Angular displacement is l xaqlq 4b/9,uusually express in units of

  Angular velocity is expressed in unitsyq0 q1mjpjk/ ) of

  Angular acceleration is exppcqk-v ysgck c8(1y: s h5fk*-f 3awz0ressed in units of

  A boy and a girl are riding on a t( x. au1sk(h r4lzm1a gk)*ji4z g6gnmerry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angularagsz jr1g6* g (.ku4lkh1min (4ax zt) displacement?

  A boy and a girl are riding on a merry-go-round which g8zcshr d m08 +iqkiz+ar .20dis turning at a constant rate.0r2gqhzks+8r i.d zc0 d+am8 i 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,lg rc+fk4ts/7vhis(; f6yx b-round which is turning at a constant rate. The boy is near the outer edge, and the girl 4cthsis+6;,k(vfblg ryxf / 7is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round*r( t/e gy6blsy )ijb0 which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has thetb6/iygl b*j ( e0)syr greater centripetal acceleration?

  A boy and a girl arezoly quj-h 6knc5c80zed s-(/ riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greatejc(o-/k0 henulzy68- s5dzc qr tangential acceleration?

  Consider a rigid body that is ro.hjr 8jy (,0t)grwdgr .novxrnmi) :3tating. Which of the following is an accurate statement?gdxr38 :jrrrn .)()vj0w .y,tm gionh

  Rolling without slippi ,xrhqfn-jf;7 ,qr/bbng depends on

  Two equal forces are applied to a dooiyopax- 9g: 3ehqsc3 ;r. 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 exerts the greatersa 39-:gph i ;ec3oyqx torque?

  Two equal forces are applied to a door at the doorknob. Tunuiafl/52g c0 .yc2j az3ryt:7kly : he first force is applrc:ya2532z/ y uju ikl.t: anl70cfygied perpendicular 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, perpendicular to ths5,ba3-b) hp-q qpyly e door. The first force is twice as large as the second force. The r -,lh ybyqqp)pa3sb-5atio of the torque of the first to the torque of the second is

  What is the quantity used to measure an objecvfoct+ m6o5b2q(l3/g+ lankht's resistance to changes in rotation 3++tm5lnv6flkq g/ohao 2cb(?

  Consider two uniform solid spheres where both have the same diameterqt 0e,l3buqa. b tuevw.+(q26zm;dg w, but one has twice the mass of th0w mutvbqt(2lgw.+,za u6 bed3;q.eq e 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 twice the radius of o-9i 2d m- lwfk (iu/69dpdiywthe other. The ratio of the larger sphere's moment of inm6i fi -udw9dd2-w/ k(oyli 9pertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the masspwuex9/ rsm26-yzr bd/7,ay l and twice the diameter of the other. The ra 67xy-urmarwp// sdeb9 2 y,lztio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere mvu6 aki( 6a:p6vbvz5 ih// d5p pnko9has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment o95a b:ih5 6iv(v/6p pupov dzakkn/m6f inertia about a central axis?

  If a constant net torque is applied to an object, 9vt ikh . *asaal23ai0that object will

  The moment of inertia of a solid cylinder about its axis is givv )3ci8;eh0glrbq h :men by 0.5 MR2. If this cylinder rolls without sgci r h;)l:m38eqhv0blipping, 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 10 kgx2js,i fec ste2l,a. 1 and a radius of 30 cm. What is the ratio of the rotational kinetic ener2a.e1cs2ej,t ,lfi s xgy 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 ra f(tux7:4w-* *iamzw+opmnft dius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottomwm *f4w(n7mat ft pz*ui :-+ox of the incline depends on

  Suppose a solid sphere of mass M and radius Rcj ixo- :-6yxe6og5kn rolls without slipping down an inclined plane starting from rest. The angular v-ko 66x jeicn:o-xy5g elocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changmo6ivyo4hd+b o3p 7fu kp/e2*es when a net external force acts on the system." This po 6p+de4fyuo3*h i obvm2k/7 statement is

  In what circumstances can the angu/g7wm2o)re7j 7e*kkk :b bl b1le; vvrlar velocity of system of particles change without a;2ebrkvm7)bv7r:j7/ glek e1ow *bk lny change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictgp t;l9egx72.m g ;eakion which may be present. What happens over time to the Earth's a;9pget2 7ekgag;lx .m ngular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movee/6*ez ctjbma4anw p,*4.)kned5 wx k /z:cdb s close to the Sun, then which of the following best describes the orbiting speed of the Earth a,x:d 54kcpwne4 bb.je a) c*kt nedzzm/wa6/*bout the Sun?

