Angular displacement is usually2-x0nn wz9mho hfo: .k express in units of

  Angular velocity is expressebdk3o)bgd0 xbiy4dx lg 76wc,bb8x( wg,lu:6 d in units of

  Angular acceleration is expressed in p0oh p2:0vm6() ftx/ szzxzoh units of

  A boy and a girl arenz2 h5n.seb h0eoe.tmxd((3f riding 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 3s.((not05he e x.2bfz hm endthe center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a : *anqshq m8f-4qm+ow; wcge:constant rate. The boy is near the oute-gs:wf+ a:h n*8qm;4q cweoqm r edge, and the girl 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 turning at a constant9 7nl ),yx 6un u*xx);qhp)tj exowq(h rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greatxq ehh*w7,xu;nl u )xt(qp6x)oy n j9)er linear speed?

  A boy and a girl are riding ahhwqng5n083w( /di ak 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 centripetal05 h 8qw3anwin(h/gdk acceleration?

  A boy and a girl are riding a merry-go-round which is turncv1 +(voz9 llving at a constant rate. The boy is near the outl v9zv vclo(1+er 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 accurate c+phn/.cfvu j 9 l i-lgmw01b(stlm+- vp0jwnlic (hu.f1 9/gbcatement?

  Rolling without slipping o2ec yr0zn:.t/w /am xmr5t2u depends on

  Two equal forces are applied to a door. The first force is applied cyqz6d.*f u 0:mekm8xat the midpoint of txm0ye:k8q6um *zc f.dhe door; 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. The first force is aibb- bcb96 a/hqa7vn8pplied perpendicular to the door; the second force is applied at 30e to the plane of the dc -h7i qbbaa689vbn/b oor. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first f,:wer ny h7f3zet 5etnp9t t)m/tn b8o3up58dorce is twice as large as the second force. The ratio of the u)zeb t h:ome, n89 twdypt /t35 3trpn5f78entorque of the first to the torque of the second is

  What is the quantity used to measure an object's resistanc g:)a1xwbz q7de to changes in rotationwb)7 zqgda1 x:?

  Consider two uniform solid spheres where both have the samex4*a 5kewlx 2irbe y/, diameter, but one has twice the mass of the other. The ratio of the la * l2xxa bi5yekw4,re/rger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have 96h(dcs+ 2r ncl,4ul ldo5cclthe same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the uo2c 45l+(d crll6h,s ldn c9csmaller sphere is

  Consider two uniform solid spheres where one has twice the m9h +bx+i.v 3tehm:op09uvn lmass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the small lh xibe++mo. vu vm9309ntp:her moment of inertia is

  A uniform solid sphere has mass M13:ix npyt9sph6i*ma and radius R. If these are increased to 2M and 3i:pm*s39axy nt6hpi 1R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is appliet4 gbuvsbc4-20mx t0l44z ombd to an object, that object will

  The moment of inertiafcgedhq5ke)gnb pep)n7:nh/ 6 * 7 :na of a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energygn5ph :p kqe/*n7d6: cen)ge b f7ahn) is

  Consider a motorcycle of mass 150 kg, one wheel of whicha9hnmv*u0 v-jyt 0ta4. p9lcd has a mass of 10 kg and a radius 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 thevttp9d4 *c0.lanma-j 9 vyh0u wheels are uniform disks.

  Suppose a solid sphere 3ojjf cw+m;anl9 ervwg3t c8, 9na4k5of mass M and radius R rolls without slipping down an inclined plane starting from rest.owjvn3c4w9 n l cjar;fa,+m9ge3t k58 The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of ci 2ex.-pzur7rv+.o :qsrw w5mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline d7q5 v2rrc: s w-x ur+ozpe.iw.epends on

  "The total angular momentum of a syste//c7 wdi cniw9m of particles changes when a net external force acts on the system." This statemen/i9ccdw/ i 7wnt is

