Angular displacement yhjyny) 8 :hy)u+qlj5is usually express in units of

  Angular velocity is exp/ltcqa-d e kzeg80tf 48hm91.5 hsyhcressed in units of

  Angular acceleration is expressed in units of t8 g11a1-6nx4cl ,*ccqle putnvqrn(

  A boy and a girl are riding on a mers3 vp*+:nz bpary-go-round which is turning at a constant ratebsnpv 3*:+z ap. The 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 turning at a constant ruwmqv a7fp o) iml783)ate. The boy l3)o)vufm8i w7pa 7qmis 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 oho5.iemrbxey k hi0:49k() m9ha ta- dn a merry-go-round which is turning at a constant rate. The boy is nea i9 edk:h5m-y0ia.(4 bker o)hxhatm9r 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 which is turning at a consta, 6b+qwtjxtr) nt rate. The boy is near the outer edge, while the girl is closerr tb+ ,)xtj6qw to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round s-sw,b l1k nxrhre;15 which is turning at a constant rate. The boy is near the outer edge, while the girl is c hkrwb- rxl15nes,s ;1loser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accuratemz*p e. :xd4dhnq9n5l statemen ld:dnm*.qhz pxn4e59t?

  Rolling without slipp : 3-ec3aecv6n6qdedp27mqli ing depends on

  Two equal forces are app 70e-gmh gwgeoj4qwmip5** g.lied to a door. The first force is applied at the midpoint of the door; the second force is applied awq*7.g* eijg0hg w4-om5mepgt the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are appm1.0j :xw*mq1- hv cjueffs k3lied to a door at the doorknob. The first force is applied perpendicuhu. jkmj 3*x :vqmffce1s-0w1lar to the door; 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 doorknob, sdupqp)/ (f l/:sx3dla)i t(+sr;xu eperpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of t+i ) (3duupar s)t/dq fe(s psl;xl/x:he first to the torque of the second is

  What is the quantity used to me c* 9y aces5hlq gxw:;7iu:d0oasure an object's resistance to changes in rotatioig:wo*c7: he0c;lq a 9x udys5n?

  Consider two uniform solid spheres where both have the samef 964loao( pcb iyxj05 diameter, but one has twice the mass of the other. The ratio of the large cily9fj (ox5b6o ap04r moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one; 5hsejaqv hmo6.lw8rl +5l3 m has twice the radius of the other. The raeajl3h6 r l;l5+m 8hm5.qwvsotio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twicpi39f- / wkv4)n fqjjde the mass and twice the diameter of the other. The ratio of the larger mokj-q3)/f4jnp9 if vw dment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and ra,pxvqhz *,m 6+xbdi.h dius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a cx 6h.hp , vd+x*bmq,zientral axis?

  If a constant net torque is appliedw;sakl *:v./u id x43gxep dl( to an object, that object will

  The moment of inertia of a soswsde(. a*n(alid cylinder about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls 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,qnfw. 0g-sx6odr4 fm which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels tm-ow0x qr ff,gd4ns6.o the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rollsje hx1:7+*lm*yqenp v1hm .vg without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom oy1pe.n1x+mm7*l ghqe *vjv :hf the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without4/ur:q4fcru1cjyf w.p g5.ck slipping down an inclined plane starting from rest. The angular velociyrc f.cfr .jwu/pu 44 5q1kg:cty of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when ag.zx hf(7 yyj+g1rhr ;y+d:pv net external force acts on the system." This stahdrg7f zxyyrj; g1yh.:p v +(+tement is

  In what circumstances can the angular velocity oq aeepdagu(7 zyt9(q+ g vd(1(kw*re,f system of particles change without any change in the system's angular mo9(q,(azggear qy (pkedved 7u tw(+1 *mentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictiahia xkf-2 u );o4g:bvon which may be present. What happens over time to the Earth's angula g :f;iaaok)42h-xbv ur momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves clos+llfu8gc5. t xe to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sxf .ul 5ltc+g8un?

