Angular displacement is usually express in un)k r(e12ziq5n82lnwp+b fjjhits of

  Angular velocity is ,qoie:r,pul :expressed in units of

  Angular acceleration is -)ededvsux6 6expressed in units of

  A boy and a girl are ridingg2 z;kjardd0ncsv-(fn viridlm5; l8v p 7(1 6 on a merry-go-round which is turning at a constant rate. The boy is near the outer ed 7rzngijf 2d(16d;-nm8 vcvdlail ;vk 0s5rp( ge, 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 which is turning at a coed hj.1n(h4bq7/w pny nstant rate. The boy is near the outer edge, and the girl is closer to the center. Whhw4/jnq y(1 p7ndbeh. o has the greater angular speed?

  A boy and a girl are riding onar;,dw5 ge x,:mlsh6m a merry-go-round which is turning at a constant rate. The boy is nearmlg5d, :xswhra e6 ,m; 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 constbrk c*s.t-,h2z l bziy 8)snganmi832ant rate. The boy is near the outer edge, while the girl is closer to the center. Whohi s*z) .r8g2a8bn-lzsyib,3 m2t cnk has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turny/1l z ;h qh;j 7p4gb.vmtt 2ji3p/apbing at a constant rate. The boy is nearhat3 jb7tp 1/2/v.miy gbjp q;;pz4lh the outer 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 follyxf,7v 26s onmic+wvef- e.3oowing is an accurate syeo+n-v3s.fv,67w oi2f m cextatement?

  Rolling without slipp + hz83(ota)lc zjdqk;ing depends on

  Two equal forces are applied to a door. The first forcehw6s-g:yo5ifqk1 u .*cn/ opu is applied at the midpoino fsnc h6-15w/:.quoikpg*y ut of the 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 a--jqvzl1j(+ k5k yjfhif-n, appq2*gpplied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. z +*q - qik(-kjp1n5y -a,jplhfvg jf2Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular gdn c ,-k4qjtvewub):id/ q ,0to the door. The first force is twice as large as the second force. The ratio of the torque of the first to th c0:4ie,)dgd t q/- jwkq,bvune torque of the second is

  What is the quantity used to measure an object's resistance to changes :/ uk8k2ib2u2abbkt jeig dldm5mu 9w2 .ti45 in rotation?lme2u bi2:a8 tkjbk.wm 2b/4 utd5 gki29d5iu

  Consider two uniform solid1 6)0hg,;vjgldov hvs spheres 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 moment of inerti ,h v6)sovgvgl j;dh10a is

  Two uniform solid spheres have the same mass, but one has twice the radim,1p eq 9, km oecrlq+p7y2vx.us of the other. Thp 2mkqexmpoqyr e vl1c,9,+7.e ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spherbpoal3u md3733vnv)qf,5dk y : w3 rzxes where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment n :d3,w oylzxm33va 3d)vbfpu75r q3k of inertia is

  A uniform solid sphere has mass M and radius +yw,b8fyc my ikxg6h 1t)wy -a/v.e7rR. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axy68 fgthab1y ,)eyrv ik.7+xc-/ymw wis?

  If a constant net torque is applied to an object, that(-vc1ln8:;fj y;jc5m8p)0yyyskvc qlwsy +f object will

  The moment of inertia of a solid cylin;d)+q97z+kny/. kdfkpwdh qw)i es 6nder about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150,bbjb*)tygotc9k l vdc5+,tsd ,e- )z kg, one wheel of which has a mass of 10 kg and a , 5*-+sjgtbc oby )z , dc9t)b,ekdltvradius 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 the wheels are uniform disks.

  Suppose a solid sphere of mass M an*)bbu5g 8aj)ru-6 mg.t ewotu d radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom * awguug tr.out- eb8mjb)5)6of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippin yd fg0(0t sh:5rwe6aeg down an inclined plane startihe ewstdgr 6fay500:( ng from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system ofll68wr -qbf3vr bk74c particles changes when a net external forwq-fc8b 4lbk73 6r lvrce acts on the system." This statement is

  In what circumstances can the a 9ygt:;,97wvtgzpa y7p*gc uangular velocity of system of particles change without any change in the system's 9gyt:7c7yv9tz p;guw,paa*g angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Iw7ojz dll68rsxq1p,zawe fu -)4f)o -;tslp3 gnore any friction which may be present. What happens over time to the Eq pol)f a86; -joel3f1xz,u 4lw7r) s pwzstd-arth's angular momentum about the Sun?