  In what circumstances can the angular velocity of systembf7-q;f6o 2jum8c(ci w o8yty of particles change withoutmwfy6 i8q;bt7u c-o2(fjoc8y any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictix(2gd zoe9dyftl. 7 g51vj /qvon which may be pr t(5xv/ ygo9z.1fd7eq 2djvlgesent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the /55k8 .(4p vu u1sdujnobswb iSun in an elliptical orbit. As the Earth moves close to the Sun, then which of the fo.inousj5( su8bp5/dwu41 bk vllowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pik*l+vav bnx(/oy8ez-vx e d5. rouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotation?.an-/8olvk(ed5xevy*v bz x+

  An ice skater performs a pirouette (a fast spin) by pulling in his 2g,hi+o;1b 0cm5 f4 dljog un-deiexrj2t(9 t outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotatioxjf, +dutn-d0 e42o hc;lt9jmgebr 21io (5ig n?

  An ice skater performip7d*hx3 hk :imd 2wo8s a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens tohd8 i odpim3:*hk xw27 his moment of inertia about the axis of rotation?

State the law of conservation of angulwb zbx6 wwr9-9ar momentum.

  What arc length does the c3 n upbw3*x4qEarth travel in a three month period in its nearly circular orbit about the Sun4bqcxn*u33 pw with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What diy bsv7rcrq-r(pvvc .n w1lop:g4* ;6n*;y xzbstance does the tip of the second hand sweep through in 3 minutes and 45 se.vyyqcon s;g* c*:-b1vr nzp;lp4(6 vb7xwrrconds?

  How many rad/s is 25 revolutions per minute equivale;r53pfik i * lgzvpo3x0i /dt*nt to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. l9ejbx/q75d xWhat is the frequency ofe 7l/xbj5dq9 x the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequenz-ghn6 ln m0 u(kjy6.z5oy(dvp49oz r cy of 0.40 kHz. The period of its rotation is6g-yn(mz4zz 96nlr5d ko(y uojvph. 0

  A phonograph record rotates at 45 rpm. Through what angle does it tg;2ds) d43l)rrbcz5guyaj1 vurn in 0.20 c rd1vaus)ljzgd)r3 yb;54 2gs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the ofk0et)s)3i ify (ct6w uter rim move iti e i6t()ckf)w30fys n 2.1 s?

  A bicycle wheel rotates uniforml3bcb t*k3zi9kemx t . ca0p9,lk 1cr)uy through 2.0 revolutions in 4.0 s. What is the average angular speed of the 3ucb*t.a)0kbrit9lm k9x3,e kc c pz1wheel?

  A bicycle wheel rotates uniformly t7tiz(;q ugcr9hrough 2.0 revolutions in 4.0 s. What is the linear speed of a poinit7 r z9;qcg(ut 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Tho4a0zwjx riujnc(j;w *frq9a 7c 6x1 9e 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 iw*w(n9oa x j r4;j9 76cuzfj0arcq1x 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 r53xh 5tpy*y h2rd3l qlad/s. Whxl 5y3qr y5lhdp*2h 3tat 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 length. If the motozdx: cg+;8hio6.f1c iu jf 9ujwu q/rvo,/ll/r rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of thcu/j 9c:ui f/rohz ;glulo1q,vf. x + d6/w8ije cord?

  A wheel of radius 1.0 m is rotating with a constant angular s6 : rry z0n;t dz8k0.mqvupo+fpeed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's rim? vyd+0 ;6p8ku0.rnqm:rt of zz

