Angular displacement is usually expres2 n*egpxqsvo,s): qn,s in units of

  Angular velocity is expres5ixrcc qb ),l6:yq ew8sed in units of

  Angular acceleration is expressed in unitsr+t7m nk8dgu* nbtub h/0 l/9p of

  A boy and a girl are riding on a merry-go-/g idaodrs -2vgx1a8 0round which is turning at a constant rate. The boy io 10adrv/xda -ggs82is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on aiqh pt zc5tc3.;q1likg(i-h8c v 2zy+ merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the g2c38;zkq+-.ic i htqc 1g(hz tpv5lyiirl 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 turni )k qowuablks:*+v.w21 vjj.cng at a constant rate. jk2 *:s+ao u vb1.kqc.v)wlwjThe boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-gna(7 r5 1lxkxgo-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the cex 75x1lr(knag nter. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constanw mre oy;4pko/:z xaz):bw3: pt rate. The boy is near the outer edg3:zr; pyo)zb/ p4me owxka:w:e, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whi lb0r0rt)jrqm e70b/zch of the following is an accurate statement?lbeqr70rj0/m)0 bt rz

  Rolling without slipping depends onpygz;-foq6x 99+yrs*m* n odp

  Two equal forces are aox7wfj2cldxt2 *p3 )98u rgpy pplied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are app3j*pr 89yo7xufdgpxl22 w t)clied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied t4.urz l/ mun+go a door at the doorknob. The first force is applied perpendicular to the door; the seconm .rgl+u u/zn4d force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendic .fy)uq0 iu,zo (-fx i6j/bvh4 zkqy/cular to the door. The first force is twice as large as the second force. The ratio of .cuz0j y f6qy) q4(iib-khov/uf,/x zthe torque of the first to the torque of the second is

  What is the quantity used to measure an object's7z4fhnj) (d kk resistance to changes in rotatio4(d7nf)k jzh kn?

  Consider two uniform solid spherf ye ov vhdv:,fi(2g1-es where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertio(de- ,vgf2 hyivfv1: a to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass g. ye,g3iwf:n;kr8 sjhd(j 0n, but one has twice the radius of the other8.jhdfj,giy30nre ;wnks( :g . The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform kdc ba:ce43 .vey-5uh36qt g y*h;8gofd-artsolid spheres where one has twice the mass and twice the diameter of the other. The racad v;t4- :e*5.gquoydh -bfg3y6 8hekcra3t tio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are ina29wl mgpwu6-gx ks/4creased to 2M and 3R, what happens to the sphere's momagx/l4k 2us9w pmw 6-gent of inertia about a central axis?

  If a constant net torque is applied to an object, that objen e2vb:50 mwnuct will

  The moment of inertia of a solid cylinder a cssa)at:w(9dc9eyyo ys +. v4l e)fb4bout its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic )o4.sy:l9 b4v)acedacsy(fty ew +9s energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, v,xlz p14uq4l9dyqrem e;i1ob;+r t+one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotationa+;yt1dq eovmplq 41rb;x+ u,9zei 4rll 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 anr(lyyv*w6 )ioh o:.vd*; 6rmdls+fhd inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline +y d:rm *6vowhds(f li)*r6;yh vold.depends on

  Suppose a solid sphere of ma g+9t;q tp3cfs2kz 2smss M and radius R rolls without slipping down an inclined plat z3fgst+p2 cm9 2sqk;ne starting 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 changes when a nmvqw+95 ;v* :m+ssr5 xdxwgfhiav:o6 et external force ;w+59o w6vax*s x5 m:q gmhvs:vdf+iracts on the system." This statement is

  In what circumstances can t u2xt c9bontj9a m,jct/-p 0n5he angular velocity of system of particles change without antjctpu,ban2 om9 9t/ jx0-nc5y change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction ..em2c zicd+gwhich may be presz.g2imdc.+ec ent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. xrc9cjhcweu j .wjq.x0);:t: As the Earth moves close to the Sunw re hjtx jq)u:jc;9:c.wc.x0, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a:bo; obe1o:)cp mi6n g fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum abgbi6; )pbnmooo: 1e :cout the axis of rotation?

  An ice skater performs runejd-1 +nh0nxh; 2nje;qe, .xo qp 5a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotationx2n+,nq;e.e up0or;e1n q x -dnh5hjjal kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche2)iki y7bgvj( d arms close to his body. What happens to his momentvg7ji ki)(2by of inertia about the axis of rotation?

State the law of conserv(xgp px;)tf t-(8 ebmration of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly f 05+29-; ymltus)f 2 ct:b6tqfk pccffdn;lxcircular orbi 5fn tsq d -)f+xcm;fp2flc2 :tcflt u0k9b6y;t about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a cloc575 zl./kijancsb sdss f: )m9k has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutelfa9:cjbs7n/5iks) ss. 5dmzs and 45 seconds?

  How many rad/s is 25 revolutions per minute fy-sw qgm ldzc vpn-k2 8x73k 6(eoq8d ef9u8-equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revoluou l,wg5 ch:w 34z2yoftions in 4.0 s. What is the fr52w34oloc,:uhwz yf g equency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at aer;czckt7q ryzkiya)hszj ( 63y7194 frequency of 0.40 kHz. The 3rkrai z9(c c41hyys67y7tzqek;j)zperiod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn w0r -4 jveutt40cc4qy in 0.20 0uc j4 r4ev4c-w q0ttys?