  The Earth moves abou 8o(sbd ykf 2rri*2yy61dxji +t the Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the8y+i ij*6 (y2d2ykbfrod r1xs Earth about the Sun?

  An ice skater performs a pwi3vguari8 wj0t )/ 1rirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum abou1uw 8 rvgi)aitr0/ w3jt the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in h2cn2q(nqtf) hm/3stc is outstretched arms close to his body. Wha/ mt 2s c3tn(fh)2cnqqt happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouetz;tyn9 *c jg/xdgrp9( / lqn6pte (a fast spin) by pulling in his outstretched arms close gn/69( c;rp*/ jpdqnltyxgz 9 to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular lpn r:mwk21v4)u2q( nbzb vl*odw10 ymomentum.

  What arc length does the Earth travel in a three month period in its ne t d/71wtdj jtf;g*u0iarly circular orbit about the wd /tg *f7utjjit0d1;Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lenzg )f9ftmt(k 2 1yzo fl 8w2dlv9n0:eugth of 0.30 m. What distance does the tip of the second hand sweep through in 3 minute:22ot9)w0n (k lfv eftf8gz1y9 duzmls and 45 seconds?

  How many rad/s is 25 revolutions per minute eq ed a2,j)zgx:juivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolup iir3b. 3uut-/ i-5jcsml:iwtions in 4.0 s. What is the frequency of thesi3wutm/:pr 3bii-cjl -5 iu. wheel's rotation?

  A pulsar (a rotating neutron7hym,y o( mk)x star) emits pulses at a frequency of 0.40 kHz. The period of its rotation o mxy h)km(y,7is

  A phonograph record rotates at 45 rpm. Through what angle doecxq,0bx )1k80k ncpl/4lr zbis it turn in 0.20 sb zc4x0kx/0 r,n1k)qi8cplb l ?

  A wheel of diameter 26 cm turns atg5u3 a +7regxejudd./ 1500 rpm. How far will a point on the outer rim move in 2.e5a gu 7/r+g xjed3du.1 s?

  A bicycle wheel rotates ufxsf 74j,*eq- vl8( hug fggo-niformly through 2.0 revolutions in 4.0 s. What is the average angula,g xvof4j-g*f shf(eu87 glq -r speed of the wheel?

  A bicycle wheel rotates uniformly through mz2-i87fo,fhg ujb3u2.0 revolutions in 4.0 s. What is the linear speed of io,ujzfm2 3 7fb-g8uh a point 0.10 m from the center of the wheel?

