Angular displacement is usually express in at w:,ijpy: ag6r2/ai units of

  Angular velocity is expressed in units ug7r(x l+. tdgrl9m;xof

  Angular acceleration is expressed in me35syi 0q , v(5pbqqk(a qk(ehz-hyl8r8 5wg units of

  A boy and a girl are riding on be7o8cw.m *rp*ix/j sa merry-go-round which is turning at a constant rate. Thm**.p sx/i8 7 jewcrboe 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 which is turna+e2:t* yx7sm z hfca *gr7,iping at a constant rate. The boy is near the outer edge, and the girl is rge+*m hya*fzxc7a 2 ,sp:7ticloser to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a co29 y8ray(uil0t f 5ky)/uujqznstant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater line( u tyjyu2)f/uq 5krialy z809ar speed?

  A boy and a girl are riding a merry-go-round which iske8j97r+hrhp ycwkrq9x/ 8n - turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal accelr/ jn7rk 9c8+w8rqkph9hx -yeeration?

  A boy and a girl are riding a merry-go-round which is turnj-lp ;s6w(wp unh 4a8bing at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acpwp 6bj (4-h l8au;nwsceleration?

  Consider a rigid bodch //l/bhqrzvbkn-ve 8,, l m1y that is rotating. Which of the following is an accurate statemqh/vvnl/b -ecb/r 1hm, ,8zklent?

  Rolling without slippin dh.b8s0 ml8hw.q /bybg depends on

  Two equal forces are applied to a door. The first fobejw.95 ya jwnfqb668rce is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torqu6n6j9 w bfy5aj we8qb.e?

  Two equal forces are applied to a door at the dooemqm-a0)pd:b ,7 hxod 00 hzwvrknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which forx0mdw :0h0zde moq,7h-avb)p ce exerts the greater torque?

  Two forces are applied to a doorknob q3mgxn unieqc 5,98t 4hw-l1b, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque q x8 9egtqlc1 h bni-w4mu,5n3of the first to the torque of the second is

  What is the quantity used to a/ 6bbol z5j 7e3cera*measure an object's resistance to changes in rotation?r j6a/zabe 753beo*lc

  Consider two uniform solid spheres wherf s*1f2fhlxo z9)g/qm1 vwbg9e both have the same diameter, but one has twice the mass of the other. The o1f svxghqwlz/g21f99bm *)fratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one hl.fkd5. -8e,9yzfr khf9 pjjc as twice the radius of the other. Thp .fk,cde h5y8j.r 9-9zlfjk fe ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twfpd e.s0yp9aw4f 9j4mice the mass and twice the diameter of the other. The ratio of the larger moment of ine9s wdefa 9f 44p.jpmy0rtia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius y:q, c*mr ;r2lzapwk/R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central ax2pk/rc,w*rlzqy;a: mis?

  If a constant net torque is applied to an object, that obje fq)r*9 sqfd2uct will

  The moment of inertia of a solid cylinder about its ahxiydy 2- o42tbd7v) vxis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to ixotivyb 2vd)42d hy7- ts translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one e /1dh m vif3.bx)oa7mwheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kine3v. am/me) d1fhb7iox tic 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 ebz1g9x3ll uh+i -q8zvn) x tz7xe2r0and radius R rolls without slipping down an inclined plane qtnrx1ix x vh-l)e z89bu0 7z+g32lzestarting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphedw+ hcc2hi:y.fmq6 m4re of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of thy2c:.+qmcdhimhw4f 6e sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles chang s1j kc837z5s3hy *. ec+anl-(lk fhuoqol6tzes when a net external force acts on thz6cqo.s k et8y 3735hj( k-asln+*hcl lu1zofe system." This statement is

  In what circumstances can thh *l v7+yjsx xy(re-7iyp6.do-yjl f)e angular velocity of system of particles change without any change in the system's angul+7xy*xjydjfl()slep.- vyo 7hr-6yiar momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which may6 jqqcbk3 qv7hc k3+/1u)m dc2hqao( p be present. What happens over time to the Earth's a3 c 36qu jq/q+dh1)vq k2mpabcoh( 7kcngular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movenlich 0mvlyb k (qb;0 k;+2f)io-y 8ios close to the Sun, then which of the following best describes the orbiting speed of nf8q ib+lm2-0i;o;ckiy y()vl bok 0hthe Earth about the Sun?

