Angular displacement is usually express in units ofy+t.t h4g h 40rcgq2ha

  Angular velocity is expressed in :gumd9rlum7-bk ;dop y+k n;8units of

  Angular acceleration is expreszrj7 :4zr(ae1h 1zlcised in units of

  A boy and a girl are riding on a merry-go-round which is turning avgd45ruvvw 4x16 h; cy3ke*cdt a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacemenv1v4 e*3vck4uhyx ;dd w cg6r5t?

  A boy and a girl are riding on a merry-go-roundfxejddw3 7 cp vba/1.; 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 gdwx c b/7jadv;ef1p .3reater angular speed?

  A boy and a girl are riding on a merry-go-rk jjp x;9tmix;yu6(-qound which is turning at a constant rate. The boy is near the outer edge, andqpm(xi6xju9k;- ;jty 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 1 e+urxwf5vq /5vloz+ 6 s5z4jsc2bbsa constant rate. Two4 6f/u b5ebcsxr zv 1vssjq+l255+ zhe boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a;zlrfb nd 49xl2*0e:ouh6p b r 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 grx l 9u;40 r2dbeobfz6:*hnpr leater tangential acceleration?

  Consider a rigid body thadmkol1: ppj7b3 nn dy)aq 9mij:,m /+zt is rotating. Which of the following is an accurate sn+b9mdi ,dop)mq1 :ky 3zjm: n/ 7aljptatement?

  Rolling without slipping depends onn rhbf2jpqwhbnfg;25 t19k 0/

  Two equal forces are appl -3kah:6 -lmwu(ygj-q8 cett sied to a door. 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 el hugttaqs jw3-k(m yc:-68- the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The fid;k(9 mr1r+amh ggm8 rvlat6,/ zrh 2emfgk4 7rst force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Whr ah48+mt7gk2/d(aezhvmg6 g rr mk9,mf1;lrich force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firschym682 (n e4xbys x *wff7er9t force is twice as large as the second force. The ratio of the tx 49 wnxcf*y62 refmsb8e7( yhorque of the first to the torque of the second is

  What is the quantity used to meastp s.jb1t9cq(p w4+o nure an object's resistance to changes in rotationpjb4t9st(cw 1on .qp+ ?

  Consider two uniform solid spheres where both have b,k7h z9(ls0n k: yyjwthe same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of theybklyszj wn:7(h 0 ,k9 smaller moment of inertia is

  Two uniform solid spheres have the same mass, but o zbo7)8uqwinycbx772tb:o/u i uk24 mne has twice the radius of the other. The ratio of the larger sphere's moment of inertia to th:ubqto4 o2m i872u7wcbx7u bz)iny k/ at of the smaller sphere is

  Consider two uniform solid spheres w 4ca1,hr h btmxb:p*y1here one has twice the mass and twice the diameter of the other. Thhabmchtpr , x1*yb4:1e ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to ;r/vsx90i4v v7npm lx 2M and 3R, what happens to the sphere's moment of inertia about a centrasn;pvxvxim07lrv /49 l axis?

  If a constant net torque is applied to an omc:z3 j7 wt;vebject, that object will

  The moment of inertia of a solie:m:fo ;5 +nd prwca*iv.beb)d cylinder about its axis is given by 0.5 MR2. If o ad b);* nwep5efb:r+ cmiv.: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 which has a mass of 10 kg anj(vxt4l)r s5w ) d2q5u)r gw/syfev 66)umhhyd a radius of 30 cj)2mwylxf5 6 y))4qhsd)tguwvhr s u5/6v(erm. 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 disks.

