee) cxnqj: tors +l) w/speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley o0vta3j3hfoz,.ld *gl f mass 7.07 kg and radius 66.0 cm. What is the angular accz h 3*vlg,.j3fto0 dlaeleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped x(whuhg-3e umgz e:n8q.lr1 9 around a frictionless disk pulley of mass 7.07 kg and. ee3(uh1qux9g rghl nm8-w:z radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can7e+z4u9 yin cc 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 r0dw,khl p-t9yz uue+0bj )2 5n4aa aiof $5.00 \; kgm^{2}$ 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 ras )-is:-(wh.7f i8wtrsreou qdius 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 :-r7oq-)t sw8u is wrf.ehi (sit reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radi-x;nc9t*lajzbv zak*- nd 6m1us 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before com-z xnzlb6dj9 namk*-a; *1cv ting to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from l/xj;h1:sbcp dmtz66rest and allowed totz6/x :61;bc hdljps m roll 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 without slipping d4zlu48su f0k -miz:rsown a 35e incline that is 7.0 m long. Assume it started fu 4s z m4:u0-rkl8iszfrom 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 ,p . ejebw) 3ip(b,dhxchanges 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 inertixk+rf tc jag69;7rv 2op)5ai ua 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 osk (ce8k8su-inertia8 k-8seos(cku of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?