Angular displacement is ui: s. q:n4bdye0r/jjboql13-hlw3rj sually express in units of

  Angular velocity is expressed in units qh p-vi,cf0ams;tpn 9;n7ba 4 of

  Angular acceleration is e jpj5- jn0yk6expressed in units of

  A boy and a girl are riding on a merry-go-3jw3hqbq4; +l,ia a, ye+ svdzround 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 dwbji3,d3,zq +asa e+h;q v4ylisplacement?

  A boy and a girl are riding on a merry-go-r5t(cl5mmw 6dalb o)) wound which is turning at a constant rate. The boy is near the outer(wlladcwm5 5om 6)t)b edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are ridihj 4wm:lq8q-+,-zrv d hg 5koqng 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 l4m-oqhzqwk gqv+5-,8dr lhj : inear speed?

  A boy and a girl are riding a merry-go-round which is turnin (yc e-m r/l50qzem)zxg at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater cexze mq c)rzly5-(0m/ entripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant raqllmk*;wyvi;u1r m22 te. Thmivr*;luk w21mq2; y le boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whiy.v*e,n s;v2 d7xmatr ch of the following is an accurate statemen.n ,vxvr2myde7 ts*;a t?

  Rolling without slipping depen48y evokk1 *me vl))5k3e dcosds on

  Two equal forces are app( 4b 2bsau8;nz,kehkh lied 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 applied perpendicular to the door. Which force exerts 8ksh, hzub(kena ;b24the greater torque?

  Two equal forces are applied to a door at the doorknob. The firswgj(zhe o 7fi6d2o8 g3t force is applied perpendicular to the door; zg wg83hdeji7(of2o6 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, pw *fi 1*pix5qm+nczt,;ra9ww d il:ono 1sp -2erpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to tlcr2wa,-too w +51w pf*z;id 9pn*sm xqi:i1nhe torque of the second is

  What is the quantity used to measure an daxf42j xp)b*object's resistance to changes in rotation *b pdjxf2)x4a?

  Consider two uniform solid spheres where6 qt28vja +,soz3g vuh both have the same diameter, but one has twi +uj3ht2zav vo6gqs ,8ce the mass of the other. 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 twickc +g+xdqrk 11e the radius of the other. The ratg r kk+qdx11c+io 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 twice the di5 5zk cxwjr;3iameter of the other. The ratio of the larger moment of inertia to that of the smaller z3i;kxjc5wr5 moment of inertia is

  A uniform solid sphere has mass M and radius R. If these at(kh qwt2k2 sq2 9x0qrre increased to 2M and 3R, what happens to the sphere's moment of inertia about hkx(2 tkqw stqr q2209a central axis?

  If a constant net torque is applie8mc0urag3eq /rry7l,) ehsh : d to an object, that object will

  The moment of inertia of a solid cylinder 96dbogyaei8fd16)7kdhg x 7eabout its axis is given by 0.5 MR2. If thdkh71 oagf6dygb ee6)9 8dix7 is 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 h ult1+b m-arb3neht 05a7xfx7as a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinet13xfln+ext bm abautr-70 5h7 ic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphe st 7p7yw8- xcvab27lzre of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of 7x8a -pw7zlby ct27vs the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls wii;l6d41trf+qk ov,- a,uo d jfthout slipping down an incline6,j+1o tfdkaiuvq- do4;fr, l d plane 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 ne gf4khprk3 o90t external force acts on the system." hkr ogkfp30 49This statement is

  In what circumstances can the angular ve 1p1-xt-i edbalocity of system of particles change without any chan1ab p 1xdie-t-ge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictikl/g5ll *5puno h 0*, jnrq fsp6m3wz-on which may be present. Whapn5,ul 6jlqsnw/f-l k o30hgm 5p*rz* t 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 motmhz0n92q :,rmvtq- vves close to the Su9ht vrmn,q 2 0-vt:qmzn, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin), 9pu 8q1)hvjlaryhaizww7( x c imo9r1ku/7) by pulling in his outstretched arms close to hryacov 7ihj17, ( p u)/a8ui)wzkl r9xh9wqm1is body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his oug r-b1 ;t* qs.vygfl0(i3rmie- * swb6y xwk7ststretched arms close to hiy ex.b-67;skg-wliq*tvsyrm0bs w g* fir3 (1s body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchedzgl vf qn c8,xc/509pf arms close to his body. What happens to his moment of inertia about the axis of rotationg0 ,x5vcp/lqffc9 8z n?

State the law of conservation of angular mome*dskm8xyx 2u)ntum.

  What arc length does the Earthjzrb7d,s31 yx travel in a three month period in its nearly circular orbit zbdj,7ry1x 3sabout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of ay8op-7prt(lm y s5wte. g )9uo clock has a length of 0.30 m. What distance does the tip of the second hand sweep throug)g5ty y97(osppoe t lru.8wm- h in 3 minutes and 45 seconds?

  How many rad/s is 25z6 u p.l9lkyj1 revolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is t4 bo8ksdnlhvta(k 7/7 he frequency of the wheel's roo(84l vt h d/sknakb77tation?

  A pulsar (a rotating neutron star) emit2t3rg acjp jn8q2 a*muz,v+ r1s pulses at a frequency of 0.40 kHz. The pejt 2* jg,arp3 m1+v28q crunzariod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle do;,dyroyws)x7c-a 5ta es it turn in 0.20 t-wcr7s) aya ;doxy5,s?

