Angular displacement is usually exkebh e37)qji-koh 57 iy2;wgvpress in units of

  Angular velocity is expre0paicz a2so(k y3 wyr)2ft rd7)v+-bbssed in units of

  Angular acceleration isyl63) h 0:lsytwgf6gs expressed in units of

  A boy and a girl are riding on a zw:l9.zci8p umerry-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 angular displali8. zwz9:uc pcement?

  A boy and a girl are riding on a merry-go-round which is turniv4r43brt m jql94in2gqlpe k( nzh5wzy81w-9 ng at a constant rate. The boy is near the outer edge, and the girl zrmv 14tb9z 9w 4yl ip5qrhn -g3kln(j2e8q4wis closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turningle72 b4rve( jfze 0h6c at a constant rate. Th2 je47h0e6elvc f(b zre 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-go-round which is turning at a conscd/3m8i1l tk;t jdjq,tant rate. The boy is near the outer edge, while the girl is closermct t1/lq,8d;k j3jdi to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which ii9ufnmg b-(.hs1) vbis turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential achb b1n -um)i( svfig9.celeration?

  Consider a rigid body that s:w:wud1psp(a- cgye j.je4d/u 1.ahis rotating. Which of the following is an accurate se ud.s pj(psh1 jyace.d1::au /-w4wgtatement?

  Rolling without slipo/i00d8iq vc (6pu kzuping depends on

  Two equal forces are applied to p/j snr/-g(h ia 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. p/ snrh-(gj/i Which force exerts the greater torque?

  Two equal forces are applied a0c8wv o4c.n rp)z vm/ztg+0pto a door at the doorknob. The first force is appl nw p+8p/0.v)gcz azto4vc0rmied perpendicular 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 applied to a doorknbjns00;6/i*g cjsi fb ob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the secoji *6g0; bfbscin0 /jsnd is

  What is the quantity used to mesg26w( -n2np ilnf.l l-v-dmgasure an object's resistance to changes in rotatio2n-v-l2-nwlsflp6ngdig .( m n?

  Consider two uniform solid sph)*::9 tynot;fy)r cpi bfin7+ ln3qh geres where both have the same diameter, but one has twice the mass of the other. The ratio of t7 )l9tnf:nqf+: phyyn *ot )irc;igb 3he 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 the radius of ft6l 6,ar wcrp3)dam6 the other. The ratio of the larg )dm6a6l,atfw 6p3rcr er sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid u*ix/4byul3 rspheres where one has twice the mass and twice the diameter of the other. The ratio of the larger momentxuiu* /3 4bryl of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M ;flh/yze-;(lv6nw cl*,r xm+7 kuk a( z 3lhzvand radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central a (3zkmlxhfvwz6 l y7;+ e(,uc*-lkhv z an;rl/xis?

  If a constant net torque is aogt fy84(4ct 8;vqxfxpplied to an object, that object will

  The moment of inertia of a solid cylinder aboutu31a 7h l:mpav its axis is given by 0.5 MR2. If this cylinder7a lm3p: 1auhv 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 has a ma.zuozmd iwq*w (,dwp;0qq2aj z *e/l9ss of 10 kg and a radius oawo.qqjmil 9/qd 0z u(;w* zp,*ze wd2f 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 yg:l7)pd:g *tp x13wckk caz ,R rolls without slipping down an inclined plane starting from rest. The linear velocity of the ,cyztkp c*a l7 :xpg3dk:1wg)sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and 5q;/(i( qesjibb4 v.wr 0 jgz7*xghdxradius R rolls without slipping down an inclined plane starting from rest. The angular veloce;4jxiq*gdhw5.jb (x0rzi(qgv / b7s ity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system k9),u4y4 waqk tr2 z 2fxuxw(uof particles changes when a net external force acts on ) 4wuat4zykr2x (,k x quuf2w9the system." This statement is

  In what circumstances can the angular velocity of system of particlesjnob(qh( hzi4 1l*f2 t yvp6rf990 bdg change without anyzv( ( robnt0ib94*h9 pyjq1 fd6f2lhg change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit.)xctw0m8o3elvxlu gd6;:x8 lf ei+3k Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the 8xcxtm)gl 33k8;l ueld0+f6:evox i wSun?