  What is the centripetal acceleration of a poihgb qxil:kw8 a7jh1)vz0knuot 54-j2nt on the perimeter of a bicycle wheel of diameter 70.0 cm whw47nuk0glz- ix jvh bqo 85t aj12k:)hen the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotat 1*n2(qckam o*2jhfw xing space station (r = 1000 m) rotate to prod(22xkf *1ahm jowc* nquce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat-t.7ljce5 x qg uy dqa-dz4, 2zuf-d(z circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by sta tf7d,udezzcd 2-- 4qj-(uyxq .z5algtic 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/ha/ 7 8uw(ivrp fos pe:1w3ea+s. The marfhe + iu /psw1e8av(3ow:p7aximum centripetal 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 ic, 6w 5mhbgs* g/o*h31gjrzr)dt 9fkrn a smooth level table. If the maximum tension thatk*m9 rf*gwj5 c6/1hs )g,3gdorbzrth 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 7mvz+weo / n jyfna+i)rz-e( .+bfc,srolls without slipping 10 m downnioy ( ,+emre-f)+fcwz .jn/v7azbs + a 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 constang:33mi67qabc qg/hc ft 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 h5ve25fpz85qu z1pnt 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-m3fo4m5yekym (t v*s4 t radius automobile tire rotate after starting from r54t3 ey4k ymtvmsf( o*est and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an anc9d xp3nd/wy(gular 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 constantu.)gijp0p qz, angular accelerationgz, p0jq .uip) of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reache:)uc2g 7a svo+qiv,sds88pna s an angular speed of 6.0 rad/s while turning through 2.qin c7sgsvsv)po 2:da+88,ua 0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformy 2madr:4qfd0 *mz*clhoa v vp87 b/1sly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates c1dym bza 02pvqvola7hr s/ *m84df*:in coming to rest?

  A wheel of diameter t;y 6 f/--mjc:)kg3d p zteygmof 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 mdc6myt)g;mft/ je y3gk-zp: -. What is the angular acceleration?

  A wheel of diameter of 684h(z+yt.k6p xhg: nqcau9ag m/ k3z ,p.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How lg4k/+,aqpzh y zam k(nh .9xcu 3:pt6gong does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 360c9: cdeuv6xi+ 0 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before com6ide uc:+vcx9 ing 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 tig b8o71eyb. gkmhtening 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 wrench7beby.1 mkog8 ?

  The bolts on a car wheel require tightenigt 9wtgydvo, v+n5 sp- :q7gp7ng to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forc-wtggnopp7qvty g+d v : 9s,57e applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner/ x i8r9la-lkg0mqp*2/ hrchqxfi/r4 tia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass2;x v4 ogk z/ea:kn4sr m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What zog v :ks4ek/2rx;na 4is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionlesdx fyn 9p8 9o(z.lqvx90n.ukis axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N y(0x9vkn xf .onl.98idp q9zuto 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 a frictionless axi0(er5zd40nz ff; :vxkl jx+tvs thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a f:x4 nvej0vt +f 0xfzd5; rz(lkorce 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 hing. *m4z6. lci hj;g(oat0lydb.i0poh fed at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is rele0bll f4...z;acjih0*y(doihgmp ot6ased? (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. Neglecta.9m2depgc-kp 0dz ybcd)ao5fgj+,zgg)/ i7 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 wheel achieve, assuming it rolls without slipgj aa.k7zp/)md-9)g,df 5 pcd z2o i0g+ebcgyping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless dxu ( 5pl+iysnok 99d1(kakxd2ie-c 2 disk pulley of mass 7.9xxd( 2oys2l5e9k upd ( id1cnki+ -ak07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapp:q4l6ogap vlj (s9xnd3h3 zf, ed around a frictionless disk pulley of mass 7.07 kg and radius 66.0 f3pzj9g6v qahls(:lx3o,4 d ncm. What is the acceleration of the mass?

  A rotating flywheel can be*y/-k)ic )azylx hft.w-h 2ry 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 inerc/o952ijj b* n)jj ex(7fiy dwtia 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 st29 f arsmbl1k -r*9scyarts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottbk-cry1fs 9a*2rm l9som of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls:o80 miikk h+69rv5cpp0 fafi with a speed of 10 m/s. How highi mk+ir ai0kp59hp f 06c:o8fv up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.2, jxbzrix5h0+9*cc zm 0 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distar5cm* xj9 +,chz0i zbxnce of 3.0 m?

A solid sphere of mafy11v33x p arxss 1.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. fyv1x1 pa33rxThe 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 mo takofm)gf5, ;mentum 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 od9,t (ka 2icok(0dq)x4k 6mbtdcha7 sf inertia 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 radgqky vzb;z1(0:xjb+j/s with arms extended has a moment of inertia o+jvy:01k bjzg( xbz; qf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?