Angular displacement is usually express in uni ioy6ktg/ w6s)ts of

  Angular velocity is expressed in uy; *ybiz6eyk) 52 eyep6jnmq*nits of

  Angular acceleration is exprkp l;c 9tq6u8k lfu3trt;p(:uessed in units of

  A boy and a girl are riding on a merry-go-round whw. fv1bpim a7o -jz1y- c*erk*ich is turning at a constant rate. The 1j7v1*i*. ozre pbky-a- fmwcboy 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 n xn3jl.3r2xdde:;t rriding on a merry-go-round which is turning at a constant rate. The boy is near the out xnjr 3tle.d rd:;x3n2er edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are r: jm0 sb 4s001wnacxudiding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge,b:1u0jcssw0ad mx 40n and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridiq0v 0ro)ta2 song a 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 haa sv2orqt0) o0s the greater centripetal acceleration?

  A boy and a girl are ridin ) zp5nm4otpll.l;5lyr 9 0dncg a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while thtzll.dy554 r cmno9plp)nl0; e girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which o3 )tuxzeybw ;5f the following is an accurate statub;w5xyze )3tement?

  Rolling without slipping depends onk3;(ziuf gqxkz;52tl ;df d 1a

  Two equal forces are applied to a door. The first force ioxt1v3j sa)4ri n n6(e8,yhsu/;rv s as applied at the midpoint of the door; the second force is applied ste 6v/8 jhan);i4sxv1r3ru (,ayonsat the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a d ,.bmpo fhp m ;sw;x3s:bfgx46oor at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to :3g sxbfm6;h s4fmpw pbx.;,o the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular ton)p+ohu5hg y1l y:1d /,yqfaz the door. The first force is twice as large as the second force. The ratio of the torque of the first yhy l,u +/qaof5 h)zyng11dp:to the torque of the second is

  What is the quantity u:zu pjc+1nod2 35onmgh i (7hmsed to measure an object's resistance to changes in rotationnim7h z1nuo g3+( :2po5djcmh?

  Consider two uniform solis3u p 1vp4y3hta c*6pmd spheres where both have the same diameter, but one has twice the mass of the other. u36mc pp4h 3ys*vtap1 The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same d3m lir:e21epse7 w- zmass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that oi-zwr72: p me l13eesdf the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twic(czk2 2ur.iv r6p2ug za4 .mdke the diameter of the other. The ratio of the larger moment of inertia to that of the smaller pz .2mva i2grkz6uurk2 (.4dcmoment of inertia is

  A uniform solid sphere has mass M and radius R. If thecop1vjm1 id pn tj3.g 3l)d(w0se are increased to 2M and 3R, what happens to the sphere's moment of inertia about a c1t.dvg3jm p ( p3ic jl)wdno10entral axis?

  If a constant net torque is applnhua(lbm (lo*2 )w8bxied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR/zuj m, 8yapb-ni gk. 4lt;k1p2. If this cylinder rolls without slipping, the ratio of its rotational kineticzjk ,b8tgl4k-niypmu p .1/; a energy to its translational kinetic energy is

  Consider a motorcycle ofr3o)g1q/rg em mass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheqgm)3or 1/ ergels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius mvvt0ma1 dp *a3l(s 3zR rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of thetalmd3sma031 *vv(zp incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down 7b 97)x laxblm5,vvzwan inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depez,v7b)l bwxv 9m7x5lands on

  "The total angular momentum of a system of particle9(-nr;zhh zrn4g m9xcs changes when a net external forcz4m -nrr(n;9xhzgch 9 e acts on the system." This statement is

  In what circumstances can the angular veloci ugwf21ih 5q*mty of system of particles change without any change in the system'igw m* hqf1u52s angular momentum?

