Angular displacement is usualld*ocmd2x3zt tt (8cw2y express in units of

  Angular velocity is expnv n,aet y*:9jy:6 e4ecuv4op ressed in units of

  Angular acceleration is expressed in unitf7 3)te/hex*a mmt y3ds of

  A boy and a girl are riding on a merry-go-round which is xxydg-ey4/ch q. hlog1x 9(; uturning at a constant rate. Th. gxo/hgyy-4h1ued 9( l x;qxce boy is 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 a merry-go-round which is tu3sf tjs)vs,h 1+9v apdrning at a constant rate. The boy is near the outer edge, and the girl is closer to the center.,hs91tadsv)+vp jfs3 Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning3, s8h m7i eb )wfoc upuyy7ws 0i6zv1+ze73ug at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has th+ wuzcz 1svy3iis77eeghy,3)u0mb 8f 76p wu oe greater linear speed?

  A boy and a girl are riding a merry-go-ro-5edat-zehd2f r 6ho 3und which is turning at a constant rate. The boy ia h5d -r2oezftedh-36s 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 a constant rako egu8z38 6ujte. The boy is neaeg 3juku8 o6z8r the outer edge, 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 ahb ,zrp2toz.i0. j n*mccurate statemen 0.jpzr b2*.m iot,nhzt?

  Rolling without slipping depends on:/g9+dxu99nl ebxz7 ntl*x uy

  Two equal forces are applied to a do4okh5a9tyae )b g g2rn)1 x8hzor. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied 4t1hra9kbz)x82ngo5ae)gyh perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doo5ozz3i9hv: )ozl2qau rknob. The first force is applied perpendicular to the door; the second force is applizo a9uzqi)2v:hl3 5zo ed 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. Ths xu/ : dgd bsj3dod)h-vi6*-ie first force is twice as large as the second force. The ratio of the torque of the first tsvx)*ud-bd -dosg idi6/:j3ho the torque of the second is

  What is the quantity used to measure an object's resistance tw6s .mix1ae*2 0.yzo1kjo4ib(ntmgh o changes in rotatiob iej z2w. ona s0gy.(4x11*h6ommit kn?

  Consider two uniform solid spheres where both have the same diameter, but one nvt9 i2vy22u9 lmldx-has twice the mass of the oy22 9ld vt uvn9xm-2ilther. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice ther9dt2 u,7pc;cx65spxc xg 3 sb radius of the other. The ratio of the larger sphere's moment of inertia to that of the smalle3 gbs t9d ;pp5s6xru,cxc7x 2cr sphere is

  Consider two uniform solid sphf,fg8lruq+ f9*oj gq-eres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the -9ug, jlf*rq+oqf 8gfsmaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are inbu4 +) pmrdl0yeg mf0)creased to 2M and 3R, what happens to th e pydrm gmbl0+)0fu)4e sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that obj.lxsjeb-d )l(ua4 ulnc0hjx )h3, 4knect will

  The moment of inertia of ag7n(r0hzhus o (;xy*j solid cylinder about its axis is given by 0.5 MR2. If this cylinder (nr(syhj*x 0g z;u7horolls 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 w;z(1pf p:az;. * axcc05fx zdnzb.alb hich has a mass of 10 kg and a radz bax ; az*b0zlffcc.(5napz: 1;.xdpius of 30 cm. What 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 slippinn* pn1acp -*v4,8 u-i w wu-rpi6etkkig down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of,iw upcn-uwe6r8 p* -k4 i*inta1v-pk the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippincx77n++a r zncg down an inclined plane sta ++cnc z7axrn7rting 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 net extel kb+os40px, y. cmwn/rnal force acts on the system." This statemks,npw +o40lx c/ym.b ent is

  In what circumstances can the angular velocity i/2:3- 0 qgxjzqomhlgof system of particles change without any change in the systeg:oijm2x q/-h3qz0 lgm's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ign:4zd6n3wo i0gjq 2her/l i,nh ore any friction which may be presenz2 d430ne:n ,iohiw6hj grq/lt. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves clos *: hhr(; vyhey(fo.isd1sg/ee to the Sun, then which of the following best describes the orbiting speed of the Earth about the .ih*:s(sgfh yr1;hdo/y ve e (Sun?