  A wheel of diameter 26 cm turns at 1500 rpm. How far willsk6jv) ov8*pp a point on the outer rim move in 2.1 s 8vj os*pv)k6p?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the iaew85)tu l-d eo3e9t averageeeo53d8)tt we-liu9 a angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wn2v2 hx*3ub / r 4wu6rez-fuyuhat is the linear sx6 - b* urzuveyu/nur322f4hwpeed 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. The cable wz(;rb l .h7)tk z6pvhuhich moves the car is dr)u.rl hz(b tpv zk6;7hiven 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 isvbd-y4 5qq)6ng i1y 1az 4qxxu rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point onq45zyq- )y1du 6xbi xnq1g4av the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the motbjqk1lcr.6 /rd1vl4un5vj n ,or rotates at the ratd r4/k.uqv,6l 5 v1nbljcn 1rje 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 a v tarbv:iyk5;uo s(jr 23 5ym4constant angular speed of 2.0 rad/s. What is the centripetal acceleratov5 aryjy;sm 4 kbr 5iu3vt:2(ion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bzlgy f)gtaa(, i;6yxqs-d w;0icycle whe-w; ;gqz yx0sda( alg)t if,y6el of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rxdfsrx5 n9o6 *p9q r1zotating space station (r =d1s r99r 5q6fxpxo *nz 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of rxl4ap5 vi 9:yph)lcx/ aa px3:adius 50 m with a speed of 20 m/s. The maximum centrph5vl:pl a )p/ xa:cxax394i yipetal 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 50b-eg r o+e4z9d m with a speed of 20 m/s. The maximum centripetal force (provided4eg rdeo+9b-z 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-mzlw3.wpl;fm1d*l57 keat 1ym1 r bnv8 string, is whirled around in a smooth level table. If the maximum tension that the striba r *p71 5ve1nl l .ymlfdt;m8wz3kw1ng 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 9.0ho+6vf1 o2rwwp.s f3f cm rolls without slipping 10 m down swp 1.fo3 owrffv6+h2a lane 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 constat, lcj(7smao -nf6 w(knt angular 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 )i3+i+ a l( w8ixfvaqqacceleration 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 ra8(b oe0odud( qo4j5wv dius automobile tire rotate after starting from rest and accelerating at a constant angulau(jv od8b o(eo045dqwr acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an aixi4en-3x0 gm6drt + wngular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deckqpwbos471, k* /y f:u)i hjdielerates with a constant angular accelerat4od/b*1: k )q kfjhy ,usw7ipiion 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 speed of 6.0 rad/c (vs/o frk0:xtgwkqc(28;dys while turning through 2.0 revolutions.skvwxd c:o/gkfr(0c2y; (t8q 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 over lo1gfslrh. u,c( aao gin,/ .*a distance ogr.haf lnoa/g,i,* so1l.(u cf 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows dpca) 4:unh(ae+ iru6t ,pf+sb 6vsb2 nown uniformly from 8.40 m/s to rest over a distance of 115 m. What is the acs:,f p+b( e h4 )66biat+nus unapvr2ngular acceleration?

  A wheel of diameter of 68.0 ciz rdmt l 0))p.voxc( (6)yginm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to y xn6lmz)0ioip) d(t.r)c g v(the stop?

  A centrifuge in a medical laboratory rotates at a rotonrv:maad+bh0hhp)2e+ p /y 6 ational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before comingbdh+h:hpre)yn ma/ 6avpo 02+ 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. Iftgvjx u06z/o: gdzkd f)pv/+3 a 30 cm long wrench is used, what is the magnitude odgvg :t+/v3d0xoj/)zpu6kf zf the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If ak fe+2 f(bjyq1 30 cm long wrench is usyfbke f1 q+j2(ed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i9/pjn0h *9z2m yqpcjm nertia $3.00 \; kgm^{2}$ 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 ork-uwl*4 )6tq oqll8ozigin, mass 2m is at x = a, and, mass 3m is at x = 2a.q4u*o-lqowlzk)8 6 t l What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thta .5 ;mmfisc4ought the center O. A rope wrapped around the outer radis4 tc5;m.ifam us 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 h ( i.qo djmik1w+nd fx*g);psxxbve*)14at2a frictionless axis thought the center O. A rope dxs +ai 1*ib(hv. qxp;wk4jmx1)eotg *dn2f)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 31k0cmylm*c8 x z 7kw9r;tdbn at one end. The rod is initially held in the horizontal position, and then reky 31z;bdmxcmc *7l t0wn kr89leased 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. 4,:e jl2 x bj(l qa*b 2oiz)su/ut8brf Neglect the mass of the axle and sprocket. If a force of 20 N is applied tb4so2 f2t )*zux,bju/i j(qlrbl8e:aangentially 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 a rope wrapped around a frictionless disk pulleyz8 uml zy ,*i(p5ohf*p of mass 7.07 kg and radius 66.0 cm. Whatz*5pupi hl(f, oz*m8y is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped a-c-(ht ss/ichs; llt53(oal b4v8kutround a frictionless disk pulley of mass 7.07 kg and radius 6s4hhc t;itkb ov lc3u(8-stl/ ( -l5sa6.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used y/p ego btm/)*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 0 ei)xi+vjgi. 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 starts from rest and ronfl, 2tu+ +pgslls without slipping down a 1.0-,+pn l sg+uft2m 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 ad i,p:,awbh 0+pip j1with a speed of 10 m/s. How higha i1+ppw:0, ba ,dijph up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50npeq7u(-v ic9y- hk 5+ y6bpub m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. Ho6ich5p9 u (7pe+b-uyyv nqk b-w 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 dvya8wr+hzh, k6 q(5qtown a 35e incline that is 7.0 m long. A( vqywh 5h,8+kqzr6a tssume 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 cdyvhcywjgjpwx-i4ej7/ 58 ; -hanges 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 of da/ejs;3ev l-n xvl4; $5.0 \; kgm^{2}$ 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 momgx48 o8 ujir67,9w/mnfm mpyqent of inertiamjf6p9mywgmrq x7/4u o8ni 8, 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?