  The Earth orbits the Sun inw8-zcd f7csk+ yn-, bb an elliptical orbit. Ignore any friction which may be present. What happens over time to the Eart-,yws8bfck+n7 d b -zch's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbf: k- r khi-vvp/op*j,it. As the Earth moves close to the Sun, then which of trpk /*i--ovv f,pj hk:he 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 outstretchvrio 4cd mi 0udjy09 kgg-7*;aed arms close to his body. What happens to his angular m9m;v-cid *au0 4drg0y g7iojk omentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretcge 5(9zt,wuy3,ztrb vhed arms close to his body. What happens to his rotati ugt(z5rby ew,t,z9v3onal kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in f7(v-i,ga dqr(w;9 x.y-cpup rx/ dkz his outstretched arms close to his body. What happens to his moment of inertia about thy,9dpgipczwuv xf.((rad 7q - r/x-k; e axis of rotation?

State the law of conservation of angular momentum. 7/abthqh1 b (/3su7 bwoh8boa

  What arc length does the Earth travel in a three month period in its nearly ci6-a6n39y 7qdzml 9 gwpqhyy0j l k3t9arcular orba73 90aqmng6yw9jht3yl d p9kzl y6-qit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock hasga xw:79m oug, a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 second7u :,o9 axgmgws?

  How many rad/s is 25 revolutions per minute equivalent t+:7-h4 2rwr)6un cpka hgb 4z yynj7yho?

  A bicycle wheel rotates uniformly through 2.0 revolutions 0r *syb9pt( **ao6vhazw8f k min 4.0 s. What is the frequep hoktw8*6m9vr*f*zs 0a( aybncy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 gn-c-tg y;op9 kHz. The period of its rota9y;pc-g t og-ntion is

  A phonograph record rotates at 45 rpm. Through dkl shjuc7y obla3+n 2)5h6, vwhat angle does it turn in 0.20 s? 6n 5 + uh7y,2hbajslcvlko3)d

  A wheel of diameter 26 cm turns at 1500 rpm. How far we k ;cpb j:z+*qyc/6wbs:c pl3ill a point on the outer rim m6b*c bc: +e ;kwc:s3pzp q/yljove in 2.1 s?

  A bicycle wheel rotatesxnfo8)u. gc -c uniformly through 2.0 revolutions in 4.0 s. What is the average angux8g f.cc-o) unlar speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions inv+huv7q v3 lv+m7q:r y 4.0 s. What is the linear speed of a point 0.10 m from the center of the wheel7l+ yrv:qum 7q+hv3vv?

  A cable car at a ski resort carries skiers a oop+ijllf 263w:b x6vdistance of 6.8 km. The cable which moves the o+x :vb2p6iw3jl 6lfocar is driven by 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 rotating with a constant angular speed of 2.0 rad.6 cyrhl(sv0-l*qr du(j 1ft6ena n80i0d dr l/s. What isu01dj8 *e lr0 .q-f6dtd6n(0sal rhcyi(n rlv the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed nv2qqlux +/k l2-n; rerf+ tov),pyar 2s;s/ecutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed,s-+n ela;okursx f2/;)p /qt v vel nrqyr22+ of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 1ec 4j/3zbte l/iw6 2szvbt,t2.0 rad/s. What is the centripetal a, z63zv4iwbs te l2c//bj1tet cceleration of a point on the wheel's rim?

  What is the centripetal acceleration oxlnz) m:q)kxbh n03mkh*:k u)f a point on the perimeter of a bicycle wheeu)hl*:qkkbknh0x xn: m3))z ml of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, ro(s/5edgag.m pk 3p aeaoea; 6 w4h2yi+tating space station (r = 1000 m) rotate to produce an artificial gravity ofi.m + ega5psaea hop3;2/g6ak4ew d(y $9.80 \; m/s^2$?

  A car is negotiating a flacl656on h) elit circular curve of radius 50 m with a speed of 20 m/s. The maximum centr 6hile5n6c l)oipetal 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 otxcoiru:e:b*o+v 1 6r qkco52 zkr;0 rf radius 50 m with a speed of 20 m/s. The maximum centripetal force (providedok0 1rrvr+cc 6bkr*2 z5t oio :u:q;xe by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attache1gb 4d6w4 45aplrf.7 x* jptbwtm,u wsd to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the j4bw,p algru1ts.t6xfww4p7 m d *5b 4string 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 7.5cjogj78etmrz b7;, 0o+ b2 npe kg and radius 9.0 cm rolls without slipping 10 m down a lane ej+jptnreg 7m ob; oz7,02 cb8at 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 co. zdeg6w :8qabnstant 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 acceleration /*d( eyffv4t))drs :vpw7ks mof $4.5 rad/s^2$. 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 starting 2tyx5 s7.aa lffrom rest and accely5lax.a2t7sf erating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and hat0 lzotr6c3k 1s 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 condltemew2nnyfx) )q qf/5) ,9bstant angular acceleratiyf )m))qw,n n5/qedbet9fxl 2on of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while turning*wxms0fbm3(z1n5; vklm kii1 through 2.0 revolutions. What is the average angular accelerati5v1bzmi *si n3m0m1 (f;xwl kkon of the wheel?

