Angular displacement is uss cr-nam;4 )hpually express in units of

  Angular velocity is expressed in units ol:knj8c 1i ie+ hlpw )8km4rc0f

  Angular acceleration is expresset7jx+7cbos kwx6d 9 kd,8+loj k):7i j)vyfx wd in units of

  A boy and a girl are riding on a merry-go-round which is tuodq o,-zuvj: k7wh x6.rning at a constant rate. The boy is near the outer edge, and the girl is closer to the center.,kuozj 6-7dxhvo w: q. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which imm-jk)q/ em* js turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Whom/mj-)e* jmkq has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turnio -qwv;r8jeg8 x1a7 pang at a constant rate. The boy is na8e xgjrq;7wvo1p- a8ear 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 whiz -s bnk/xfqd pvb6728ch is turning at a constant rate. The boy8x7sq vpkbn6dz2b/f- is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-gog;v g/1s+jes r-round which is turning at a constant rate. The boy is near the ; rv +ges1g/jsouter 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 followin6fcb,d ze,.w *g 4hv:xy 4jrnhg is an accurate stathdze v.4,yhjb *x:nc ,g4f6wrement?

  Rolling without slippit+:ucig; s, tqng depends on

  Two equal forces are applied to a door. The first force is applied at th tpo8u8+ 6r. pqa/fx(je+myr ae midpoint of the door; the second force is applied at the doorkna+8 u( r+e oqrpj8yt./ pm6xafob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are appliedt32 vc) xlnu2t;mtsj;e,;dei to a door at the doorknob. The first force is applied perpendicular to the door; the st;dst;ne 3i2leu j 2vcx)t;m,econd force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the dooci:43h0schd k ;.ufxvr. The first force is twice as large as the seconk3duf0s: .4;c c ihvxhd force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object'gm,dzp/v3aet - .ng2es resistance to changes in rotatioa pztvneg- g d.m2e,3/n?

  Consider two uniform sofog(o,05 ru,gff4c lflid spheres where both have the same diameter, but one has f54gu , r,l(goo0f cfftwice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, 7d 56q w,kacdxob*vm8but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sp w5m*d86x d7aqbo ck,vhere is

  Consider two uniform solid spheres where one has twice the mass and twibmlwi7s hy kgo3aur; l 80u8,/ce the diameter of the other. The ratio of the larger momentbmk;08 87r h io yalg3/usl,wu of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. agn3;4fr8eeq1f( ve snk* k, mIf these are increased to 2M anav81k (4nqs*n;fr, keeg m 3fed 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, thatmz1wa g ax:z w+28yxm3. ub4ht object will

  The moment of inertia of a so;5yi)0g q.d citfszo1l 8 h7aflid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational king81t hq0 io)l;z .fai7fs ydc5etic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg j5oeu8y 942 mzqmpxkv/3wrn6 and a radius of 30 cm. What is the rpx936j8vk wqr2y/n me4o mzu5 atio 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 R rolls without slipping down an inca7gt )zu7 /rpp1lx*f kg1 y,zg)i5gwylined plane starting from rest. The linear velocity of t yu rfy/ 7)7gz)5t xakppg1z,*1ggilwhe sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls with2e z ;zpt3y(toczc9o(out slipping down an inclined plane starting fr3ep;t (oc9zyczo (2 ztom rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes whl. z,ah-2w -/scc ,dharkl -saen a net external force acts on the system." This statement is, s-h as/lalcrhc- w za2.,-dk

  In what circumstances canf5dg v6b e2ua;2bgbf5 the angular velocity of system of particles change without any change in 5fg 6 a vged;5b2b2bufthe system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frict -gro /p)ml+l-i-qg loion which may be )-g g--ml+p ir/oq llopresent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. i/5 a:t(gmuk1a/v*8k lwjr+ mwj bpk0As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Eapamj5bw/ju:tlwm0 1*+8 /av ( kigkr krth about the Sun?

  An ice skater performs a pirouette (a fast spin) by p:xu7 /b m8rcpg(9shu hgp3 h6vulling in his outstretched arms close to his bodyh/v7u69gp8c rp(hh us mb:3 xg. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouq 1wyrtz dk(iy)e v--;ette (a fast spin) by pulling in his outstretched arms close to his bov)qik1y- d;rw-ey(z tdy. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouettjxk8h:3r3tu xe (a fast spin) by pulling in his outstretched arms close to his body. What8jxt3hx k:ru3 happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momer0 o/() x.uiqzuj- ho4db o,hbntum.

  What arc length does the Earkhwf+7p.gw 1m -apz(j th travel in a three month period in its nearly circular orbit about the Sun withpw wp ham z+-g.7fk1(j a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a,tlwae23a iz89 uo2rk clock has a length of 0.30 m. What distance does the tip of the second hand sweep throuuwe328ka aiz9 2lrot ,gh in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent tont)n n93qe:d r?

  A bicycle wheel rotates uniformly th0mbgcvo qs.i,z 84ib 2.)ej qxrough 2.0 revolutions in 4.0 s. What is the freqscxb8zqe gqoib2.v jmi,4)0 .uency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. T flmu t9 xeny;50s3gn8he period of its rotation i0sn9x5mgte8 3ynfl;u s

  A phonograph record rotates at 45b-cdqeuw9a 0f.ni p)8 rpm. Through what angle does it turn in 0.20 s0 d n9)qiafe-ub .8cwp?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the o/na;d07l83 7 o dua5pvw utxyvuter rim move /pd ;v7uxlv5o30a8anwy7t du in 2.1 s?