  A wheel of diameter 26 cm turns at 1500 rpm. How h5mg j s66;ms *mu:zcav1is8z far will a point on the outer rim move in 2.1 s?ms* hmsz sv8zg:m1jau;65i6 c

  A bicycle wheel rotates uniformly through hj5/omo*ooy i bvr,xz68::34hurvjz 2.0 revolutions in 4.0 s. What is the average angular jox,j 8uyo6 bmoi:*zozr/ 3h5vvh4r:speed of the wheel?

  A bicycle wheel rotates unif4ne;valj 8-tg gzkw d k 900-;qz,qciaormly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 ;tkanqjq0-;4d zlkg8ga- ivw0, 9 eczm from the center of the wheel?

  A cable car at a ski resfv-pv8m:zn hq3 o/+hsort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Av-3 z8hsv:/nhp+qm o fssuming 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 speed of 2.pw*b 32e vj8puojoxrru-2k (tzo8 ca a0wj.05 0 rad/s. What is the lineart-cwbk 2oor0zj 8x2p jjuve 0.r ou(*a5 3a8pw speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutteat s38rcjsgz wvciy0: r:k (,;r is 0.16 m in length. If the motor rotates at the rate of 0rr (yi 3wz;8gvs: jc,a:stkc20 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 of 2.0 rad/s02cpd;.p hpaq. What is the centrp.hp;q2 0c dapipetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeu2e7 e9 az6ti5fqa) pbter of a bicycle wheel of dpz)7 e aaf65b2uq it9eiameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rom6 v73 bhlg 6s3ho9tw:s/xr tmtating space station (r = 1000 hg6hlt63sr /m9tm :bswx7v 3om) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiatingp(pn)za q q jhrtg5,k1f;l)84cgqz o5 a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by staticqp5 hgo 1pclg 8rzat(kf54)q;z ,qj)n 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 20au sibctowk2 n5.;4s- m/s. The maximum centripetti-b.5u;n akws24o cs al 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 i 5/aqyzd6h sg,;sd +ydn a smooth levelzhdd/s; a qgs5+ 6dy,y 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 9.0 cm roll fub2dp* 82ptns without slipping 10 m down a lane at 4.3 t*fp bd8u2 2pnm/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 wibcfwvcn;c7 kf954d0j9;zk4 k - dbp nhth a constant 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 constawmpuj2pmp7)nc3s6 p6 dnak9m* :g4nznt 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 starlquu ( .a fb,zxy )qn-0zx4sv,ting from rest and accelerating at a y4uxau f0,lzs, nzqxb q.) -v(constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and hasjk5 al7sx4 2zhr:nudy9wy 9y2 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 aax 5d,s6hv:mg constant angular acceleratigahms xv,d 5:6on of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest a6y4izw r i el5uo*8a0lnd reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the averageowi *ly56z4l8ae 0uir angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slowsxad+ sev ,uu4r/;gx)v down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates/+ au4r,guvv s dex;)x in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to res9hdb 7cckmh,2ofr (d rl3 2-nst over a distance of 115 m. What is the angular acceleratihf,d2rn7cchbdm- s93 (2olkron?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to hb/ 9vrx28yi u+ia7 wprest over a distance of 115 m.xw p29vi u7b+a/yh r8i How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational spepg4gdd8s.8 ebed of 3600 rev/min. 8 .g pbsd4egd8 When switched off, it 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 reqf)lb0fn u7;hj 2o* azjuire tightening 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 perpendicular to the f nalh0b o7u2*jf ;)zjwrench?

  The bolts on a car wheel require tightening to a torque of 9of-u v b4(uctg12 tjt:0 Nm. If a 30 cm long wrench is 41ft(t :bjvct-ou g2 uused, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia 4a; ei:,rk itgzjr,4q $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modely1 4kf ;pbjab03 4pxvr e+ps15dw rx)wed as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What isa xk41jwvs3 d0pf)px5;br 1ebr pw4+y the moment of inertia about the origin?

  A solid cylinder of mass 10 kg c6lyh/fp:9 qxn- pu;g is pivoted 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 wrapped around another section of radius R2 = 0.50 m exerupc pn9gl-:x/ ; yq6fhts 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 frictionlesnpr4i g4ay ,0yk2 8zsuqa.ei:s 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. How many radia zu40 p,ga82y.eks n riaqy:i4ns 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 ini+xll 5afdz :x,tially held in the horizontal position, and then released as the free end is allowed to fall. Whafl:5l a+z, xdxt 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 )v u.5ktma lm3and mass 1.5 kg. Neglect the mass of the av53 tuamm.) lkxle 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 wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless dis6ru5cj/y ye* dk pulley of mass 7.07 kg and radius 66.*j 5ry c/deuy60 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk :sm: ,,mkezpk pulley of mass 7.07 kg me:ksz k,p,:mand radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If i4g q5zn2dehiylj 5xkk2o;3v6t 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 :y u t+; vzu. 59er3hhaq:mrvg$5.00 \; kgm^{2}$ 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 radq 2 qee-qjssw 94m;wp8ius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. 8q;m-qw ej9ss4qe2pw 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 with a speed of 10 m/s.c ljp90d5x yq; How high up an inclined plane can it climb before q5l yj px90d;ccoming to rest?

  A hoop of radius 0.50 z5vl bnvlmfj)e9b.s 49*n4 py m and a mass of 0.20 kg is released from rest and allowed to roll down an incline9yv f.s b e59zjp44n mn*lb)vld 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 cma2yh 5o8twquzd 2( /.(ivezq s rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia o (a5u2hzd8t.y woe/ivq zs 2q(f 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 changesp9jg:gjt-/ko 0n i4fm 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 inertiyb* vp997 i;haa/c5lgl+ymqja 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 ob9t*v/5 lor1 ;qpn mxif inertia rqt m*o/pnx b51l;9 ivof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?