  A wheel of diameter of 68.0 cm slows down u3; 9 hgnaijk (u6tq2wpniformly from 8.40 m/s to rest over a dis k36hpw ;u2ai ngtqj9(tance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slg253-b( waiae ,ae tu;y,mo5uj6l kqsows down uniformly from 8.40 m/s to rest over a distance of 115 m3-gt,; em(6l2 5we5,ajoq aukbausiy. What is the angular acceleration?

  A wheel of diameter of 68.gels 0 s0:vg5u0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel tlv geu5 0sgs0:o come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/m xrl;iida;,t.coup/z gms*. t,vk55min. When switched off,p atc.olgir*vsxm5ik ,m;;u/t .z5d , 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 torque of 90 Nm. If a 30 cm a;xd (3cuzgo 2ztj1y:long wrench is used, what is the magnitude of the force rzc;j zytg3a1 oux2(: dequired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90kd m.cek 3w s+-t/ay2m Nm. If a 30 cm long wrench iat-wk .c/k2s edm+3 mys used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inel/a rja)xr uf68qy; t6 ;bup3xrtia $3.00 \; kgm^{2}$ 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 oriw;fp2kosai (am 5bdx+ :1l5b tgin, mass 2m is at x = a, and, mass 3m is at x = 2a. What w5bsf 521(dla+tpb;mkoai: x is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted abouk7/0rz,sysf i 8f+zlct a frictionless axis thought the center O. A rope wrapped around the outer yfz cfl80sz s7,irk+ /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 piwt/ , 6,2dlz4daozqb /b0 tqopvoted 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 exerts a force F2 = 6.0 N downw,bd lqwt4p6t,zo 2 zo/b/aq0dard. 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 he o,3hnbc0 hvqysr::/m ld 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 momem:cshyvr,3 / o nbqh0:nt of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30c1me llqc1c 65l ,a+:x ef2wcdmy;q1a cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangec,6wceex1fclq aq1a+ m1ylmc 2d 5;:lntially 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 wrappt7 h ,0bkgcs60vbltmuu+k0y *ed around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accel7hb l6vst u,0t*0c0uk ym+kgberation of the pulley?

  A 1.53-kg mass hangs on a rope wrapped 1eht*au nd:jp9l;u6z around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Wh1 ajt;*6dpuue:9 lnzh at is the acceleration of the mass?

  A rotating flywheel ck070fficqkzp i;lvv b sjf* g1;3r5+can be 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 inertia c8l xh, na)*ws-y9i u6ucn (bdof $5.00 \; kgm^{2}$ 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 radiur,3 ,ww e8utli1ou9rg s 0.010 m starts 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 bottom of theg3 lwt1iru9o,r eu 8w, inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s ms 5/4gjs)z0t 8kw7gzg-wlj x. How high up an inclljjwg80zxm /k t-4gz s5 7)wsgined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kgaw 4*jmhhmzkx 1o-v i(8p8 ul) is released from rest and allowed to roll down an inclined)w (uj 4mh1m*8l -p xoaiv8zhk 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 slippinhj 0r 1+9zq/vumc+x wpg down a 35e incline that is 7.0 m long. Assume it started from rest.xv uw/p9cj+0r+qhm1z 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 m7e lzmd )*;.; sl,fotaq*r g+upbx0hvomentum 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 x5vaucdho z71(4l.x j 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 rad/s with arms extended has a momec3io5qj(-l,( nvopp ch h(q 0qpze/.rnt of inertiar.q phqp,ij noo - z(l(p(v0h5q/ec3c 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?