  A bicycle wheel rotates uniformly thi9r z,hogl1;v o+l3 zt3xpp0srough 2.0 revolutions in 4.0 s. What is the averapozg,+r;t x1z9 h3 o 3lli0svpge angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutz tq3r ekix8 / g6,id2pek4 sra4,b7mbions in 4.0 s. What is the linear i8ti, kk3d2 z,rx/se4mbaq67r 4pe bg speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries ski6latbo f +(2vbxfew ,z2n ly87.nwp(zers 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 fasznw6ywffl t+n 7 (( obp,b8z2 eval.2xt must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatingixz:* ebxlg 76 with a constant angular speed of 2.0 rad/s. What is the line:*6xbli zx7ge ar speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If -,zmwoqee6c.ig 8, ij the motor rotates at the rate ofz,i ,igee cwo68-jq m. 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotar j tvle4v 2b pzn9kj/v),f:t(ting with a constant angular speed of 2.0 rad/s. What9fzl2( jrtv j:e)v4,p/b ntk v is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point na8:3kqgyo1 o on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.knqy:13og a o800 m/s?

  How many revolutions per minute (rpm) must a cirs2+e 6zocqob +cular, rotating space station (r = 1000 m) rotate to produce an artificial grav6qos2 oz +cb+eity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed od 0zh3un9qyv, lg6x0vf 20 m/s. The maximum c,u0 hd6l v0zgyx93vnqentripetal 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)j. m)h ay6 ko3m,frly curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (pro 6mj) a.yhl,ory3)mkfvided 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 0g / f6j1o3cmqjbt7gb3u4/ ga i.750-m string, is whirled around in a smooth level table. Ifjgjtb gg3i/m 1a7q /36 obufc4 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 had33u bjskyb dh,d jtz,5. 7dl;3q:fradius 9.0 cm rolls without slipping 10 m down a lane sqbh5zkdjh;dy3ut3jf . :,,7b a ddl3 at 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 constant ak8 esm zj-26tmngular 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 of e*fs 8h 8d hv0pw0h/ce$4.5 rad/s^2$. 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 radiu3q;on rak76 ug/7tybha:ne +ns automobile tire rotate after starting from rest and accelerating at a constant an3ag;t: 6hq 7 yeo+bk/ unnr7nagular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelera1mr y )ufti,e/tion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s dewmg-cd1,6+z4aa tl.tm d ix x-g-x u9dcelerates with a constant angular acceleration 4 - 9dti -ct l. x+mxgawz1umx6ga,dd-of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and lkp9i3: /erwbu yc4d)9 ,mzdzreaches an angular speed of 6.0 rad/s while turning riecd/dwmbu pk94)z 9ly,z3: through 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ov .w/wx):m 2b oywhjj+her a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?jj2h)hbw /+y :w m.xwo

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to resevz who5 5l:5tt over a distance of 115 m. What is the angular accelerat5h:wlvz5 te5oion?

  A wheel of diameter of .w* ss h3agz1o68.0 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 to como*s3hg .sa z1we to the stop?

  A centrifuge in a medical laboratory rotates at a rotatiofnjn gbyxl-b( 1 -,ayr.b+ x6unal speed of 3600 rev/min. When switched off1ng +--l ,(b.ba xxury6bnyj f, 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 to3wac vf yvjt.2t:1: l0hxh1rm 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 r:aw1hm v 0v23l1ty jh:fxt. cwrench?

  The bolts on a car wheel require tightening ckbi1x*4,4 fdd+f dxbdvj-5 jto a torque of 90 Nm. If a 30 cm long wrench is used, what is the d+4jxk45bv d- 1fd,xj*bcifd magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofhvn k50; r. zw(nc4kgv 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 mop03jl qx*mr*s+ f i,8m l;l hgp40rjjsdeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass + q *4*f;llp,s03rjsjl pmhxmr8i gj 03m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fry3 ugdnc00/-w:aaf sqictionless axis thought the center O. A ro0f-ucysn3aw g/q ad:0 pe 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. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoteaq gfplgnz;40, d5c1a d 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 aroundalfzq10 ,d5gpgcn4; a 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 initially held in the ho++5mc ohf-g9n8 dgvmqrizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The moqm -vm+g9gho5cd+8fn ment 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.d mr xy,oj tt7,i,fegcyf 29)qt9 y:1j5 kg. Neglect 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 wheel2mt ,ft:)gr 1,9 eyfoy7,qjict 9dxy j achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped a7o0j sf62jifk round a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the sjojf7f206k iangular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aro/yff16-na8rc q gnp9lund a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What isf/r-1a8ngy 6f cq nl9p the acceleration of the mass?

  A rotating flywheel can be uoi4cr.l 7gbz 1sed 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 ouv:v19u xi5akgdxsamk77 5/ . d h2id -s1ochhf $5.00 \; kgm^{2}$ 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 masxfl8ro 4elj dd3q k 0 b1v1(dlde63zz:s 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 whe zfdvelqor46( 0d 3: 3zlxldj81 1bkden it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s gbo)pf-x(vu*qan(j(. How high up an inclined plane can it climb before com-qvof g)(nj(p x*b(ua ing to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest an3:0a e-*hjoz rs,ayd pd allowed to roll down an inclined plane. dj po3y a0:,ra *zhe-sHow fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg anjep3a),9k q y2dpq/c3 t4 luted 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 spher2pjlp,3dceq k4t9t) y uq3a/ee 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 changec2)4ta95z-f9m nff* o guo,ztd wh0bus 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 : 1v 0b;lx ch:f1b:qplzhsx+i 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 wq kuemv bqf;,8qnt* *ge5-0ieith arms extended has a moment of inertia oi8v 5ef;q u*t- 0qmnbe,ek g*qf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?