  The Earth moves about the Sun in an elliptical orbit. As3j38kr vbkwr 7rl) n;i the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the E r ;3nvrklrbi7k3w)8 jarth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pul+ igo lnoik310ling in his outstretched arms close to his body. What happens 13iookngli+0 to his angular momentum about the axis of rotation?

  An ice skater performs a pir9pw qjp 68+qwsouette (a fast spin) by pulling in his outstretched arwsq+8 wp9qp j6ms close to his 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 g6 79aqda zeb/ q0ctsh;o*vq 6vv5p0k his outstretched arms close to his body. What happe sv7e0bh vdq5 /p *g oqqct96vk0z;a6ans to his moment of inertia about the axis of rotation?

State the law of conservation of angular momesoo c4 bd:z y9o,c9(a)g1wfnhntum.

  What arc length does the Earth travel in a three month period in:-i60*1jbe,ku0y okq ajezg t its nearly circular orbit about the Sun with a rou6k:yqi e,a-0 jb1*kgzje t0adius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does /5v3 i+jd- )d.s fercyng+pxf the tip of the second hand sweep through in 3 minut d pf)+-+vxe fj.ynr3i/c 5sgdes and 45 seconds?

  How many rad/s is 25 revolutions per mil gs: )j ;n1orz(1kukipn0v:bnute equivalent to?

  A bicycle wheel rotates uniformly through 2.y7 b)4 h 9xdnv,qvs;gq0 revolutions in 4.0 s. What is the frequencn, gq7qs 9yb)hv ;x4vdy of the wheel's rotation?

  A pulsar (a rotating lv. zdjimpzn5 )9:x m-x0c4goneutron star) emits pulses at a frequency of 0.40 kHz. The period of its rotatipx 9. d0vzzmo:mc-54j ix)n lgon is

  A phonograph record rotates at 42kjajr ,-xao7 ;zskrk4zc /o+5 rpm. Through what angle does it turn in 0.20 s?xjako4z;o c/r,rj- +s kzka 27

  A wheel of diameter 26 cm turns at 1500 rpm*z 56px .c,)ljjqxqj0bcjn s/. How far will a point on the outer rim move in 2.1 )bp s .5xz,j* jjq6/q0cclxjns?

  A bicycle wheel rotates uniformly,ux vnvlf-zw8 aki ,4p145p x5 1 /gbcyh;idtu through 2.0 revolutions in 4.0 s. What is the avera 14v i,hpx1cygun,a-zw4k8f /v5id pt;b l5uxge angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What isw;,g *5 4zk8y x*kh l ka-a4uwutmdmy3 the linear spee4a yt, 8du lw u*whxkkzm5-y;g*3mak4d of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carp +r4 qy5s (dzv;fqs2yries skiers a distance of 6.8 km. The cable which moves the car is driven byrfqd 4+ssz ;yqpv5 (y2 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 is rvadrz( ty,8z.;mx*i yotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on tz, vrxmad8iz(* t.y;yhe wheel's rim?

  The cutting cord on a gas-poweredxx e2 kdls;b/zx)o)ud 9lpe.s c:b v.: weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of ebz.k:o): d vb x;2x e9/cs)splduxl.the end of the cord?

  A wheel of radius 1.0 m is rotating h-2pzm2gyl wxy :8qsa8(dfm+ with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel'sw+gy22 s pxd:m a8y 8hzql-(fm rim?

  What is the centripetal acceleration of a point-fsl9z 7p rrl84+pvmf wo6wk+ on the perimeter of a bicycle wheelw 6vf7plsprm -k +z9ow4lf+r8 of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space 3 5 p,yw/zycxhstation (r = 1000 m) rotate to produce an artificial gravity 5cwpyh zy,/3xof $9.80 \; m/s^2$?

