Angular displacement is usually express iycl2n qr +9n igt2mm2(n units of

  Angular velocity is ex s0)c.xg0ebh cpressed in units of

  Angular acceleration ot+cf r9all;t ra 02j6is expressed in units of

  A boy and a girl are riding on a merry-go-round-9lkug,2gr x jcyg1; t which is turning at a constant rate. The b ctg9x2,1uyj k gr;gl-oy 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 risn*0a nhlvlx kr;cp4n 8o9u0 3ding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the 003 nls h9cr unvok4pnl*;ax8 girl is closer 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)sp :qzc u1fzku4/p zqdbv3 6. a constant rate. The boy is near the outer edgzf4 3zc.zu/1 psku:qd6bpqv) e, 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 consh8j3sgad-q5o :l 6mmib b:w8d tant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater c 8:5ml6o8gdsqb-w j3ba md hi:entripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at amjph ( 6y/t) s+1ejmzf constant rate. The boy is near the outer edge, whim/j6)eyzh1j f+tp(msle the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an a7r f6s am8+bup.2hfpaccurate stap7bufr as8map.62 h f+tement?

  Rolling without slippiu tp rsu)c:xvnj*,w9-ng depends on

  Two equal forces are applied to a door. The first xmhw6am,t a7 *)q p3m)uvv8awforce 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 )av) mm7 x haamwvpq*t6,3 wu8exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is apprcopvkag )j4v:,qwhl /bue9f* 0 v1p ,lied perpendicular to the door; the second force is applied at 30e to the plane of the door. Wh4vv,)* egau0fp 1wlr vj c okp:bq/9h,ich force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. o 8gj-5h*d 5b.v muff-hlftu )The first force is twice as large as the second force. The ratio of the torque of the first to th 5bhu j8 htf-5vl.*fu) gfmo-de torque of the second is

  What is the quantity used to measureeu sju207t u0b an object's resistance to changes in rotatioe02uj 7bst0 uun?

  Consider two uniform solid spheriyw7*.i csoe: :gvr1jes where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertiacivir.j 1 y*osge 7::w to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radibf 0sprm/- i/p7v82+th zw hayus of the other. The ratio oftpy s-b if0whr8m 7/za2p +h/v the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the-ic0kz f v93(a3qefmdj49vd a mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller mome d edcv3k(a4a3-f 0 vf9j9zqimnt of inertia is

  A uniform solid sphere has mass M and radius R. If these vweu jtunia86 dg jam/f*55 -j-eh-b9are increased to 2M and 38uw-tijgu-ab j/e*jne dvh5 5f 9-a6m R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that onewv t5z)pv4e*c78 cs lo ;s;pbject will

  The moment of inertia of a solid cylinder about its axis is given by 06rhzehd/u8h 17ehg5 4jk8rg+7zck xc .5 MR2. If this cylinder rolls without slipping, the ratio of its rotatiochkr4+g8zu 7xc5g71h /ekdzh 8er6 hjnal kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which hv rq (x d. /e0(k2w2ui9nalvccqky6 3mas a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of k( c9qmilyq6(e0v2cwk /v.3nua2 r xd the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippa 3-5l* etvqpdsj xe9l. +zgi+ing down an inclined plane starti+lpljez ast-qd +g. vi xe95*3ng from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an incs ixmqoj9di: vq- 7+ul+)3b-t lsvud*lined plane starting from rest. The albluudj3:)o x7ts -+-d +i9i *v qqmvsngular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of partic nuo kx+82zqkgo yu)+/d :pio3les changes when a net external i u/p3nzok+k gq do+2:yxu8) oforce acts on the system." This statement is

  In what circumstances can the angular velocitym 9 tbyzgzpoi/;x1q3 nt 4b6n7 of system of particles change without any change in the system's angular momentu yq i m7xp/o6b z1nbgnt94;3ztm?

  The Earth orbits the Sun in an elliptical orbit. Ignore any/z vxhfgn+,.g friction which may be present. What happens over z,gfgh+n/.x vtime to the Earth's angular momentum about the Sun?

  The Earth moves about i pd9 m16suxb-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 the Eart9sm dux-6b 1iph about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretc.e+ u9x2kb svxhed s 9kuv+b.ex2 xarms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (1*q)+7aeswb -ru6e p/x* /rvbbwn2yz0owt z ra fast spin) by pulling in his outstretched arms close to his body. What happens+*/bn1 6vp/w-a)ow0ery qw rx z rtub7s2 *ezb to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirlrsss)n 60 w1ioubk v*+; /dbqouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about 6sswu )n*kslvoq1;dib r0/+bthe axis of rotation?

State the law of conb 5.d/r:uxgfc servation of angular momentum.

  What arc length does g/k0 jd;hov3.lopp5ht/ ad j7the Earth travel in a three month period in its nearly circular orbit about .hoog/;d3 5hap 0/7l vpktjdjthe 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 l:srzr3lx-xb6 ba0/t distance does the tip of the sllbxarx 0 r:3t/ z-b6second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 p. n24do8 qrxcrevolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2. 0x:lumof3yveh8t y0j0n +yc- 0 revolutions in 4.0 s. What is the frequencn0tvyhx l8 uy - c:o0m0f+ej3yy of the wheel's rotation?

