Angular displacement ov1c13wnu (xv is usually express in units of

  Angular velocity is expressed in units nbr+:(dfqd*0be a-jj fen(+ o12oo . svng(lrof

  Angular acceleration is expressed in unv i r+lt18:-fjey6hsbits of

  A boy and a girl are riding on a merry-go-roun brb9y3sy*-sa d which is turning at a constant rate. The boy is near the outer edge, and the girl is closea9sb*y 3yb -rsr to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-g,1pb;uvfi pu3o-round which is turning at a constant rate. The boy is near the outer ifv,u b3p1pu ;edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are r t k;6zh ;shhsuxn3)6hc2:b(z b5jokbiding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closjhk2shztu:53bboh; ;s 66x (nhb)zkc er to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-roucrbeu bm0.4d 2g2s np8nd which is turning at a constant rate. The boy is npsg2r82nbcb .m4u ed0ear the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are)dv6t kt.6jf d riding a merry-go-round which is turning at a constant rate. The boy is near the outer v.6 )dtfdjk 6tedge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the follow4gp 0md-gk)sj5 g 3hjbing is an accurate statememb0g4)sgj- dkgj5 ph3nt?

  Rolling without slipping dep2.kkpw2bj ; df u 3 hxnlj6+m;jroxeyr):a 40pends on

  Two equal forces are applied to a dozmw7pp,t wtt1 xhiyv;. 88x3dor. The first force 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 exert xzm xt,d1wpth; p8i8ytv.w73s the greater torque?

  Two equal forces are applied to a door at p 75sh3mg7al bthe doorknob. The first force is applied perpendicular to the d5m h7g3a blsp7oor; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknobwu10xk0 p nrj2)k4jdu+ hac;g, perpendicular to the door. The first force is twice as large as the second forux0jjcdn +4u21) a gh0r;wkp kce. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to chan/s ku3u hrhd04ges in rotation?4uhshk0 r3 u/d

  Consider two uniform nba5f7+18xk j oj /rbssolid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger m bn 8ab+f/jrs7jk5o1x oment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the r;owcyg a37fy1a5 7 lsuadius of the other. The ratio of the larger sphere's momentg 7a ywl5ayu;s1c 7of3 of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and tj54 pp 07ho++3yqhmh 8 hqxmrxwice the diameter of t+y qh opj73hx4xhqh8+m pr5 0mhe other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere h0 ho )j obe wj56p):nnwn*lp,has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a ce6jo)p l) hp:ejh ,0n 5wbnnwo*ntral axis?

  If a constant net torque is applied to9ywc1r )/r7bs go4ik e an object, that object will

  The moment of inertia of a solid cylinder about its axis is givo3 4dv* / *baclume q8tk0b9mcen by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translatiota3/d**9kv c08clbeo bm u4 mqnal kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a i1;h(xh+5d osmy 9 wtymass 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 th9hty5y (w+ 1h xdosm;ie bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down an g y 9/8w8m7gd-kvvqd pinclined plane startinq d7pgy8v9 /mw8-vkdg g 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 withs irgzd::5hzm52*od cout slipping down an inclined plane starting from rest. The angular vdg 5z*: s5cdr:oz mhi2elocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net (wom/v. v k z4kg/fak-external forc//kv-mwaf(4v kgk.oze acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles change y6hc)6y0 zo4bp4uw ltwithozyt0)y6c6bh 4p4l uw out any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictiuyg omhf5903o on which may be present. What happens over time to the Earth's angular momentum aboutf0g5oy m hu9o3 the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth5g*ddg+0nss- u fwv iigs + :bqbb:f+6 moves close to t n5 *bubsss0d viwf:g6b qif+-+gg+:dhe Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretcha 88zb5onc)k; l wtmv( ,wy:ated arms close to :z;(w8m n c8,alaty5 wobvkt )his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his -)(sn s wez;qamzhd5m 2.ri y:outstretched arms close to his body. What happens s. rm): szz5y(2 ma- eqhwin;dto his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretch qf;;utajn: hfdqqb64 o7u 65zed arms close to his body. What happens tojuhfq:6u;qb qofn54z76dta ; his moment of inertia about the axis of rotation?

State the law of conservation 4j4wb uw0 i1c;u puxw0m)*chlof angular momentum.

  What arc length does the Earth travel in a three month period in itjbnjwh2f*qm as v)l2;;g/nd) s nearly circular orbit about the Sun with a radih 2nbjw;*2; /vsd l)g)maqf njus of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a :ntnncqkfp-1nlo wv +;l70x( length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 seconds?nox(w cntnv1f7ll pk-0q:;n +

  How many rad/s is 25 revolutiohg0f0tr d n-d,ns per minute equivalent to?

  A bicycle wheel rotates unif oww: 71b egzv4z/huq1ormly through 2.0 revolutions in 4.0 s. What is the frq174:huw1 e/ vob gwzzequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at k0jyu. 04 dz8by cae0ka frequency of 0.40 kHz. The peri 8u00yke04j .ykbzdcaod of its rotation is

  A phonograph record rotates at 45 rpm. Throum*sr/ :vq 6xi1moj(ryrz;u5jgh what angle does it turn in 0.20 vsr*u zj(i/m r:65 j; 1rqyomxs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on te tq;jf8gr ,c(y5:;q +czv+oiqv/ a bphe outer rim move in 2 by5 qcvaife/8+r ;z cgpot(;+ :qv,qj.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What;nm)q 9l9r/8ps+ nggo jbnqn .7f *bgj is the average angular sps*7 bjgnr9qj bn)o; ./ 8gnl9qnmpgf+eed of the wheel?

