Angular displacement is usually express in unit+pq .yp:rwt y(s of

  Angular velocity is e uha(zkhjm/5*f)xi g9n)hir 9xpressed in units of

  Angular acceleration is expressed in unit6v ys1g6 k+r(7rx xls5mqvp; xs of

  A boy and a girl are riding on a merry-go-round which is turning cded /p.9 s-9dexdyv 3.fp+ p3nsy0yz at a constant rat zf.ye c9sdv dnydyp./93+x03ppe-d se. The 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 whiykb capu-i;k- tzy5;+ ch is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Whok-cb+ykap zti;5;y- u has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning atst)9e 6/cr7 foty*bmy vb u3-t a constant rate. The boy is near the outer edgte/tcr-b 3 yv7tfs9mubo*6y)e, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merryyn / tc3yx.* ovlk(p*g-go-round which is turning at a constant rate. The *l vy3kt /oyg n*(cxp.boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ripp+ixr, )g ab.ding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, whileppr.ab,+gx) i the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which os6+ -6y k.:dx j+o+vtdk0om6tvcpxwgf the following is an accurate statement top d otg-:+k+xmxwyvv6sj6 +kd.c60?

  Rolling without slipping de+rxxu- vp9epd +y1 w,zpends on

  Two equal forces are applied to a door. The first force is applied avl 4qe,y a,j;g3i+sjh t the midpoint of the door; the second force is applied at the doorknob. Both forces are applia; hjiq,l,yv s3 e+4jged perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. 5 a pyuco,7gd5+p-afw The first force is applied perpendicul-w ,gf 7+5o 5cpyaadupar to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applii+)rl+ 4ifopo ed to a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the to oif+4l+)pro irque of the first to the torque of the second is

  What is the quantity used to measud iex-7*bznm tt9/yb)re an object's resistance to changes in rotatioyb 9d7zt)i xnb-mt/*e n?

  Consider two uniform solid spheres where both haveqo8 +o imyt*zl-fm: 1y the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaf+18mlzyqmyi o-* o t:ller moment of inertia is

  Two uniform solid spheres have the same mass, but one ow;u du5-vkl2mj2tt.e *cg3 rhas twice the radius of the othe-.3*lutvu k2e2owtdc r5 mg;jr. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where onepbw(hay j:tr.j,:8k 7a8h,evt ydl 3p has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller mpe3j8h rya7 lpbathkj :w:yv ( ,dt,.8oment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M azmx/ek e 7k:*e2 vi-zl ,m(gqcnd 3R, what happens to the sphere's m(i z*z-/xeg,:c2kklqe7mevmoment of inertia about a central axis?

  If a constant net torque is applied to an object, that: ,tx brr vi3dz; cva-mb0 ob.6s3gsk* object will

  The moment of inertia of a solid cylinder about its axis is given bytxzed x:0(e r; 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinee0 (e tzx:dxr;tic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has b d* iqki7x33oa mass of 10 kg and a radius of 30 cm. What is the ratioxqi3k o3bd7i* 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 wita2 zd:ew 1o;nyhout slipping down an inclined plane starting fr: we ;dozyan21om rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere 2;xqx kvk;a;d of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom okv;;q 2xa;dx kf the incline depends on

  "The total angular momentum of aiu 15y ;tvsty( udx6d( system of particles changes when a net external force acts on the system." vyy u(5d(; uit1dts6x This statement is

  In what circumstances can the angh,0qdveq vweu s 0 upu-1rm,*5ular velocity of system of particles change without any change in tv u,1u5qv-, r0wh pmd ee*uq0she system's angular momentum?

  The Earth orbits the Sun in adbu5w.m2 v:0ibhaxr, n elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentrbh 5vxi, db2uw:0 a.mum about the Sun?