  An ice skater performs)nsxv uk.kbf )k8)yg: a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his )syk )nfk8 :ubgv kx).angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pm9yhoync) 66 ( ftmpj9kg et-3ulling in his outstretched arms close to his body. Whatfom96m6- p3j g entyhkcy)( 9t happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a tnp,g r7 j.(mg d/t4ivfast spin) by pulling in his outstretched arms close to his body. Whatjt d. rnpg(7v, /i4mgt happens to his moment of inertia about the axis of rotation?

State the law of conservation of angul0l )8rc ahg258aghob6-w dos jar momentum.

  What arc length does the Earth travel in a threqpr;n..qve+ (k5ceh ye month period in its nearly circular orbit about.qy vch+r 5.e(;qnpe k the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock -6i65a- .+vy 3buj zxf :ustn ysfcbu8has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 su buv n-ybica.syusf3f8j: 5+-xt66z econds?

  How many rad/s is 25 revolutions per minutev//fiohnlbcg2.l g1od4rhg/4m 2+ c u equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revxm 7b0 y 8;a3 id1 kmy9y*amuzx,v9awwolutions in 4.0 s. What is the frequency of the whee7u0ambdxwy 3y ;m8wm, 9 ivk9zay*1axl's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.4ryie.95z1mj q;h5zka 1d( hvx 0 kHz. The period of its rotatio1a .5z mdk hez(hij1;q rv59xyn is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.tusat0/,of )+bttb0w /q /jju20 s /+ bw,obt/0ftujatj/0 uqs) t?

  A wheel of diameter 26 cm turns at 1500 rlug7qj,9pd/ xpm. How far will a point on the outer rim move inq l,pduj9 /xg7 2.1 s?

  A bicycle wheel rotates uniformly dpd -di wpoi w.u6d2+2li0.vj through 2.0 revolutions in 4.0 s. What is the average angula .jv 2idi w6l+iwdu0dp -2.dpor speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s6 46avdzk qzkm 0(4mlw.i lud9. What is the linear speed of a point 0.10 m from the cem9klklqd w6 vz.4a 46uz d0mi(nter of the wheel?

  A cable car at a ski res.7 ntu hd1cx jewzic)a07z0- rort carries skiers a 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)0x ijena7 .c0rzduth1zc-w 7 cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant af.aa*ra qy/+ rngular speed of 2.0 rad/s. What is the linear speed o+*raayfr / qa.f a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in3im:hkfm2: i h length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end o:f2kim :m h3ihf the cord?

  A wheel of radius 1.0 m is rotating with a constant ang c doc1rq+ev+eul )*22clvq6 lular speed of 2.0 rad/s. What is the centripetal acceleration of a point on r+ 1vlo*l26ee 2ul qccdc) v+qthe wheel's rim?

  What is the centripetal acceleration of a poi: +ng f7*e5aq e2bblsont on the perimeter of a bicycle wheel of diameter 70.0 cm when t2+:q5o *7labfnees bghe bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a fu5n; w,e mk(rel0xz7n 7sc -ucircular, rotating space station (r = 1000 m) rotate to produce anu 075uwse;ez r -xl ,c(fknm7n artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a pt-s62p4 rb :c3ue qdispeed of 20 m/s. The maximum centripetal force (ppdu2pc 6 3 br:es-tqi4rovided 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 m,n*(yej m rpd5tds .gr i9t(o,/s. The maximum centripetal force (provided by static o(5e .stdirpn *d,9rjg,tmy ( 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 arounj 93l+mr3p oz- e .n6h)1ouafkry dmj2d in a smoot.rj3e6yo- hak) o mmu21 9z+djfnl3rph 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 to break?

