Angular displacement is usuallylgi)3 yanf +k mwy;o9efiah x,d9n5+- express in units of

  Angular velocity is expressed in unck0+9y i.puzfca;f0 n its of

  Angular acceleration is expresh j(x9g iqeg27sed in units of

  A boy and a girl are riding on a merry-go-round whichlh--tis, 6hn nn z j-rcheejtc-(4j.3 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 displacement(z--4nri-6t .j c-teh jn,cnhh lsj3e?

  A boy and a girl are riding on a merry 4cl cvjyp9u0)-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 au)jvp4 c9ly0c ngular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a const/l0.zxem ; vlsant rate. The boy is near the outer edge, and the girl is closer to the center. 0zlsm;lx. v/eWho has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a consm )eb oe7 b;+/zbnohe r/,w8pltant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal accbeewoe/pm/ r 8+h,;)zbn7ol beleration?

  A boy and a girl are riding a merry-go-round whichm4zuhpg-j(oi vr c3- s2 1(rwv 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 tao12 r( ir(s4-vu3m pzhvcwgj-ngential acceleration?

  Consider a rigid body that is rotating.q 7x3we8xvav0r;ivj ,fe+tn. Which of the following is an accurate stateme8twa+e.x; v7x i e,vnqfjr03vnt?

  Rolling without slipp-gek(:mzuf ;b 6 dix8gt+m9r ying depends on

  Two equal forces are applied to a door. The first fo ;u tsn:tt,n hpay+8y*rce is applied at the midpoint of the door; t p8s:ya,n*nt ;ythu t+he 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 door 5sm x)gxw6s v3cl.hj,knob. The first force is applied perpendicular to the door; the second force is appliedjxsxg,wh. 6v35cml)s at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The fvgw z,8f -w.7ioimd.uirst force is twice as large as the second force. The ratio of the torque of the first to w f.iuvgwi-,z d8om7. the torque of the second is

  What is the quantity used to measure an object's resistanch45it t pi ,gy 4.jac:)r-o42nsa qnkre to changes in rotation?ta:ka-oyn4 ,s n45itjg h2icq.p )rr4

  Consider two uniform solid spherdakm r 7l1c9 zgvbctyi+e(r*/ do3w 9*es where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller mome*+1odr/k elvt 993dwy7cgz c*(amibrnt of inertia is

  Two uniform solid spheres have the,1i0-56 plrite tz:xh:d.r3wkyiv rj same mass, but one has twice the radius of the other. The -ly.1 ker zw5,3:pit:r6r0ijthi dv x ratio 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 thec.x9 y.ns a2 oc8ec)lu diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia la)oey.u9s 28 cc.xcn is

  A uniform solid sphere has mass M and radius R. If pp6d arc)ycj 42(nlv 4these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axis?acd cv pn46()pr y4j2l

  If a constant net torque is applied to y9ymmq9d hw72an object, that object will

  The moment of inertia of a solid cylinder about its axis is given byjkd, x8, nocqw::3 fjz:0 ea7tz3vekx 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kij8zxf, 0 wknk:qcta j:7v:3zoee3,dxnetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a massg(1 hj5h) hpegbvg((c of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy ofvjbh1 (hehgpg g5 )((c the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M andy zg8jcl;ik o(fl/pp ;w7ut9 ; radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of th(y i8;gl;pj ctfzk;lu o/w7 p9e sphere at the bottom of the incline depends on

  Suppose a solid sphere ox c3d);7dj ;qnkgnujibge3c9 701 spvf mass M and radius R rolls without slipping down an inclined picegjn v )dc7jd33b q 791g;k ns0;uxplane 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 partvosg196( ob l hre28pbicles changes when a net external for9 lpvh 8o o(1es6b2gbrce acts on the system." This statement is

  In what circumstances can the angular velocity of system o-f+3nd-lbi5dmb6w t0 fjl e; gf particles change without any chang; 5 -d-wbbdmjfn6 0fgl+i3tele in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore f7k u.pdo8*js any friction which may be present. What happens ovfpj o87u.s *kder time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As thn3 o:xj9f89ev soaf4re Earth moves close to the Sun, then which of the following best describes the orbitin9roejs vfn: f84a9x3o g speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretch70yh; tc4u/hl*x: d5*e:f kscqhvxoaed arms close to his body. What happens to his angular hov;ch/0xsyqx 5fdlc 4 h:e ku:7*t*a momentum about the axis of rotation?