  The Earth moves about the Sun in an ello b a74o8s9e:k4sn6kvj rrz8 liptical orbit. As the Earth moves close to the Sun, th4oez : jos 89v4687 sknlbarrken which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outsbl4ckibr(,/7 /24ti9gnj hmbrr4 kastretched arms close to his body. What happens to his angular momentum aboumk(ita/k nb47brsi/cg2jb r 44r h9,lt the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outsth;x*)bsv 0y tzretched arms close to his body. What happens to his rotvsb)ty h0 ;x*zational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullinsfg-s89d lshc*cnyuq r -9fc/6 swt12 g in his outstretched arms close to his body. What happens to his moment of inertia about the axis ot 2ccsnlycsr g u*-f1q9 /9d-68sfs whf rotation?

State the law of conservation of angular momentumsep;vms 9lqw(/90 pdh.

  What arc length does the Earth travel in a threvou2kw ,x er*-e month period in its nearly circular orbit abour *kw-xoe2v, ut the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lx010zb/ wflsey q6r. bength of 0.30 m. What distance does the tip of the second hand sweers.6 f 0lbexw/by1q0z p through in 3 minutes and 45 seconds?

  How many rad/s is 25y -b+8f7*ltd:*yikqsdh j (*onzz v4x revolutions per minute equivalent to?

  A bicycle wheel rotates uniformly throuwyjd xf9xb /59gh 2.0 revolutions in 4.0 s. What is the frequency xx5 y9b/wjdf9of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. t.bghnz-n3g3 v jsbg-(:nu 2jvt/ j,n The period of(u3njvsggz-. t -/2t j,j3 gvn:hbbnn its rotation is

  A phonograph record rotates at 45 rpm. Through what ang45p ln-y:gs+x*()xho- fel2 eptg ltyle does it turn in 0.20 s(-fp2n+h 5*ptg e xoleltx:4lgs- y)y?

  A wheel of diameter +99m:c r xtmhw26 cm turns at 1500 rpm. How far will a point on the outer rim move in 2.1 s? 9wxcmrm9+ t:h

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wh9ldpw g3e .uewm3b yb*:bv1(oat is the average angular speed (blv:dm3.b*9 oy uw1g3pbweeof the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What v0lt6*yurwi 1 is the livu* 60w1rltiy near speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distan 2u7a4qsidgp+ce of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 7s2 ad+u4g qipm. 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 is rotating w-so teo k mriyzgtc1.5l96e9x 9ac.g1ke6o5bith a constant angular speed of 2.0 rad/s. What is the linear spt1tck 9 s5bk91ey m 6ceo-gozagoi 5e.96.lxreed of a point on the wheel's rim?

  The cutting cord on a gas-pow17ub0d9u d qpsered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s,s q1 d9dubpu07 what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angula*vt*n3 i serq4mn2.bgr speed of 2.0 rad/s. What is the centripetal ngrne *qi.3smt2*v4 bacceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on tdk : w7t,e0dia,t 9xonhe perimeter of a bicycle whee :n 7wdotx,di0e9ak ,tl of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute c(x:m oazml-p42f mw) .+2 :rasejbyq(rpm) must a circular, rotating space station (r = jxm fq+yz:aea(lw:bc2p)s o m2m4r. -1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve 7w52 7qju7),h 7ltjumjsed kvof radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fricj77wv lju7k,u5 2emj7st dq) htion) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flati(.xk) za yb:d circular curve of radius 50 m with a speed of 20 m/s. The)bx. iadz: y(k maximum 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, att 4;)m7hhg7r ryx3yv1+em lpreached to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the strvheh;r x73)7myr e1 ymprl4g+ing 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 rolls without slipping 10 ei /.7kc wmtbqgc9+j bz1 t vb-c8jq:.m down a lane at 4.8qc. /vt bcewb1.b+9:qtcz j g-7kimj 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 constant angul49i xm ,y0pgow wx)f3x -f*fcnxsd /:var 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 ay-sjidfwod 4 wz.: l,/*c veu2cceleration 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 ;pqo0x d,+qc lstarting from rest and accelerating at a constant anguopc0;qq+d xl, lar acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at res3g l9gb7) nu zp2qdfr9t, 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 decexqfiwkp n+zr3dm )rn j7)7/ ,gb+jm9.- ztjyolerates with a constant angular acceleration o9 dm q). )mb/kt,yn77zprfjr3iz+jog wx +-jnf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed v w6hfei(3o5cof 6.0 rad/s while turning through 2.0 revolutions. What is the avera(c6e 5hwof 3vige angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows downv,28*/9dmgu .gqs iysf uu2 ji uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number 8/22u9iq i mjgu. dfs,y*ugvs of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformlio..tuysm+z5ivw c3d* j .u :py from 8.40 m/s to rest over a distance of 115 m. What is the angular acced* p. t5i ui3. us+v.yw:jcozmleration?