  Suppose a solid sphere of mass M and radius R rolls without slieyk4/t 14hc /mg.mf qopping down an inclined plane starting from rest. The linear velocity of the sphere at hogm.4qt1 4/e k myfc/the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls wiz d3 ujuheq6f5h f.vp/88hne0thout slipping down an inclined plane startfd8ne/0v 3hfhhj qup.6e5 uz8ing from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system oqccp astoz21is - 5b32 d3pz9; jwts4wf particles changes when a net external force acts on the system." Thissdz;pt 4bw-p9icws t2a35z3cjs q 12o statement is

  In what circumstances can the angular velocity of system of particles chanc an/q8kkxd(eh1ou2z n,9iod3 d)/hjge without any change in the syqcn/ jzu8 2kx,(9 dahded31o)hk/inostem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fricytle ,u n 4e a :1sjtt0f0/9cmtlurf1-tion which may be presetlfus1a: - tje/1m et,4un0yc flt0r 9nt. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Ear +*t5wov 5dhxkth moves close to the Sun, then which of the following best describes the orbi+5khvw td5x*oting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) -131k(:b efz mldg wccm 2oy7mby pulling in his outstretched arms close to his body. What h yc32(ez 1g1cmlmwk-7b m:dfoappens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouztf2cc.blb vpm(h. vo:s+.l*ette (a fast spin) by pulling in his outstretched arms close to his body. oc:+.b(mbfsv.p*hct vl .l 2zWhat happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) byboy,cz3zpk1+ pulling in his outstretched arms close to his body. What happens to his moment of inertia about thc3,k 1py+ ozbze axis of rotation?

State the law of conservation of angup zgq:y fix4adtc-g++q* w90vlar momentum.

  What arc length does the Earth travel in a three month period in it9no0ar7nva5l+ : pxod s nearly circular orbit about the Sun with dn:o ox0a9+n l75vapra radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dis4q(z+fp11q/ )mqbsju mod6b jtance does the tip of the second hand s) +1bqq/jm zj1 (ps mb4qodf6uweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per mi*y;i+o :z/ as)mig hjtnute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What u u5dt70vbe3k c6:vaz is the fruk7 veb 5c6t0du3avz:equency of the wheel's rotation?

  A pulsar (a rotating neutron star) emirocjeo)pp)+ l+ye2 :yr09 uj sts pulses at a frequency of 0.40 kHz. The period of ioe)reypp+ yr0+cj) 9j:2u sl ots rotation is

  A phonograph record rotate.(m 9d+1sw 8il(u(ltaev hui dfj 0we,s at 45 rpm. Through what angle does it turn in 0.20 sf.ujewa1, twsvhl +mu edd ( i((li098?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the )bh7 sw be*:2b dt2.m*qqwyag outer rim meqtwy 7:bdb2 2g**.hwsa)q bmove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What l a05xrs* 0,hhux gn-kis the averagxu,0r ghanlkhxs0-5 *e angular speed of the wheel?

  A bicycle wheel rotates uniforf5nwmez:u 1z+imxtb0pd :9z+mly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the wheelb9z m5::wxt + zimdfpu0+1n ez?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable w rl9;0ro( oribhich moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pull i;0(rrb o9orley 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 speew/4 i7gnh-t11;sw ghh ot7poj d of 2.0 rad/s. wt;1 h-/ w hs7gj471oihotpgnWhat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered9 1tqlyzg/ +wtw9lqd: weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord? dw/l tqw 9+:qgl1yt9z

  A wheel of radius 1.0 m is rotating with a constan iun )a-p3 nrhk(:vsb;t angular speed of 2.0 rad/s. What is the centripetal acceleration of a point onu3-)vprn ks( hab;:ni the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of au je0sn* +x 01fcfjd+fdc x5f5 bicycle wheel of diameter 70.5jxf1f+de5fjd +u00xc n fc*s0 cm when the bike is moving 8.00 m/s?