  An ice skater performs a pirouette (a fast spin) by puln qe3h f:k,nt8ling in his outstretched arms close to his body. What happens to his angular mome fqtkhnn 3,e8:ntum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulbubl+ p ay8m purh69mb7+:om85 ekn.tling in his outstretched arms close to his body. What happens to his rotational m oamtl+ +65 78ym9hpb:run b8ekb .upkinetic energy about the axis of rotation?

  An ice skater performs a pirouette (apj5j4pi2aiu, 2) foof fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about p2iiopf4j)ou 5 fa ,j2the axis of rotation?

State the law of conser66kt /t2luatj0repuya 9q8 c )vation of angular momentum.

  What arc length does the Earth trav9r vn0:k 7j hav c0d1(laf6huoel in a three month period in its nearly circular orbit about the Sun with a radir lv9h:(a fv 61kc7ua0jn0o dhus of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has x/ e 5 mnz:c+txv(9 vfi7q7o vqdu81aba length of 0.30 m. What distance does the tip of the second hand sweep through izva1 :xvvtib+m9(5fe cd7q/ x7no 8 qun 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minvocyu j6g473b;*6(bymu b qalg a 96foute equivalent to?

  A bicycle wheel rotates uniformly th dtgb723x;3 ksqkt yqw0ntf)*rough 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rf 073qttd2 ;n ky x*g)wbqk3stotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz.f9 u. mjii)rfv(,a3gw 1g+8mqaxm2tc The period of its rotati( riwg.) a9v ,+imm2t13mfx gf c8aqujon is

  A phonograph record rotates at 45 rpm. Through what angle d3wqr v.1gb pzm6t/ cm5 rg, upph40y1joes it turn in 0.20 s1t 6.p5jb1ywv3r4cphrg p g,m 0q/ uzm?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the w dj( hi,.8krjouter rim move in 2w8, (jijrdh. k.1 s?

  A bicycle wheel rotates uniformlymbs83)dxmq qvs0)ioxw6y4 c7 through 2.0 revolutions in 4.0 s. What is the average angular speed of t6mcwi)qx o 3)smd 0b vs84y7xqhe wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0x*/ ct: ,gn8g*uny hqy s. What is the linear h g*c*n qy8/t:xyng ,uspeed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiersdx:3q d ;+zunkes vln((no-t9 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 +l9 :nn eo;ktu(x3vdnqzs -d(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 co7818 (iqjkjhqalp1 sm wd rrz)+7m4 bknstant angular speed of 2.0 rad/s. What is the linear spm m 1(qrr sk7j4z8a)q+hwpl8j 71k dbieed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. Ifpjfhl;jxil*ro 7 -p ,5 the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of th7 ijrx *ol;l hfpp-,5je end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular ubv*n t.o9:k j)fmro8 o1tk6qspeed of 2.0 rad/s. What is the centripetal acceleration of a point on the mk1r6o9 . kqovt ):nt8ujbfo* wheel's rim?