  A car is negotiating a flat circular cul,ven wqyd1xf; j9t:1rve of radius 50 m with a speed of 20 m/s. The maximum c:l1dj;qt1,n fxy 9evwentripetal 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 6x w ,;nxn-r;ii,0rj78yu ysn j)ggglof radius 50 m with a speed of 20 m/s. The maximum centripetal force (providinrrjx8n,y jwg inuxy06)l s;;,g7-ged 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 z (sr997ufuhw(jcgx;0.750-m string, is whirled around in a sz f(;7ruxcuw9j9 g(h smooth 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 9.0 cm rolls without slipp; yufs9)r agv(ing 10 m down a lane at 4.3 m/svru ;y9g a)(sf.
(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 b(dg :eoi.knq; 68a ydk2ukul0rvv-)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 6feybjq)o2k1 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 rotafo3sm ymt- ;.k : scpdz1wi38ote after starting from rest 3wc: om.1; 8yzf-p osmt 3isdkand 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,h, gmkqwp6e+zcnsbu q /4:s+ 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 abxpo ++dka -oe8xg (o. constant angular acceleraexo.gd-b+a8p( ox+ kotion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reach*)a x755w(b /fxa ninpis(gdyhyx 0s2es an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleratiob)hanyxix(wf ( 5 7*05xdsai 2snyp /gn of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 mpslu 9hs1m-/b j2on7l /s to rest over a distance of 115 m. What is the total number of resnupm 7l lohs j/9b-21volutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s 6ijl8,vx+k2pxw8w mu to rest over ailu+2vm 6 wk8jp xxw8, distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows dow6do x tgf f/dw4p9s.+qe;*wuhn uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the w/;po +w*guqdh4e wd6.tfsfx 9heel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rdrpxcl h+* ))wotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at +lxd )h wrpc*)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 6rh)0; nbp8 ooqniz nsc /-e*t6r:vt otightening 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 wrencpn v6;6i/- sh8nooe0r:t*zq)t b cno rh?

  The bolts on a car wheel require tightening e qll18skuz +f3tot.: to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when ltqf k8t:e3o1 sz l+.uthe force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in gtqis zz6ax; 6+8hdj5ertia $3.00 \; kgm^{2}$ 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 0 6-jjsv*ljv*mazedrng 423 .j qw+wi the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia 6i4d sj.*e-2lw3+q znmrjav*jgj v0wabout the origin?

  A solid cylinder of 8pton fnxq3+hg+o)c/adr5x 2j q h12qmass 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around thf2r nn5qdo2/ath+gq1c) h+x j3p8o xqe 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 acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted aboub i54ba (c izv xyot5;9fz;za.t 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 exerts a bi. xf 5a9zz o aci4b;(tz5;vyforce 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 b1a;ytt 3 tai04wta- whorizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is releasedbta1wtat04t; -3ay iw? (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 mapu;-d xm,y;l9a 9woavs c 9 873rva/pnn:aetrss 1.5 kg. Neglect the mass of thev ncrs;vda-9,n8/;:waa9olp 3ayme x7tu rp 9 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 frictionlesbxm*sz) b96-x*tcl ff s disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratioxs*)tzb cfx-9*blm6 f n of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a ):9mkfu9* ejnwaoov 6frictionless disk pulley of mass 7.07 kg anunw k:*6v of9)o9emja d radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store epcjl.f/ 7r6d nnergy. 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- +6t2wr d:jyda bk5h i3+;btlg-j nhj 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 an 6*vk,gu3bd -r5hyulx d radius 0.010 m starts from rest and rolls without slipping down a 1.0-mk6 ug bv*-5luy3drxh, 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 with a -) papd p(/nk 8:mlupnfi(4q ospeed of 10 m/s. How/ a uppmpod:l8)(-nqpi kn f(4 high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg isyd1gn /7,w wss released from rest and allowed 7sw,1dw /nsg yto roll down an inclined 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 cm rolls without slipping downas: n(s: t/whndilc:9 a 35e incline that is 7.0 / :(s9t hc naswdnli::m long. Assume 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 moo cq kut-/ nu)zv(kq 1r4-5*uwnt ra9zmentum 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 hd)z bv;b8 :ssof 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 rm-pxg3 ;zz r5pad/s with arms extended has a moment of inertia p3-xg rmz5z;p 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?