  An ice skater performs a pirouette (a fast spin) by y6q7smx3neo o;-uv.gb2 /8jbcr tg+h pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotat 7gb n ycj 8rgo2uqs6;xe+.m/v-3tho bion?

  An ice skater performs a pirou)9/1wyg rehldk qgh ),ette (a fast spin) by pulling in his outstretched arms close to his body. What happens to hiw)yqg)h egk,l/h1d9rs rotational kinetic energy about the axis of rotation?

  An ice skater performs a s )9tju uz5kxuxf;eoxok)3-( pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertiz-o t x ) u3e9os(;5u)ufkkxxja about the axis of rotation?

State the law of conservation of ankg qzdo;u(,90ute2 h vgular momentum.

  What arc length does the Earth travel in a three month perio83fcxl1j8x,r jd.t w hd in its nearly circularhj jfl38xtd,cw 81 .xr orbit about 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 dis am/zkeu e-i70tance does the tip of the second hand sweep through in 3 minutes and 45 seu kzame -i7e/0conds?

  How many rad/s is 25 revolutions per minute equimeax1b8 sse7r m)); usvalent to?

  A bicycle wheel rotates uniformly through 2.0 re5t)n ,9gcm6jfv4xma wvolutions in 4.0 s. What is the frequency of the wheel'sjmn)46mt ,a5xw vg9fc rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Thedmn.ji /n 4g2 3udnn0jj i0k/f period of i mjkn i /u3dj/0.n24nj 0fngdits rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in1m n/;: f*,hrpggdyhg 0.20 s?gphng *dyg:rhf1/m,;

  A wheel of diameter 26 cm turns at 1500 rpm. How far wbgzvu 5r n3/jp*k v0zcf60uf3ill a point on the outer rim move in 2*guzp vb z 3rn 5/6k3cuf0f0vj.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutiozg fd8by8oo7 iu -//zpns in 4.0 s. What is the average angular speed of topb8u/z zg 7fo-di/y8he wheel?

  A bicycle wheel rotates uniformly through 2.0 revoluud uctp8k yhq041lc6.tions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the why 8 0l4tudphc.1ckq6u eel?

  A cable car at a ski resbrrpln5+to(b;qa; gc , ,,uhla7 e8 a l*zhlr.ort carries skiers 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, houra,g*l bhlrb5z. +q e;ar8(, l al,7tn;p chow fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m iel6o2cp vgy82yy3l 7x , dc7tgs rotating with a constant angular speed of 2.0 rad/s. What is the l28p6g l,vg37dcyeyo2yl c7xt inear 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 rd, yrd .ucl;f1( uvdiu: ;0uruio/,ithe motor rotates at the rate of 20 rev/s, what is the approximate linear speed of t lvirf du/uuydr u(i ,0,1:o;c. rui;dhe end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of j(y9gg vxp okl*i:efz+)2 wj 02.0 rad/s. What is the centripetal acceleration of a poin0f*2ve 9wy: lj+k(igpgoj zx)t on the wheel's rim?