  An ice skater performs a piroue9/ou5 p rxry7+8b6 uhrjt ;knkz2k+z ctte (a fast spin) by pulling in his outstretched arms close to his body. What happens to rxk5rzu t /9;z 7yjrn8+ohkc+62kpbu his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling irf 06.qdap5e *88chxi 5o.en flfyw/ en his outstretched arms close to his body. What happens to his .f8 o lqe/i a5 hxre.86*yc0pef5fnwdrotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched keyb86k/fbzgkp w:p )7p tc/7hkxw ;1arms close to his body. Whaef 6bk8z1py:wxb7 pwhpg; 7ckk/ t/k) t happens to his moment of inertia about the axis of rotation?

State the law of conserindgiv+x/ u)-vation of angular momentum.

  What arc length does the Earth travel in a three month period in its nevqh / 1 ma9-p4z)cl3sdpxwo 9parly circular orbit acm pa1/-sw)h pld z pq9439ovxbout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does tvx9n/8-pmx fjh ez4;htt* *pof,p2 bmhe tip of *hpfp2/h-x,tejx n;o9m ft v8mz4b*p the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minutelx re;fyl,z8rm: mh1; equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What w5 ju9 ,f g2mn/va; h,w9pnrswis the frequency of the wheelpnrhg9 , an;v/m suj w,29ww5f's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40hi :8-likp0i d kHz. The period of il k pii-h0d:i8ts rotation is

  A phonograph record rotates at 45 rpm. hdhaqa/8zk5j56vj4(iscx ,q Through what angle does it turn in 0.20 5 d(aavjhzi xh8,465 /qcjs kqs?

  A wheel of diameter 26 cm turns at (ex60aqvx5gw 1500 rpm. How far will a point on the outer rim move in 2.1 x(qwa 5vxg06e s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 44+igk2 f qqavc()0 r ozpbp 23ycx8,qd.0 s. What is the average angular spee)yo 2(8 qcgvk3 +zp2ri,0dfxqc4pq bad of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W 7 j7vezu9(n;lkeuq-phat is the linear speed of a point 0.10 m-ze7pukq l(nvj u9;e7 from the center of the wheel?

  A cable car at a ski resort carries skiera no*dl08mgt o(hf ver4l/w)*s a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley )w8r*0 (dm*/eng 4 lhofl avtorotate 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 13p)oj r wx2rd2.0 rad/s. What is the linear speed of a point on the wheel's1x )2dowpr rj3 rim?