  A pulsar (a rotating neutron s sylw h vd+o03a /5tjam6o rs:4ftxj/3tar) emits pulses at a frequency of 0.40 kHz. The peri/3j:s h/t50a+aoo4d jltvm 6w sf ry3xod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle doepff-)cs6 a;mueog8 : os it turn in 0.20 s?f:p-a osgoce m6f );8u

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on t lmd.fipcx15* he outer rim move ii5mdlx1cp. f* n 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whatc3e ;cfhcl93r is the average angular speed of t3cel f93 chr;che wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wumorohg0z2,x c 5j4gq ru49h 6hat is the linear s06ugrhm r x z54g,j9quo4c2ho peed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skie7r,dhd1zos4j 0 j8j ,xap*sus rs 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 fast4hs 7j0s,xs ur1djp aodj* ,8z 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.9iy ; kz yl0 w+bs+e yz1zx*:)qlnpln constant angular speed of 2.0 rad/s. Wha1+ eb+ qlk0: ;.nlzszyl9iyw zpy*nx)t is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered wr)z-c0s ,t axseed cutter is 0.16 m in length. If the motor rs zr ,a0s-xt)cotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angul3fgv f/d 65f bec3bd/e:tgiak3e w-hj tj.1 /yar speed of 2.0 rad/s. What is the cent g3:ah6c g/tvefw jef5di//jy b3kfb3.1td -eripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycleu7gc j s22:wfh9fw6s i wheel of diameter 70.0 cm when s jf6g:c2s hwu i92f7wthe bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station (redk +2o/3xvpi = 1000 m) rotate to prodi3kop /v+2edx uce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular-59pl3 tg kkvo.hx4u q curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stati3pxtv9gu4 5qok.hl k-c 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 wr;uh6lfrw:.y c3o:ba9ncv l/ ith a speed of 20 m/s. The maximum centripetal force (provibcr:9 .:; nlr/3ayv fwoc hl6uded 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, isb/ hg*tcyur)0c 5n8ec u5byo, whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if the *cec0co) b/r un8g5th,b 5uyy string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rollsyqwfb)8*27 x: ax;g qek8 gmdr without slipping 10 m down a lane at 4.3 m/s.ydb7g;fk g 2exr:aqm 8*)qxw8
(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 acceleration of y.(ntfh-)3vv jet w2h$4.5 rad/s^2$. 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 audr*f5so j68l7ea7 kacceleration 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 tif(p y*jr0 k; ..knms3zj q2 qjtr*i5fere rotate after starting from rest and accelerating at a constant angular acceleration; (rk zfq 3.k*ms t0y2j *jir5epq.jnf of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelera2i:vf)ewzzkm)gg3 q0 hox0 7 dtion 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 zlt pjl. )eh/x) 7+kyx4,tmzpacceleraz le,)ztjl p/h x.x 4)pk+y7tmtion 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 z7 +k*xy 4qhbmrad/s while turning +hqmk4 *yz7bxthrough 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from em b:kcj+(0 .x(kseap8.40 m/s to rest over a distance of 115 m. What is the total ( be+scejkkam0 (p :.xnumber of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of w- 8qk9ubapac6qx 6e) 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accelerationa 8xu)6q-cwkp6 9beqa ?

  A wheel of diameter of 68.0 cm slows down unif)hk1*0v l5/cvf-s(ci xf)ssc pzc :ukormly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to c0)c/s: vscu k15zh(sik* p -fclfcvx) ome to the stop?

  A centrifuge in a medvvrc s (u7;2;llpp05: qxjbnd ical laboratory rotates at a rotational speed of 3600 rev/min. When switchecs 7djr l:; ; l(0bpun2vpvxq5d off, 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 torqu.: /2.n slfsg lbt 6 ucxfx02kp4d.zbp4yp5hb e of 90 Nm. If a 30 cm long wrench is used, what ispk0ynblbf24z . . ls5tx:. /24p6pdxbhfsgcu the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. hff o95f(3cdyIf a 30 cm long wrench is used, what is tchyf 5df 9o(f3he magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia wf-ypkt+,eka z5o/t/b1 p1jz ej0wg3 $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mata.6*p pvnho( yp3)joss m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about tpa 6(o.np)h pt jvy3o*he origin?

  A solid cylinder of mass 106.b wgqxs rmyv/i9 6w) kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a for)9/vi 6sbxyr q6wm. gwce 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 pivoted about a friv o7d--l yv;zx (bgy)gctionless 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 sectilv7yv;xd g ()-b z-goyon 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 - g l;sighfjne k:;p6p:(:auv the horizontal position, and then released as the free end is allowedafil;6(g :egpj: u: p;svhn-k 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 1.5hiu.n4 r/f+ kf kg. Neglect the mass f.ruikn4h+ /fof 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, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pug-d (1j hwk20bayw(l 0yc wly/lley of mass 7.07 kg and radius 66.0 cm. What is the angwbacwy(y jl h1/- y(2w0gl0d kular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around:c0 .wbp:js k/mi 7bxq a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accwsb/.x:m 0icq p j7b:keleration of the mass?

  A rotating flywheel can be used to store energy. If it is requi xibxay 5q .)mru2j) d:cu*xs+red 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 oor atg1/kdwablq p;:-9sni ay+7 d7i:f $5.00 \; kgm^{2}$ 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.egbhh3i: 7sb my+l/q4t ty /o8010 m starts from rest and rolls without slipping down a 1.0-m h ://74t+i glty bso mq3h8ybehigh 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 re;8x y y5:lj8alkh9wcadius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane5 y wlye8:;hx jkca8l9 can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fqyf,ry- :j 9dhrom rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance offhd- rq9,jyy: 3.0 m?

A solid sphere of massgjq*hok:33znbk)jhjl6, sr9h c h, -w 1.5 kg and 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 s)n-hh,r3zcj oqh, w6*3l gsjk:k 9hjbphere 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- 8we 35xli0yy m:th8w3 ckmut 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 momekx j ul8;bcj9(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+*f u,cqdw5i9tr6 oaj arms extended has a moment of inertia 6*q t r,adfujw5o9i+ cof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?