  A bowling ball of mass 7.5 kg and radius txilu7n q/2s:vv*eu * 9.0 cm rolls without slipping 10 m down a lanevlt 2 u:/7ei*qn*uvx s 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 c 0 rz yb-5(fzj0r1 xuc9bpgo,ponstant 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 accelr4 k8w vi9nowy7ok5 :glab,4peration 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 rotkgv04/heh-*,ltp dx hate after starting from rest and accelerating at a constan0hlvt xge*kh/hp d -4,t angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at re7p*xuj2 xrn) z:8:yymzf5 s88 genfnmst, and 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 rad/s decelerates with a constant angular accelere6smn,27zmdb :5ullf 51scwq ation ofw7ulcb6ne 1m qsdl 5m:f,s52z $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reache xh;yuv e5g72ks an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration ovx5g e72u;ykh f the wheel?

  A wheel of diameter of 6vfqv:/ s4b:tqxu 59-pvhc ,*pvyhtdclvh)+ 48.0 cm slows down uniformly from 8.40 m/s to rest over a distancevqvsl::vphc, *d4yth4f+up9vhv 5bcq/) x- t of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 6 ,nhrvac0f6r4 8.0 cm slows down uniformly from 8.40 m/s to rest over a distancec 6,0h ar4nvrf of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 c1yn;s a+enm al3kkf63m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long dn6l nm;+13yef3ka a skoes it take for the wheel to come to the stop?

  A centrifuge in a mefgx: g 2vgwa.*fjp )v5yec)2kdical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times:5v*2j e)g.wgy) xkgf2vpcfa 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 tightening to a torque of 90 Nm. If a 30 cm 8 o7phk.rzeb,w+sx;f long wrench is used, what is the magnitude of the force required when the forcewb8oek,pr. s f hzx;+7 is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 7sbyg)nx/0 e0k1c xskflxh83 30 cm long wrench is used, what is the magnitud/70sxnlk 0)hsf x1cbk y83gexe of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine.hejwpv f d+6*rtia $3.00 \; kgm^{2}$ 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 2mqns l2 3mie8 mo-vn)s2 is at x = a, and, mass 3m is at x = 2a. What is the mo2 in 2-s)olv ms8eqn3mment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionl.5eich )rpp8zp9me; -up fx/mess 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 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 acceleracmreppp;u-e ) pm.h i9f 5/z8xtion of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis tb+l:y gihd2ls g8m,*/rs 3td-(zxsu zhought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 =d/+zx y2 m *ls drs,lht83-sbi:zu(gg 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 at one end. The rod is initially held in the horiu :c;ghz:, g*l) sfeeozontal position, and then released as the free end is allowed to fall. What is the angular ao)efgszchl:* e ;:g,u cceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to en.xh+fi :4w;onqoas7k+0. o p dj*xjbe a ring of radius 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 the pdio j4jxqh w0xe+ ao*; .:osnf7k.+nwheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrappe ytbxb pux-;hh- 88x)dd around a frictionless disk pulley of mass 7.07 kx; th8) pbxuhdy b-x8-g and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped arounf- ::hvzj qg8,tav1*omla9 df d a frictionless disk pulley of mass 7.07 k,ojgfaqt8al9m hv*1 :- d: zfvg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to stov7yw// xybhyu y,:b1pya*io9 goh2 ;cre 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 o,)zktev +c3 xr , 9a9fy2svgtbf $5.00 \; kgm^{2}$ 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 f ( u/mshjd-e.rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the he/u-s (d.j fminclined plane?

  A solid sphere of mass f07w)4*dwav 9h lkoks 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. Howhf7wskv0 *kalo4d)w9 high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m a v,vnmv1 jhms (--9cxgnd a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a verticag,v vm-( n1-m9svch jxl distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping h4iigtzaf (*8 mv,7)x w3ckgv down a 35e incline that is 7.0 m long. Assume it started from rest.g v i(v3 wmgacx4)fti7h, *8zk 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 changes by d,)nk u xb)xo*9/deh z0h) (qg :hpazw$20 \; kgm^{2}/s$ 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 inera*am8 jfb1 etu0pb :d7tia 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 ine ln9qfh :t lzde.-p5v77rdh8brtia off59e 7l.hndvt: rhqplzd8 -b7
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?