Angular displacement is usually express i 1ayce c(8x4rr c0fqc/n units of

  Angular velocity is expressed i dr 0 82fo( 9;mjdmfeisbm7jnsj5i01on units of

  Angular acceleration is expressed in unicegsr7/r 3j0j ts of

  A boy and a girl are riding on *c tope-z92as6s sl0ba merry-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 angular di20za *ltss9cb -sep6 osplacement?

  A boy and a girl are riding on a merry-go-round which is turning at a cosj2hv) :u(3vq4 3fkf toy k/gl3:xeqnnstant rate. The boy is near the outer edge, and the girl is closer to the center. Who st:3fx 4j2o (f/y3kqh 3u) n: egqvvklhas the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turningwvao34 ;bxm vn2s0vv5 6.rds4qzupe1rjh /i 2 at a constant rate. The boy is near the outer edge, and the girl is closer to t 1/i453o2 avxjhm0p vs w vrdrzv6q2;bnus.4e he center. Who has the greater linear speed?

  A boy and a girl are riding a merry-g6 r uo f2:uon;gy oddgfm34y(e8yh74 bwt +q*so-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who ha g;g42tnbqd uy4s+7 oyh 6rf83w *yf(deomou:s the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a const283hoea4fv o iil9 4idant rate. The boy is near the ou4lid 9oi3 foe i8vah24ter edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body thatr i; (jejlwbh,j nn thyve07a1smv 33p+7*6zv is rotating. Which of the following is an accurate stateme;*isan3+3znwv mr jtly( ,vvj1bh jh7 07ep 6ent?

  Rolling without slipping dep-nbq,diwcb * +ends on

  Two equal forces are applied to a door. The first focz so9 yj)06zarce is applied at the midpoint of theaosz9)60j yzc door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The wufm1buv +9sk5f3j w+ first force is applied perpendicular to the door; the second force is applied at 30e t mv9wwu 5+jff3k+us1bo the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob,s ttjhl,;j 1nv4tr+ r8 perpendicular to the door. The first force is twice as large as the second force. The ratio of the torquj ,+nvjt ;r48lh r1stte of the first to the torque of the second is

  What is the quantity used to measur5 3-iv5bve bl3pnbj(ddn9 : q)lr mjo*e an object's resistance to changes in rotation?lrn 9-pjl) deo n3 5bbi(*vd5mb:j3vq

  Consider two uniform solid spheres where both have the same d) e,.uzvqzf+qnj44vr g f79w qiameter, but one has twice the mass of the other. The ratio of the larger + u4q)vfngez9r74qq, jvzfw.moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheresgixkzw)t5*msj hp d,y8f ,m5s /up 7*x have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere ihutm/5gksyw 7,8d x*z),pfpi5mxjs *s

  Consider two uniform solid spheres where one has twn.qa kr-3kn.e9i fm5lice the mass and twice the diameter of the other. The ratio of the larger momentn35-a mfqilrkek9..n of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius +(r zeu,p0ro yR. If these are increased to 2M and 3,eypzr( or0 +uR, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, thd:tozr4brz e o9j 4 (2/ohvg3gat object will

  The moment of inertia of a solid cylinder about its axis isgfmb91p w u.3d given by 0.5 MR2. If this cylinder rolls without slipping,ug1dfmw.3bp 9 the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whiczv bju7zyu8x-x5j w,) xh0-hch has 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 the bike? Assume the wheels are uniform 0 yh )v, j58-xwzzbx-ucx7 jhudisks.

  Suppose a solid sphere of mass M and radz5oksq+oq m( 6ius R rolls without slipping down an inclined plane starting from rest. The linear velom6qq oos(+z 5kcity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls witho lev6o6alyvdf3l 71w 8ut slipping down an inclined plane starting from rvvoy 3lfal 81 wle66d7est. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net exts4*k.v vz ray*4rey3e a0n*hhernal force acts on the sy 0.ra4 v* z*y*he4narhevys3kstem." This statement is

  In what circumstances can the angular velocity v ued77en3-biof system of particles change without any 7vbuin-e ed37 change in the system's angular momentum?