  An ice skater performs a pirouet;/y3 u8c 2qvamzu6:steq toq*te (a fast spin) by pulling in his outstretched :tv2s e83tq/ yzcq*um;oq6uaarms close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a :4nwsq;f(3bzcsz8,pj1ey x z pirouette (a fast spin) by pulling in his outstretched arms close to his boe; ws8zn(x bpzszcj3 f,:4q 1ydy. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of anga5hpoc84vozr 3l t5f4 ular momentum.

  What arc length does the Earth travel in a three month period in its nearly6mph6zp .wyq gki+t 0eqhqfd,,detj3/-kq9 ( circulak e9 p(-6 e+ i6 qtyph,zdwdg0/,tmkj h3fqqq.r orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lengt.2 4g8ssxla8y wp-yp3nx0y ej h of 0.30 m. What distance does the tip of the second hand swee 4yayg. e-p w2ypsxj3l08x8nsp through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute eqtg o16qv;j wo4uivalent to?

  A bicycle wheel rotates uniformly throughzxi mob l+ 4 38+-pzurfoowp/- 2.0 revolutions in 4.0 s. What is the frequency of the p-z- 3z/o 8o+4 lbuoixwfmp+ rwheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencyo b wqt))-g)fy.boz(r of 0.40 kHz. The petg) y)q(b.-)rb fzowo riod of its rotation is

  A phonograph record rotates at 4nv;b pebl6j )g: ,2d wzrg,l2g y2zil45 rpm. Through what angle does it turn in 0.20 l 2v eiyw4b b jll;pz26z:n2ggrg),,ds?

  A wheel of diameter 26 cm turns at 1500 rpm. Hl/rll; kfqj pts,y7(/ow far will a point on the outer rim moq sll,j /k(fpr;y/7l tve in 2.1 s?

  A bicycle wheel rotates uniformly through 2.07i gewbq1.fk( rvo:3 r revolutions in 4.0 s. What is the average angula.(be:gov7r3r qwik1fr speed of the wheel?

  A bicycle wheel rotates uniformly t2fh( 4az* lrhfvl*c*0hn q)n . ci8wuihrough 2.0 revolutions in 4.0 s. What is the linear speed of a point 040urch z(w h*2ill) fcnvfqah8*n.i*.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cablpq nu8gf e- 6/w:lwpo4e which moves the car is driven by w4np/ qpu8 :6fe wo-gla 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 anp5p/ 7 x+namdugular speed of 2.0 rad/s. What is the linear a/5np+dxm7pu speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cuowlas; ) m9p*tu. v:xatter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed o. x:ou;ms)al t *awpv9f the end of the cord?

  A wheel of radius 1.0 m is rotating with a cp wq;*15n bcxzonstant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the w*n5cx1p;z bq wheel's rim?