  How many revolutions per ming yqc,l sb: w sdx2,e0 ws(c8bkm*z4v,ute (rpm) must a circular, rotating space station (r = 1000 m) rotate to pv8z, (ylc s,,xbbgsds*k ewq04c :wm2roduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a spe6)3j, vi/sxm 4adjq lced of 20 m/s. The maximum cen/ casm vx6) l34,jqdijtripetal 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 5b n7pul-ttc2, 0 m with a speed of 20 m/s. The maximum centripetalu2pct7lnb - t, 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 szc- uuvc2dn+2qbs 6 3dtring, is whirled around in a smooth level table. If the maximum tension thatzdcbu 6+s2 2n-dq3uvc 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 7.5 kg and radius 9.0 cm rold6umy w5a f//fls without slipping 10 m down a lane afy5mfd u6w//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 ir5 q*h yw py3n+;iyr.x*hjb3 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 z9l4rbp h lo46with a constant 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 automobile tire rotate after startingj2-z16gvvfk e from rest and accelerating at a constant angular acceleratij vfg21z v6-keon of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acce26c(tpiq y0gz5 dkdl9lk 86 a6krh6csleration 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 a con*ie9wwzoy :.ys5 t ,dbstant angular acceleration of st eoidwy*9,.:ybz5 w$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while tu,-4ead pym :rvrning thr4 vryd:p,- eamough 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down ujb7ra*fb t s(*y4 /1g ul6byvcniformly from 8.40 m/s to rest over a distance of 115 m. What is th6ysurlvgj7* (*f ybbb 1a/4t ce 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 olm dx,x9cjl (pbkpq6;/og/n -ver a distance of 115 m. Whapl ;oxj/l xk-gqd/9 n(bc6 mp,t is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest overevsyb jfu ;ubk6 +b x3v u8kh 3u/dgfn-*4a56r a distance of 115 m. How long does it take for the wheel to come to the s*u sv/a5kkbnrv -6 fy4 h;ub+f3ug6buex jd 83top?

  A centrifuge in a medical laboratory rotates at a rotational speeg 1v5rwjyxa. 7d of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to resty5j.7 1ravxgw.
(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 tighte3,grp * / w3zs;jp*bvn2aydaqning to a torque of 90 Nm. If a 30 cm long wrench is used, what isa* ;,gvrpa2jq d wn3ypz3s*/ b the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque ofszcf;h knx:0 tl /35lgcu1lo9 90 Nm. If a 30 cm long wrench is used, us50lofz n;x9/tc:3 llckhg1what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of kxnd p e03fbx6e 75:lrinertia $3.00 \; kgm^{2}$ 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 orbaie1rydo 0wn-p-+7eq1b;l ;ib c)iw igin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about t-- ;e)aiw71 +q rni1 wdbi0 lpbb;eocyhe origin?

  A solid cylinder of mass 10 kg is pivoted abouyjn:,d+y 8wqgt 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 aroudjn8qyy:+ gw, nd 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 anc69pfpoxwd,;x6-h1 y u 7 ftis 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 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does the cylinder rotate thr; hyxdfx,6 o-up1pwn 9t7a6 cfough in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged atckqy bi-7*aa4:,l.czz4 dk;m /olua j one end. The rod is initially held in the horizo -c,kq: mz./o i4j*z7cldb4aaka ;uylntal position, 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 wheel to be a ring of radius 30 cm and mass 1.k(d:mzr 4bkehr,)6 fglg ,o.a5 kg. Neglect the mass of the axle and spg.:lbeo r ,z fm4har,dkk6g)(rocket. If a force of 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 wrapped around a frictionless disk pulley of jjlvi jzhb+( q d 1pz rq2:1.hktw4d*:mass 7.07 kg and radiusq:w 4 h 12vpddib( zz1lr*qjk :.+jjht 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around .* dc2bh6ndeu a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm cu.n6*bd2ehd . What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. rweys*ax 1c7* sv/0zr: aiq.jIf 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 +olhg6s.i.:yv kjw5ni5ih0r 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 rest and rolls w*ga 1y5e8 6znk s*mplbithout slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottomkm1y5sbg* l8p*z en6a of the inclined plane?

  A solid sphere of mass 1.0 kg ww9u76pbebq4w -ur4qand radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can itu- 9b7p4 u4erwbq6qw w climb before coming to rest?

  A hoop of radius 0.50 jibd*3rw4/r0 r3-ta; tpdai y m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane4*3adr3a -pyr/ twriidjtb;0. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radiusk .b7 ba(mh zysitg ,8b;;e z*-j2nctq 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from .cn z2baj;z*( miq8,- gtby;sb hte7krest. 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 mo-4 (mqy9o*)8nklogv rq2tb,f b3gafwmentum 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 of inertia ee8 z-wg.rn 6bof $5.0 \; kgm^{2}$ 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 )pfn/o j, w1zxinertiao,j/)p1 zfnxw 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?