  The Earth orbits the5prrp a56tq i( Sun in an elliptical orbit. Ignore any friction which may be present. Whati 5q ap6rpt5(r happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about thek d(e*ldt jg.6 Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the or*l(e6.dj gdtk biting speed of the Earth about the Sun?

  An ice skater performs a pirouh n bl+bv8zfm s86mb*+ette (a fast spin) by pulling in his outstretched arms close to his body. What happens68h8 +lbbnsf *m m+zvb to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) ksg83wfq cgc4p/d80p by pulling in his outstretched arms close to his body. What happens to his ro0gf c8pp gqwk 8dsc3/4tational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullint* je63ilvdu p*d6+ mrg in his outstretched arms close to his body. What happens to his moment of inertia about the axis of *djt l3er*updv6m6+i rotation?

State the law of conservation of ,k nbtic5 tf*+angular momentum.

  What arc length does the Eh zgb.n ghhp9z(hz5g 9ybuhl5g(-n(5 arth travel in a three month period in its nearly circular orbit about the Sun u bg 9p nh9 -h. ((5hhyn5lzgbzgh(g5zwith a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the tip 6+lwos o w:-hqof the second hand sweep through i:hw wo-+6sqol n 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivale ad jvv*)1f-u cmm2rj8nt to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in(kwq 89h.g7x cyzf2t grap-;s 4.0 s. What is the frequency of the wa;gzcx 98yh(pf. tgsw-7rk q2 heel's rotation?

  A pulsar (a rotating neutvs,z 6fyp 6h+mf-/k.rej1l. 6guffl eron star) emits pulses at a frequency of 0.40 kHz. The period of its rotation isg.erl f6vjf1.ze 6k p,+s /lf6h-yfm u

  A phonograph record rotates at 45 rpm. Through what angle does )h;f sv9y 6:j)jfu.t/yvu wwkvi c5z-7ls ;klit turn in 0.20 s?9f s;:cstvuyjjw)6h;5u y zlfwk. v7)l/i-v k

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a xqb .(w( a8 nhjpjig63point on the outer rim move 3w86 bqnj.((gjpxiah in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4. kuj:+zhrh7( 3wq,6as wpk9ud0 s. What is the average angular speed of zhph3ksuw j,u:a7w6kqd9 (+rthe wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions i9w8c u7(xuiq1rh 0ljw/j zn i5n 4.0 s. What is the linear speir97u5(uqnczw 08jw1/hxj li ed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort cd2htlp8vh,dj)bk47 y:k k p3 kp+ dvi.arries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.iv p87t ,jlkd:.pk phhd4y+32kk)db v0 m. Assuming 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,g4(- fwyzirb; k *xf5kd0hyo.0 rad/s. What is the linear speed of a point on the whe*kgbrw-0 (4,ixdz;hy5k fyofel's rim?

  The cutting cord on a gas-powere,;;nenvky 1 r: 7nucwt)s.; nfxgo8nud weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the knsv ftn1r)n8:;,nuc .; ;u exngwoy7approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.078weilr fei *oj67tbgo(:/.r9cga+a4h ssj j rad/s. What is the centripetal accelerace7r / f 74wab o:( is glgha68i+o*.jrjejts9tion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimetwom2a whd2/-ldst ;3 hl9nn c6er of a bicycle wheel of diameter 70.0 cm when the bike is movicl9n; -23s hadwld 2o /nhtm6wng 8.00 m/s?

