Angular displacement is usually r jost 4dfoc zc1zr xdx0:4815express in units of

  Angular velocity is expressed in units ofzvw78 z c8got,

  Angular acceleration is expressed o0 )* vrq0igj)rpr/zg *0psmzdz3 6w1rgx cb) in units of

  A boy and a girl are riding on a merry-go-round which is turning atva,j:bf 36x wss,yv:j a constant rate. The boy is near the outer 3w6sa,ysxjv:,:vb f jedge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a 9i w. f;mhja.mglut08r a:h/alq()acmerry-go-round which is turning at a constant rac .h8;(h j fliqu/aalra.a m)m9 0:gtwte. The boy is near the outer edge, and the 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 iezp;96p. ewflxp kg 3bpp l*eq.(51 obs turning at a constant rate. The boy is near the ou(z1b5.g fqxepe ;9 ppwbo3 e.kp pll6*ter 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 constanp +x,09mou rtft rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centromx+u9p ,fr0t ipetal acceleration?

  A boy and a girl are riding a merry-go-round which is tur6gvi 3l al*7mining at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who ha 6il7la3* ivgms the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the followin1lkc.n+ m( iqng is an accurate stati1(ml. kcqnn +ement?

  Rolling without slipping depends e4 dl2 ita/h*qgnyi0 9on

  Two equal forces are applied to a door. The first force is appli3/ q bb vtt+0xf2 nb-eanjv1s:ed at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Whv+n:ftt10 -sjqbbn v23 abe/xich force exerts the greater torque?

  Two equal forces are appyi/sp *5jqh)a;ucg9vt 8. en alied 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. Which force exerhg8c 59t/vi*j)eua snyq.;ap ts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first wif ,qofg18s8,nijj16 g,ebh force is twice as large as the second force. The ratio of the torque of the firstjs qi8fb fngj,6hi ,,g118eo w to the torque of the second is

  What is the quantity used to measure an object's resistance to chawvf fya j-6 /z* zzd(zdjp1e8(nges in rotatio/*8 zp((fz yddaef vz1zwjj-6 n?

  Consider two uniform solid spheres where both have the same diameter, but onsbw t8dqp)loejf 40.tl6( 8v:puz1 sde has twice the mle4vtu.t z jd (s8l:8qfpsbp1)6 0odwass 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, but one has tm-cixr0oqyun. 4e l1; wice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the 4i c lermon-y1u0;qx.smaller sphere is

  Consider two uniform solid spheres where one has twice the mass andi)d +;e z89bzsbo-ctd twice the diameter of the other. The ratio of the larger moment +bo8d9)cs;zid-ebzt of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are incre2+ 5ot c bmt6i eim hvg(+vn4zrxm.+-uased to 2M and 3R, what happens to the sphere's moment of i+muz4+h ttm5+(gb-cxevr2 o i6 vnmi.nertia about a central axis?

  If a constant net torque is applied to an object, thzoo;g. ib2 gz g:e0d s:s(q0+:ct ggovat object will

  The moment of inertia of a solid cylinder about its axis is given by 0zsz* .4nv0s6 o3zdi km.5 MR2. If this cylinder rolzsv*kz.z o 6m3id0n4sls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of /nf3m q zkem3710 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic7ke m3z /q3mfn energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without sliphyf/zq3t +go9ping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depenyfq9tz/o + 3ghds on

  Suppose a solid sphere of mass M and radius R rolls2pwa2+ f . jg2uyyka+b without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottj+ gu2y.wbpak2+y f2aom of the incline depends on

  "The total angular momenx .-(5;dgt2yglzof+ bepwzd8tum of a system of particles changes when a net external force acts on the system." This swpxzgotf;el 8(+yz.ddbg52 -tatement is

  In what circumstances can t 0w 3fc75cwuiouc c l3c ncv9ky1iw)*3he angular velocity of system of particles change witho3u1 wi 3clwvyw nkoc9cu*)53 0ccc7fiut any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. kp q;k+)5xcqlIgnore any friction which may be present. What happens over time to the Earth's kl+pk; 5)qcqx angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical 9.ek bka37eh8zbvj:q orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Ear ba 3eqkh8. zj7kbev9:th about the Sun?

  An ice skater performs a pi/.(x a+39 :k7cblopjx pfzjhqrouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotqj hc .9 (x/k:3+ oxzf7blpapjation?

  An ice skater performs a pi)56 hl kippni-rouette (a fast spin) by pulling in his outstretched arms close to his b)i-nli6h5pp kody. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling inwdsys 25- o+eufhb)3v5/a)a mme ;ofn his outstretched arms close to his body. What happens to his moment of inwny5b;oa s2hefev5mds) mf/a3 u)+-oertia about the axis of rotation?

State the law of conservation of angular mome-gupc0f mx20x :xo yz4k, r.vxntum.

  What arc length does t-,xvuh cp05dvvs 67 tqhe Earth travel in a three month period in its nearly circular orbit about the s v70hdtcv,6x5-upqv Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has ag94kw 6u3;(xcfgcfd o length of 0.30 m. What distance does the tip ofd ucf cf;(w6o3k 4gg9x the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions pe9j(rvn7v(r: ,v+ rg5atfvo cwr minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutit *ux1l3h. cv iama8)zj 6yloao5b a aj;ep;3.ons in 4.0 s. What is the frequency of the wheelajyx.1zhbpu5oj338v.i taa6m a*) a e;l ; ocl's rotation?