  What is the centripetal acceleration of a point on the pef tia5uw:l7t- 9l9wqprimeter of a bicycle wheel o ip7l 9:-u9lww qt5aftf diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space statid ,rc 4(j bo+oton67(ynof fv-on (r = 1000 m) rotate to produce an artificial gravity of,c( n64f y+jrt (onov dbo-o7f $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve o vzt)arw-qyd-(hy1z- o. f ny1f radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictio) h y- at1wyz(vdfqoz. 1--nryn) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curwe vy0)r8d6eqve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static f e6rqy v8wde)0riction) 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 0.75 nxhu7sp ..+su0-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 t. usp.+nxu7sh he 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 dol+oi6vlm mt8x 3 ny-edcog: )-wn a lane at 4.+l-3l)vmgco 6:xty-8 niemod 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/moy jx:j5912sh svfc angular 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 cofkt6/,zm)m lovtbgpd(, c n71nstant 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 automob j7+rg)bocad3ile tire rotate after starting from rest and acceleratin ba)+r7jogdc 3g 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 angu2 6 yao2 jhbtixs4;w6glar acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/h3/aohdem 4 9bs decelerates with a constant angular acceleratim3hdaeh4/9b oon of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angula9i-v0 g-;y ryzgra n;pr speed of 6.0 rad/s while turning through 2.0 revolutziga;g-y 0 rp9r- ;nvyions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unc fz/4)ovoctzy)8(h xil0 )gxiformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel ro08g)czx4)ol/h(ztxv fo y) ic tates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformll)yj/i9 p5)e5x sxfszy from 8.40 m/s to rest over a di psxj95z e)x)5/iy lfsstance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from j,n...bhfk(r+uxc wt8.40 m/s to rest over a distance of 115 m. How lob h.twj.u+(kc nrf.x ,ng does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational ucg h) 8-ez8fbax635 -nfaw-ezfwhw :speed of 3600 rev/min. When switched off, it rotates 50.0 times at a nu 8fhaww :g6-3-- efzecaxzh)5 8bwfconstant 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 30 cm lnkna4gqfo dq+x7kr /q 2(/3 yrong wrench is used, what is the magnitude of the force required when the force is perpendicular to the wq3+4n(nr/ago2 k q/xkf7qrd yrench?

  The bolts on a car wheel require tightening to gv1hgk:h/nawk 53 tpr5e,a (la torque of 90 Nm. If a 30 cm lonkwp(n1h 5,5 krae gvl3g:h/ta g wrench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti-nkt*fs ybkb ,n*5 ql9a $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mn nso 7:x)f8,ub17lur .tvlli ass m is at the origin, mass 2m is at x = a, and, mass 3m ir8n l:f)lsi1 .bluv7 oxut,7 ns at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted agl 10njr d/7orj64e6rwa jtz9bout a frictionless axis thought the center Ojl /j67ntr460ao r1eg d9jrzw. A rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted avbe f, 9ln, 1(dla6 frhq+vm0rbout a frictionless axis thought the center O. A rope wrapped arolah emvq f,0+,r6l bn9rf1d(vund the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 thd jn,v4o0r-m ,vbm(la e horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as itmv0rjb a-v(dm,,ln4 o is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wh ql* ta(benevn i;m+ x+oh21x7eel to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 2bix (+n mnx l2+h *va7eoq;te10 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 pul;.k v/pky 4auvyp p; ./7ujsdsley of mass 7.07 kg and radius 66.0 cm. What is the p/s.u ;.k4jkyp ;sdavpuv/7 yangular acceleration of the pulley?

  A 1.53-kg mass hangs on a rop)u8fe .bkv9(oz kk buxj:b fbux+3 -+te wrapped around a frictionless disk pulley of mass 7.07 kg an8k)t.-b :obb 9uvfxfk(bzux ++uke j3 d radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requ6fgb:,n,:5y h pv vwiaired 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 inerlfn 7b 0mx22e5n:o nuftia 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 0.01traill( sp.++1sa9e, gu g9vn0 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. s+,eur9glpatn9lvs 1ga +(. iWhat is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass za50o3iz :t2nd.n uhd 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane ca :u50.haitzdnod zn 32n it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rx) mq--7za zplest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical dista) paz-7q m-xlznce of 3.0 m?

A solid sphere of mass 1.5 kg and radi. fq.di,y: 1f7 cqyefwus 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertiayy i ef.:cq,fq7dwf1. 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 momentum changes sv0 8d/yg9o++ 4odwuqgex rq) 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 e dinurx-ta1/m4h:c 3inertia 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 of iner)3nbm3 ks2x+fyh- ye rtiamey32 xf-)hnr3 sk yb+ 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?