  What is the centripetal acceleration o cuucbhg2qp j((1 1+orf a point on the perimeter of a bicycle wheel of diameteqgucro(h+b121cuj p ( r 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) mu bef:h -fyg62rwj -:jvst a circular, rotating space station (r = 1000 m) rotate ter - -ygf :hb:j2v6fjwo produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with 1wo u.b)zu6wo a speed of 20 m/s. The maxiwb 1)uuz6wo o.mum centripetal 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.i9 ur0 gs(0oqzd (ina flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal fo nz(dr oi09a.ig0 suq(rce (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 arjpsacu( yy4, )k0-p wau+aihs7m:ctrr/9+dm ound in a smooth level table. If the maximum tension that the string can withstand is 250 N,s a 0arsp7 ( ,4hdma:9urywp/ui t-kjcmyc++) 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 withou n zzdc,26;gymt slipping 10 m down a lane at ;yn6zm d,cg2z4.3 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 angular accelerafw/gp rz+l 0c4tion 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 a06yqs4 - gjpme.e3 prangular 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 starting fm;l/txfy,5) oc ayrjs-*:c nt0ggo v8rom rest an:c8ag0ycts/ royf lvj) m;x*5n-t,og d 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 angular acceleration yq- t.l42bmojh+qjin a cb+4+ of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerao ae9mk1r;/ lftes with a constant angular acceleratio1ef;lo a k9mr/n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and pmq4*b5ck , h:qlrjqg v:w8-kreaches an angular speed of 6.0 rad/s while turning through 2.0 revolutionkj5:hb 8:* qq-,rmq 4 cvlwpgks. What is the average angular acceleration of the wheel?

  A wheel of diameter of, npb39ywcd5s9ub keu 4q41t t 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel ro qut93sky pw451uneb9 t4,cbdtates in coming to rest?

  A wheel of diameter of 68.oiea. 9o u,5uu0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is, 9 u5uaiou.eo the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest1p74 c dm1t 8 suactvs:pz(7tg over a distance of 115 m. How long does it take for the wheel to sst(ud t8tac1p14 :7zpgmv 7ccome to the stop?

  A centrifuge in a medical laboratory rotates ti- f9j nae*7lat a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant a7iet 9lfj *n-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 tight79ls 6nt.:ugm2hn devening to a torque of 90 Nm. If a 30 cm log m:7h 6tdl9s2nuven.ng wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening ,c osl ( 6(,q)lowl dy2ydmr:xto a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force r:6d,yl o(2 , lldcxw(ryo)m sqequired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertrpjf27lnwf76i1 o ikof)4.oed * ( kslia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follow: ty2*1lcu s6ljzu*qw s: mass m is at the origin, mass 2m is at x = a, anll1*6u 2u:w z ctj*qysd, 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 frictitbae-n 7se8 o*sd,f* monless 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 aroba t 7-s8enm*os*f ,edund 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 axis thought x-fhlzycy:x 9h d/5;q 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 radians does the cylinder rotate through in the first 5.0 seconds,/ 9 -xhq:xl cy;dzy5fh if it starts from rest?

  A 4.00-m long rod is hinged gn*v2wk3fn t ;at one end. The rod is initially held in the horizontal pos;*g3 tfv w2knnition, 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 end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30vi.shd3nuvt s2)* m.s cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied t d3vtu* .2nms.h)s isvangentially 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 frictionle*xasx z(xp 6*mss disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular pa* s*zm 6xxx(acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of ma2tz wq8 komna48 ,r1xvss 7.07 kg and radius 66.0 cm. W2 xkr ,z8namwt1v48oqhat is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it i 2ik.tye 4b.lauudm+8s 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 )2vz 3ueq6vukinertia 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 h:s9 co(rll3c 1.0 kg and radius 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 reac93hll(cr s :cohes the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radmq wj 20,f9.sg qmbp7b0dn8beius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb beforb8be2 gms wbn9 mqd.f qp07j,0e coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is f(stxr a(b9oij m ,:c435+ mep5mg ngqreleased from rest and allowed to roll down an inclined 5jq(:rfi9xpmm4 e5bsmt a nc+ ,o( gg3plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius gl 07qy*t d2z6 t2alap15 cm rolls without slipping down a 35e incline that al alq76dgztpyt0 *22is 7.0 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 momentum changes b .kxaxo yue6m8ecd;/24lr,af y $20 \; kgm^{2}/s$ 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 momeglr b4rp 3on(+nt of 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 vpu x0 jm:e,6;vyykp 2has a moment of inertia;vpm62v:x 0ey yu,kpj 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?