  A cable car at a ski rexfli/a , 5jb/rek)v3 nsort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m.v/5lj)afbx , ir/n3 ke 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 ra,y ok a*y qi4fgyw8 p50n)z*mid/s. What is thi,yk q 8f054) inampzyw* *oyge linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in leng xw+rm4/i /yksmtw1w:th. If the motor rotates at the rate of 20 : wx+4kwrt/ 1im /ymwsrev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is 54( dxzb4n qfdrotating with a constant angular speed of 2.0 rad/s. What is the c 5df4nxq( b4zdentripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of(8hviuo(f8pq3 kp97m 4,ygb fho.w oa a point on the perimeter of a bicycle wheel of diameter 70.0 ,( ppwhi( moog q.48fabv8 9kuh3oy7fcm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circulgwsly i dz2(:6ar, rotating space station (r = 1000 i lsgyzd: w(26m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with aozw u;fg.g 4a1,iv(/ op f g:wlf6ku.r speed of 20 m/s. The maximum cenv.giw.gou4z(:,1f rwl ugkaf ; po6/f tripetal 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 of radius7yy h(i;m vd)b gj65qz 50 m with a speed of 20 m/s. The maximum centripdbymivh7j;z )(5y g6qetal 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, is0jggpzommg 3h483y* z whirled around in a smooth level table. If the maxiogzgzj3 mg 8y 4pm*h03mum 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 u4)uc x.wv jx rf:l*4hcm rolls without slipping 10 m down a lane at 4vf:xujw c4ux h.) rl4*.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 cond,x4c,ioi fb(hs d8 z9stant 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)r5o5oyue j)dz)-epmup 41 xx a constant 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 rotate after st 90i zfk1duyg-arting from rest anu1idz9y-k0g f 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 acc9 f0y 0 hwxfsp:t m qvc:u+*m6./caeag 1jutg0eleration 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 constant angular a4d6p(4jn an9, ncw zvgccelerati(vj4 p 94ndnn 6zg,cwaon 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 wh9qrcnnolahpy;u.k:k41 3i. -j /v irkile turning through 2.0 revoluu.9kh;i:ncl v-a1y.4r/ko rkip jq n 3tions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cmt f1kczu /-33uxd8 tir slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total nuctdt 83u i/zx1-r3f kumber of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tomrxtdb*c978sfpeuk gyj3jt:,u( 1 8 a rest over a distance of 115 m. What is the angular7k 8ducb89t j,gps1em f x(tj3:ay*ru acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to uz*l/imc4xt iy /. :7k/)jtcpl9l+h qk,q rqxrest over a distance of 115 m. How long does it take f+il//itt*ukh.qyp :l , rm )kj xq4czx/lcq79 or the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed ofhs5nxs sk;ezeb: (x2d,9 dq;m 3600 rev/min. When switched off, it rotates 50.0 timesezqkbxde9;:;n 5sm,x 2s d( hs 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 torrnm 6f*xkdxa4y0 .qog0sfj 1 ,que of 90 Nm. If a 30 cm long wrench is kfromyj ax4gfdq, 01x0n s*.6used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighte*rv0-b+)a9 bntttl-n khqrs 9 ning 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 applied av* h0 tr9q br9nt+nst)-abk-l t $53^{\circ}$ to the wrench?

  A wheel with moment o ;nclg.5lf zi(b-cr /lf inertia $3.00 \; kgm^{2}$ 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 origin, mass 2m wahl+8 )bb*gf0; edjl is at x = a, and, mass 3m is at x = 2aw e+ablbdjgh0;*8f ) l. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about ab-qlk9:d2sm,/ae q )qbl .33brf nxdn frictionless axis thought the center 9 nl2bsqa dkdn mqf.r-qb/3,3:be)lx O. A rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thf ie9+ren.1jl ought the center O. Aj.en1 e9rfil + rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 hrohi6d6cd rer(4p xp65s(+xy grsg/1orizontal position, and then rel6po(dy61 e r( xsdc4ggxr/rr5+h p6 sieased 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 30 cm and mass 1.5 kg. eit1)8pbde8d qs g(6wl k k2;*+om vkxNeglect 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, assumk(e 8q ie86vkgp)tl;k2d*m d +os wb1xing it rolls without slipping?

  A 1.53-kg mass hangs on a rwfd(pz g35+(kfc jl9qope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the anf9 5+dfkjg3wp(l (q zcgular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless diskj 6f;.c fsq8zm,;zjh3afsx p 1 pulley of mass 7.07 kg and radius 66.0 c;1,sszm ;fhjxja.fpfz83cq6 m. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required tkden0s :6yp hlk- f9h,o 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 iner8ycj)7nxgks) jcti . fqs+x,n./rw bp3:yu (jtia 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 starts from rest and rolls wiuquj70qm a-v/hmlow z;i f+5 gx6/gq9thout slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the x-aq 6q z5w/g7m9 u+j0hg;mlufqoi/v bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a spn+m,hnni3 bys)g -gfipi51(f eed of 10 m/s. How high up an inclined plane can it clih-f n( n b35)is1+,ygifpgmni mb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fwyx9ftfm5r0z iy jfawt52,:: e 7+ o v.ycvuw5rom rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vert.5 uwow:e:2t5vw , c 5ji yam zyf9rxff0v+t7yical distance of 3.0 m?

A solid sphere of mass 1.5 kg a t zhn/ r)zzk cxn)s.ht18i;.ond radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is gixh ;1tonsz/r. zhkznc).)t8 iven 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 3e bc*2geg;tc 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 6 daj))3o ks6v *-zjsgcx )l1 lznnad/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 momennp m7m q;1*p5db/cvy st of inerti bnpsy1 cpq7vm* ;d/m5a 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?