  A wheel of diameter of 68.0 cm slows down uniformlfzg:d) al0m,92t s bvjy from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to coz0atf29d gjs :)m,l vbme to the stop?

  A centrifuge in a medical labe)m4cla qp5/t shgb2, oratory rotates at a rotational speed of 3600 rev/min. When swiq2,phcagms5e/l) t4b tched 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 require tightening to a t sph;jrwj d/+*orque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicp/*sh+jrd jw;ular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If sv:xet1, lt74 nettfo6zdg- 4 a 30 cm long wrench is used, what is the magnitudn4gxo:e e,zf7 6l-s4 1tvtttde of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inz:o d-lfp7-jy;u. xox ertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows odwk8hj8p v )ay9v)-d: mass m is at the origin, mass 2m is at x = a, aodjyh v88w )d) -p9avknd, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought the1f5(*intus wj 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 Fij*wn(5 fsi1t ug. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionlesutj))/vddu ; v9+igpy s axis thought the cen g+p/ t)u)9 uvi;vyddjter 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 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 nk+jtol nbxz-uj)p* 3e *9qj. 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 released? (The moment of inertia of a rod about one+jt9qn* z u pj)ne blx*k.j3o- end is ML2/3.)

  Consider a bicycle wheel to be a ring of radiu -ktpnq b*)3dxs 30 cm and mass 1.5 kg. Neglect td*3tq )x-kbpn he 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley o(vuwvn hdzh)i).3des0h u (y4f mass 7.07 kg and radius 66.0 cm. What is the angular yd4n.vve0(hhuu3wh) i z)(sd acceleration of the pulley?

  A 1.53-kg mass hangs 4-gbdhigt xq . r0xy+.b2cvo/n uh8n3 on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is thht3 8+qc.y42bxbnvnguhdo /r0.gx-i e acceleration of the mass?

  A rotating flywheel can be used to store energy. If it i(.2bvqpplo14 e if-n cs 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 xt5ra0c kky-un7g*p,lbage 3 y*-e6r $5.00 \; kgm^{2}$ 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 rolls x l-.,2mine*hg9in gd5ksh p-without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the incs-xepnigg,2h5k l*-m hin9 . dlined plane?

  A solid sphere of mas /cgqdi3: ch/, k(7kyxxdl.zds 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to zkg (dihy /3dcq. xl/7,d kcx:rest?

  A hoop of radius 0.50 m and a massw;i;6id7gc uo)m4/drs-xaja /a)m sp of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving a ;s-ra 6cd s/jax)p4mu7)dmgaw/ io; ifter dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5k.(xy.d6 ,q y6xd 25jcdotd fg kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The mo ,dg(dcxdtjq5 ykf .o.x6d y26ment 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 mom/n ,+pjk::jk )xytjpventum 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 of ineru(qc rwj9 edf: wtmd-h/dzc o92)*+ nbtia 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 extended4 /a7pao11 vmfchku -j has a moment of inertia ofuafa1-m h4pvj c 71/ok
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?