  A pulsar (a rotating neutron star) emits pulses at a fr6tfbw5)qtj q)equency of 0.40 kHz. The period of its rotatitqt5qj ) bf)6won is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in wc0 lfae*3 q8o0.20 qafc0* w3 l8oes?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point 4y1jtf o/1p mpon the outer r1pt4/f1 jymopim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolud9y.,m6 cet+k j/rf yxtions in 4.0 s. What is the average angular kf+ 9ryc mdexj.y, /6tspeed of the wheel?

  A bicycle wheel rotates uniformly throug h)0n:s3tlzn dh 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m fron0 3hszd:t)ln m the center of the wheel?

  A cable car at a ski resort carries skiersjcw p2-: hnng) (3vcau a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuminp nh:3)2a v(un gwcjc-g 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 r l2jm*u aekj/1ad/s. What is the linear speed of a point on theuaj 1/2 j*kmle wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. Ifkjx4 5 tt5plog t,le(3 the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the e tl5o(5g t43,kjtxp lcord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rb oc 8o6pfkb-9zphb t .+s:x/fad/s. What is the centripetal acceleration of a point on t6f /h9bc kp-+ o.b s8btzpf:oxhe wheel's rim?

  What is the centripetal acceleration of a point qcgfuu nnyz(c,ih:er8 l.: . jx/4+ gug8ok:hon the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.0 un :u,g4r cf./q8nyh:eg:8gho(kc. lzj iux+0 m/s?

  How many revolutions per minute (rpm) muhg: 4 u(fss h.smmzai80 uj1b3st a circular, rotating space station (r = 1000 m) rosj0uzu:hs .smab hmf8(1g43i tate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with x2e, vx 98,uc 0t4lgxko(uznr a speed of 20 m/s. The maximum centripetal force (provid9 0u g,u2 o4vtz(kx,lnx8x creed by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiatingpkm ,nc6vadk35. o6yud7 j:nq a flat circular curve of radius 50 m with a speed of 20 m/s. oud jkpd,q6ayc5k3.7 : nn6mv The maximum centripetal 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 6) d65dl6ut wqy+ei8ay ya6ta d2acx :of a 0.750-m string, is 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 massx2l td 6aayy5c+68iqdw6)taud6 :y ea have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm roldt x3rs t ;m:yayqae1l2-0v f*ls without slipping 10 m down t v0*ya2:dsr qtfl;3e may-x1a lane 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 angular ac d0 n jmezs8va57fb-3pceleration 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 acceleratioqe k+ pxf3p3f6n 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 radiu fq- (pwy3rev)s automobile tire rotate after starting frope qy f(-)3vwrm rest and 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 accelew*p4 ,sigvf6+atr7h f8 (x fsxration 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 0nmps j vi25+wa constant angular acceleratis 0n5+ji mpwv2on of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest an4-*isvxyy u.,xsj e1c d reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions.yx4x,.jcyi-1e *vuss 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 h y 8j i23.b4)tqrbujdover a distance of 115 m. What is the total number of revolut )4jjrtuyib 8.2b3dqhions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down g g9i 3 ;4tav(v3vuw35 ibzzspuniformly from 8.40 m/s to rest over a distance vi34bv i3a9stpgzw5gz3u(; v of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows dow8v( etud,xk)9 sxfkf+ n uniformly from 8.40 m/s to rest over a disfd8ef,xk+)(xs 9tukv tance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/8 f0g 5k/x9yfqd+jvl gmin. When switched off, it rotates 50.0 times at a constakvl+ggx90 j 85qf dy/fnt 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 tighten8qds+/ d(llcar57i kging 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 is perpendicular to the w lq(cilsd a5 7r/d+k8grench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm lge n- axm96,7zair5bf ong wrench is used, what is the magnitude of the force required when thz iabaf95-m e7nrx6,ge force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inert-*3nlwe-g vef ia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follono8o6 e9pvd )fid1m8 hws: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of in on d)fh1 d6eviop8m89ertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoughtvfg/6yye bne(9lz4 y5 lmp+x ( 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. (See Fig. 8-1.) What is the angular acceleration of the 6/lzv+geenylp9 5mb(y4yxf( cylinder?

  A solid cylinder of mass 10 kg is pivoted about a friccbvu lj6b-9 wte4hv; 4*gc*jn tionless axis thought the center O. A rope wrapped around the out ;ewh9vg*u6jct j-cb*4n v4bl er 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, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initiald1z (cx1wlxpax4 a5* vly held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration ala(p1z xx1w x4dc*5av s 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. Negl;: bzsewy73,i-nnkb5 m/ab cyfxk*b 8 ect the mass of the axle and sprocket. If a force of 2mby: xk37/y- z bnfn5b*8a keic,ws b;0 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 dis nsi vt+kh;/vm iihdx+kvt;;- o;( yl-k pulley of mass 7.07 kg and txi k-n s;vd-+hm;;ti y/i ;h(vklo v+radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around3p ya qzbsg8po(j9t3k(6rl 9m a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of th 3a3rbqk((6j mo8tg9z y9p psle mass?

  A rotating flywheel can be used to store energy. iul9+mxw yh:sre225y j.c 8ytdr q2s. 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 of gyj :7qo:syj8ts1 rqiq9fh45 $5.00 \; kgm^{2}$ 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 rc* dv6nye9xi: adius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the s: en6 *9yxicvdpeed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass g y ugf;+5nk+q1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an iufg k;y5q++ ngnclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a8ogv18ku m5f0 2kn plo mass of 0.20 kg is released from rest and allowed to roll dowpm58go 820okf u k1nlvn an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass yp/vp.mi. zu 21.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started fpi2m /.uzvp .yrom 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 kqmk d;) gk95smomentum 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 mome-4u v);wc 7depopgbs* 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 has a moment o/dpub oz-l/rnc3c9a ;f inertia 9a ;uczrdb/-3p n oc/lof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?