  A bicycle wheel rotates uniformly tfjmp//e77- chgg6jm5k 6mj c dhrough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the 7 5mp/ekcf/ jdjg6g mcmh7-6jcenter of the wheel?

  A cable car at a ski resort carries skiers a distance of 6. ftda06ay f94bsad0,yf j8ab8 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 rotate for the cable car to make the trip in 12 minutes? 0 8ffjby49a a8dybat 0f6sda,

  A wheel of radius 1.0 m is rotating with a constant angular sgkva7 j( f, hbe2n jcr8)d)gi;peed of 2.0 rad/s. What is the linear speed of a point on the whege gk)cdf;87v,r hn2 b(j)jaiel's rim?

  The cutting cord on a gas-powek9ig cmqtrj 3d)(ae8brh2r)8 j4 tzr1red weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is tmrr 3j(airtrt9eckg) 8jd18) q zh b24he approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speedb4zi s.iha1)q of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's rim?4sh aqb.z )ii1

  What is the centripetal acceleration ofnk0. pb vxa1doiyf3(9 a point on the perimeter of a bicycle wheel of dp9nakd fv1 .y(3x0o biiameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating qa55wwq( 7maispace station (r = 1000 m) rwq5am(aq5 7 iwotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 r j-c2)ykq8ps m/s. The maximum centripetasj- )pc2q8kyrl 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 curves rhh2mj3obhf3- ovx v7 b21;y of radius 50 m with a speed of 20 m/s. The maximumh v3bb sh2voj7ym-h3rf;x2 o1 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 of a 0.750-m string, is whirled arm+5rz7bb7mf aound 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 string is not to brem7 7rzbbm+f5 aak?

  A bowling ball of mass 7.5 kg and radc )za*agm c 3u4td(n/lius 9.0 cm rolls without slipping 10 m down a lat az/( cu*3mca4ngld )ne 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 acceleratim2zd90a hg9 nuon 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 constantnlnt( 8 stna*0 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 9g8nvitaj.fw7azga92 5 qd*0wcp c. aautomobile tire rotate after starting from rest and accelerating at a constant angular acceleratiod 29 ac5.g9.7pvjwwa fgcnqz* 80ati an of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleraap28;q4zr uw 0ui:-8yp iksjztion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerah oj+b8 )xw;7pydu6sktes with a constant angular accelerati )uj poybd7+6h8ks w;xon of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reache2y hf yxm;f *7gm2i.qjmj1cg6 s an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accemgq* ifmfmx2j h jyc 67.y1;g2leration of the wheel?

  A wheel of diameter of 68.0 c,2d lm xzjq7m8m slows down uniformly from 8.40 m/s to rest over a distance of 115 l,2zq7dmjm x8m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 6z jh67/o 7oe5h:oq 5d/ w1rz fdudtz6k8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. W6odq557zeot7f uw1 z/rdjh/ d :ho k6zhat is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest op7atfk(j r 35oc8e*ucver a distance of 115 m. How long does it take for the wheel to come to58e t7j pcf (*r3cukoa the stop?

  A centrifuge in a medical laboratory ;poh p;q6kxq ,jy 5h23sfwlit8k6 r7 mrotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at jtyqr piph;k6m ;6w328l5ks, qfox7h 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 90 Nm. If a 30huap -sqg l*.*h11o;jo -iqto cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the wre-*t*1 lig1o js-ooa.p h qq;hunch?

  The bolts on a car wheel require tightening to a torque n.f- )n.cmr (,ehqlw qqmfj1/of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the for cnwf.j ,(1mqlnre.h q)fm-/q ce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofrsq i(1vz3n*z9t /cut 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 mt)k87 5e/bdp :c+gna uo/ufvnodeled as follows: mass 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 the uk7t :pbavo5) fge/nu8n/dc+ origin?

  A solid cylinder of mass 10 kg is pivoted about a fri:tx 9sc/ac1aim3 8jomctionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exertm cc:1o9 38a tsaix/mjs 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 kagfju-za,z2cy;f3yny6z0 x97hcj e )g is pivoted about a frictionless axis thought the center O. A rope wrapp;g ua6-c3cxzz0a)j nf9zyjf hy, 72 eyed 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. 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 iy0o yb (im92xmn the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? y(i9ymxob0 m2 (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring oamu0:k69w mw jf radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprockem w:j0mw 69kuat 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 frictionle( (qo8ocbve5gaa b2y5ss disk pulley of mass a52(y(8v caq ooegb5b7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley c6xxj+.aeqibu2r5w8 of mass 7.07 kg and radius 66.0 cm. What is the ac6abx.85qu +ri w jx2ecceleration of the mass?

  A rotating flywheel can be used1f7:emj+.xzc b2 pf/y pws,ft 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 inertiah;o*cm3.1dh xg(rp *p doa - jrncj6r0dq90eq 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 teet (h/wp7nh-t: lq95n:s pjif6f (arest and rolls without slipping down a 1.0-m high inclined pl6nttpth-fnplh:swj a 97:5ief /( q(eane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg andtz8qx77h35 vyhur mi 2 radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming tr2tm x3hh7 5y8vuq7 zio rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is . q(v pn)no;dgd0tr bc)y9xmf * a+nu5released from rest and allowed to roll down an inclined plane. How fast is it mo) b cgp)nt59n*dy o0f vr+nm;duxa.q(ving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 35.kkxi9tt8e /w e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is gtw9ek8 ki .x/tiven 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 mome hqyy1f9ztu2 8ntum 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 ofyg994ryi6 9f7 0vtiekzw fs(hbimo/zi9 e 36z 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 mo 0flapo/x,i:d.pi mc ;ment of inertiamp/f. ilciodaxp,;0: 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?