  How many revolutions per minute (c,nfu 6g d soff/:3d6orpm) must a circular, rotating space station (r = 1000 m) rotate to pr:gudf,ndff6c o 36s/ ooduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flazj 8qg 5t,y(nux6 yvh:t circular curve of radius 50 m with a speed of 20 m/s. Tx,(q5un:y8tj6zh v yghe maximum centripetal 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 curve of radius 50 sp )e4p-f rh*y udf)) pe5tv)gm with a speed of 20 m/s. The maximumfhvye-dt5p4pe)r))gf psu * ) 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 :*fh anz 4m1fmto the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension4mm:naz 1*f hf that the string can withstand is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5gxxtro/w0w-zq * rp93nkl u 7, kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.0l z*,-u rg9otqrw/xk7xw pn 33 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 k kah 3u5l qd.b)a7hg3$4.5 rad/s^2$. 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 accelerj*4u.sxtzsfj 6e 1j-mation 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. l-wuo74z6*t2u. jxz p3ap0ptaa lsb 0.300-m radius automobile tire rotate after starting from rest and acc..tajloszx uzp6ba0a*l3pp-ut w 274elerating 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 acceleration of01p ez q2chz 3ex,ki2hua+ r8f $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with nk +-wt5m/xug5r9 paoa constant angular acceleration of /-5kwrnaupx9ot 5m g+ $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an an,k6oi o67t motzhfv7 fa/i+t4 gular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of tt,ziai 7mo6t+ofok6vh /4tf7 he wheel?

  A wheel of diameter of 68.0 cm slus 8kujkwul. fj 5)i79ows down uniformly from 8.40 m/s to rest over a df7u k)js.ikw895 uu jlistance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest oo1 wtb r5ln3*k/gq 1a. gecy5bver a distance of 115 m. What is the angular acceleration?b1b5rk/a31o5 gyng. tc*qelw

  A wheel of diameter of 68.0 co dgf g(2dlt6r-t,h ;um slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it 6u,ogdlh-tt (fr 2;dgtake for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speep+ozsv 3s7h p x7l5p(fd of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before p7xl vs5 ( fhoppz73s+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 to qmtb.:c b6; c imm9jgc62b.lprque of 90 Nm. If a 30 cm long wrench is used, what is the ;.mim6 lccm9bjcg6: 2tqbb .p magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighteni2c(r;vo1 dh2-ab gmua0yo9nv ng to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the d o21 vgy9cr(nv 0hbau;-om2a force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertic8j2do,j /qi da $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: , 5l v/vtja-g :)kfxshmass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of xltk- vf, /5)shva jg:inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought5d1w8u ybby) fzkt oy))pvk, -g2cq o9 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.coq b p)w52btyzkdy y9f1kv8ogu) ,)- (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg in )iawwcd25:eu.s8a ts 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 wrapped around another section of radius R2 = 0.5tdu 8). wawn:cai 5se20 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 in7dtxl qi-sqkx;ca.(5 the horizontal position, and then released as thsc xq;5k( xqa7l .-dite 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 wheel to be a ring of radius 7wsbrb-qm 9w2 s;t- pp30 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 sprocketbw-wst;mrbq- p 9sp27 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 fricl n383yy fqt vrcho986tionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?39rly n qhft 63co88vy

  A 1.53-kg mass hangs on a rope wrapped around a ,;t )pb0(mojyo iwa jih2 8vk4frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accao0(4yjki itv2pomb); 8wjh, eleration of the mass?

  A rotating flywheel can be used to store energy. Ife1xx.wnmmv0 0b 3 rj7b 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 inkf7p*oy e/ fk ua8a:60qhwzs 8h-7v gbertia 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 0.0y,2*b,50lohr+ la yp 5bpr6yxkw w +pv10 m starts from rest and rolls without slia op0,pbr+w xk+65 rbp5v l*h,ywl2y ypping down a 1.0-m high 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 radius 0.010 m rolls with a speedzkw :: b6/r vd:mmx;;am.ud*hgvg- ;ky9ng se of 10 m/s. How high up an inckg*n :b:m; w :g-hms6d.vde9a ;k/ vgm;xuzy rlined plane can it climb before coming to rest?

  A hoop of radius 0.5-i p9o3c;c 6hkxbqo k,*1t* vxr,x wgg0 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after droppi,;cx*rhiqox93 ob,x1g vpc*kt g- 6k wng a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls withoutfpgm y :93yzqdvj w6)/ slipping down a 35e incline that is 7.0 m long. Assume it stfwpvgzq39) /y6y m: jdarted 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 chany ;c5x r; 4px5tnck 1xgaacd:*ges 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 (j1jdpe i s4uuet.x.6v9k v e: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 ra vjvw+xnbglw,dk.*2,8 ye8tod/s with arms extended has a moment of inertia of*wk,.lwt8,jngy +xo 2d bv8ev
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?