  What is the centripetal acceleration of a point a7qwhz a lz-/3on the perimeter of a bicycle wheel of diameter 70.0 cm when t -3a/wzlqz7 ahhe bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating y gs.p5z8-g7uu 9 poclzhck :n*qwb.* space station (r = 1000 m) rotate to produce an arti uupgzqyn5p 8h.loskc9: * 7 cgb.z*-wficial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radiud004j+thmc 76f skq bds 50 m with a speed of 20 m/s. The maximum centripetal force (provided by shtdcq7b40 6ksjm fd+0tatic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circula.jxg v5uan56br curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (providea5uj g 6vb.5xnd by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to y:*l31hbc6 qgyg + y7 llpldsehc 6*;pthe end 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 ma1y7g;6cqph: 6sy+gle l 3 lyl*phd*bcximum linear speed can the 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 1lzwx1 b3 qgm1ne2;xzz4)rc-u 0 m down amz4nxl ubcz 32e )xgqwr-;1z1 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 acceleration of l4yyb,n;pu zr0 zs ge2/j;n fh06f 2jw$4.5 rad/s^2$. 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 akq.f3cpbsa-8pydr oup/6;mb1 r g 4;rngular 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.oq sk*,c 7r3to300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular acceleration o3ckts7 roo q,*f $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has 0alm+n6w c9 cxan angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotat/-pn.d nlu5 l, b1h 2vwfknda*fe +r0eing at 20 rad/s decelerates with a constant angular acceleratio1 kd dfr.+-bn*el0wvln hf5an 2 ue/p,n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and+ 7cg0u silc2,bemv m7dc56m e reaches an angular speed of 6.0 rad/s while turning throiu76clvmecc2m0m + 7gd5e b, sugh 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 overl p8ati 7;.ysjzrdh41 a distance of 115 m. What y ;4s.h rld7tiaj 1z8pis the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from w 8qyz8luu,0d6u 9uxg8.40 m/s to rest over a di0 ,uzwd 8lx96u quugy8stance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 uxrs qx -u64xn0y/4cc m/s to rest over a distance of 6r4qsx 4-xyu0ncc/xu 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 36cy.oew 8v u;g900 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to rest..9ewu;8g cyov
(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 requiragr 1lb8(x 5mme tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the m5r8 mlg 1xm(abagnitude 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. Iocj dujz; 14u 3n 8yb-e6xz2qmf a 30 cm long wrench is used, what is the magnitude of the force required when the force applie864 uz mzb ydq xco;u23-nj1jed at $53^{\circ}$ to the wrench?

  A wheel with moment of intil804jb;nmk9f m06um b2 getertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass m is at the origin, mig) v+avu+g (tass 2m is at gg(t+v+ua )ivx = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 ( leaf w/.,d1v( p(x o/f4chu/ftihfnkg is pivoted 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 wr/aoi efnc, 1d/htvw4( fx((/fh.uplfapped 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 frictionless axis thought t4tx+yqr 45hjm)5 e gbihe 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. How many radians dbmrt+e54 g jh4iyq 5)xoes 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 entp:.ujli: 9dc4 g )wynd. The rod is initially held in the horizontal p) dn iy wc:utpg94l:.josition, and then released as the free end is allowed 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 wheeeyql s -(q h)dtw1o0yl(r5wom2l8,asl to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force o)ylslydw(aq l s80mhtroo,(w 25q1e -f 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 wrayl8vjsg k7q7+ x,ck fd1y -h3ipped around a frictionless disk pulley of mass 7.07 7hvc7s k+ijy1 xkg3fyl, q-d8kg 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 o*3a m5lv;n5l qqvwjix3p.*ci f mass 7.07 kg and radius 66.0 cm. What is the al3acv;qx5j3*pv5nim .l* wi q cceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requizs4alt59u ,s8v lf;5 -n phnmbred 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 i mdx cdkk+xp+;o:,,e fhz)c*jnertia 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 mas32hfa/ )2fzgafe8k suf . gn(ys 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 when it reaches the bottom .2s g)3fn 8h/(affgak2 ye zufof the inclined plane?

  A solid sphere of mass 1.0 yxs d6y)x,mjozv)n0- kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plyn)d -6ovx) 0 jymsx,zane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest as2istooar- 1yfh; dw8s+6 q6hnd allowed to roll down an inclined plane. How fast is it moving after dropping wf siq6r2s-+;dto 1 ayo6shh8a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg an7nfv-vou rc9 g3l gnyn v)a7dg4 (0l(md radius 15 cm rolls without slipping down a 35e a go7)vdnn(4( gc3yr 7lvf ulmn9-0vgincline that is 7.0 m long. Assume it started from 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 momentum changrh8/ov 3ahgybmfg h1c28a(cdt1 m 7k:m nwj8/es 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 momu 6kue5c0t1 jsdw3tfs*iurfrs6 + h83ent 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 clh7j2qxk6 d)ws*stel 54n7f k2ob6 khas a moment of inertia xb2 l ssc2 7n*jkhf7kq6dloewtk)45 6of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?