  The cutting cord on a gas-powered w9ijed vpd ahc-ruq0 u04ya31;eed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the appq- vdup09e; ia1c 3r ah0ud4yjroximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is royb y ftxs)l0,3tating with a constant angular speed of 2.0 rad/s. What is the centripetal accele y fty)ls,x03bration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a qk0)yf /vh y6kjj-kx-(82uq f8 aeevj bicycle wheel of diameter 70.0 cm when the bik ej uy /xkvehjkfq)v82 kaqyjf 0--8(6e is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a cir,stc59tm5y:.*kl 5iq5x o gryn )d quscular, rotating space station (r = 10m.) gt*5qxltsyc:ruo s,5id59y5 kq n00 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular c,pieaqezb ecb3 ,+ h*ux;ab 0i -ag4i8urve of radius 50 m with a speed of 20 m/s. The maximum centripetal fo ihb3z* ec aiau8 ipxae,4be- ;+qb0g,rce (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 radius 50 m wit*x-p f:jqf/v/2zr glu h a speed of 20 m/s. The maximum centripetal force (provided byxj/f-uq2rl*p gzf v: / 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 mk 8,+)k8ijxbzw 4vsx y1nu6a string, is whirled around in a smooth level table. If the maximum tension that the string can withstand i knjim8x41wb 8a,zsxu y+v)6ks 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 m dlx :.eln2sgjv ih59u7 e0zb3o:0whi oown a lane at gvwj3 lhiu:seil59 z0 :h.2 0xo7nb oe4.3 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 acct4hk/9aw5cdks 9uf*y/c mifx z4i2c0eleration 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 w-l6pr x60xosov 8 uav5ith 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 start )ydb6/rwb .ups0w8nu ing from rest and accelerating at a constant angular ac/s)uuw8dybw b p.06n rceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, w0a(-*zw8c 5qk3bxh aqk5dy k 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 decelerates withp(i(xxj, tvz(op ;od id5v( 1f a constant angular acceleration jd v(,ziptf5 ;p(io( vod1xx(of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches za0x anm;.my7an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular az.n;7a0xym macceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over 0 9z lnr3 7xhwnbwwjv vg17+.3hktb s)a distance of 115 m. What is the total number of revolutions the wheel rotah b7w0bwt9wzvk3xsv 7nnh31.) gj +lrtes in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ove0emkc7 )i9hrm r a distance of 115 m. What i9mecrm 7h)0kis the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unifori.aaal+ f.pn6-1yrx3v5 fml cmly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel toan.pl fxyf65i+-. 3m cla v1ar come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational spee bmbh5bf4u2o h41st.ld of 3600 rev/min. When switched off, it rotates 50.0 timbsh1 mo 2h ft4b.ul45bes 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 i 6muzj m73hw-zy 95p) ailu)u90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when tha7pw5 z u3-jhz 6im my)liuu9)e force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. Ivuy* / dwql,b,f a 30 cm long wrench is used, what is the magnitude of the force required when the force applied at ,*uw/qybdv , l$53^{\circ}$ to the wrench?

  A wheel with moment of inerxav ab p8qok 5xgj5li1ai ,6b5up4p6)tia $3.00 \; kgm^{2}$ 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, massga-)/d.,lus 0e gzf 7:yayj,kbga jk- 2m isjdzyjk7),/b g,gg eay.a a:fuk 0 -l-s at x = a, and, 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 frictionlcq:l;7a y. uxhess 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 exerhcx7.l :uqa; yts 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 x0 q+7 bdlj;yah5 ewqkq0l*4v kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, eljke vq+qd54l*qy7b xa0;wh0xerts 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 end. The rod is iniuu+ st:pliw 1gx3l5/ hk3b6gdz k *cy3tially held in the horizontal pos3+lh*3/g31p l5:b kugsx uwty6dzci kition, 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 30 cm and mass 1.5 kg. Ne3v3tq,x3x2d7r zxzqiwe3:wkglect the mass of the axle and sprocket. If a force of 20 N vxq3wq3wzxd 7 3z 3e,x:rikt2is 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 diskpc +, l d5f2ejvn;amvz1y,y 1p pulley of mass 7.07 kg and rad zemn;1pp dyjvc+,15 a2lf,v yius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a f1522 d :* dim)sbtk )skaaix:7j edble2o;zbbrictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accxbbb :k2t7eim da5b1je2; d a)s)o2zdks* l :ieleration of the mass?

  A rotating flywheel can be us9/lrdh.sas3,ygb s8 ned 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 in2i 4vvbtgtq l5u b51q0ertia 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 sami7,ocq 2 y6ctarts from rest and rolls without slippiccq7 26iom,ay ng down a 1.0-m 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 r ab,t,lppn )1;v1gp n5-s3 a5eku dcrnlhr7s /adius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can itvp/h5 1n;ndl ) anks3s5ug7p1bla ,p ec -tr,r climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from2bws+bi5v. v8; j2h1k hrqw my rest and allowed to roll down an inclined plane. How fast is it moving after drohbh58+vjk rm22 bw1;y .sivqwpping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radiuse+ql- 8i,) xas f/ygms 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertie/l m)s8ayis, +fx-qga 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 m(1lezaev q-)homentum 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 inertia of 4 m ;xafs-it-va9 t7ez$5.0 \; kgm^{2}$ 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 moment of ine t(uqi/*r exhm4xb,h)m/ )lakx v.b4irtia oa4m )ib*(xv,xeuq.k ht r/xih m )b4/lf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?