Angular displacement f20 s8q:ebxs6/-eo biqrr 2wnd9l;q y is usually express in units of

  Angular velocity is expresp 0 v8jdn3m g/4epkm0xsed in units of

  Angular acceleration is expr6 *5svku skf 0-9i3auxuyjme1essed in units of

  A boy and a girl are riding on a merry-go-round which is turninge4 (4 ld; hy2 8qipx1/-0sd wcx ql*ariwf:lbn at a constant rate. The boy is near the outer edge, and the girl is closer top; l(w4bnl2qqixeys4- rxh/ fc:l di1a0*d8w 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 con ml04xq5-o97x qeg slt-q.+1o(p udntxtx :vgstant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater anx esxtq xnq +lvq-.51 dx: 4l90o7pggmto(ut- gular speed?

  A boy and a girl are riding on a merry-go-round mw 9+ov( ,ldngba z/m9which is turning at a constant rate. The boy is near the w /n(9vma,9olmb+gdzouter 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 constant i)mt; czvyr. t0-rumy d. 4s)drate. The boy is near the outer ed0 zti)rs yd4v)utc m.m rdy;-.ge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry- -mcw).nhkzg.sa0 l*yn av6t5 go-round which is turning at a constant rate. The boy zn- *nhgtysla av cw 056).k.mis near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an acc9f.h,cnf + /qm. iixmrurate starmifxq..c ,m ih/fn+9 tement?

  Rolling without slipping dtb *nq h-.cs 3o;sbid+epends on

  Two equal forces are applied to a door. The first force is applied at the mbr 7 n4s;3js5vf,nc5 rmztza)idpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendiculs,j mtz va7)5fr 54znrc;s3bnar to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is aplswd d 4ic4y.uzh 0nrz9av6zp3e5g +.pliedu+h d44 ze0. 6rcs3wyz.vgd azni95p l 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 doorknh:khi v.lxbmpc:x0, r m(o(d+ob, perpendicular to the door. The first force is twice as large as the second force. T:m:x(p ,lrhkdh mi 0 b+vc.(oxhe ratio of the torque of the first to the torque of the second is

  What is the quantity usedeb7n row-2;oj0z w-ha to measure an object's resistance to changes in rotation?-2- 0wwo7hjrb nzoae;

  Consider two uniform solid spheres where both have the same diameo k*,dwf 9y5;uhaox5vl oa2a/ter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller momekfavyo a lo,5/wxd*o5ua;h 29nt of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of ms bop x au2jc0+4t-6athe other. The ratio of the larger sphere's moment of inertia to thata c6 pmx-0a+s2b tuo4j of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass0vc1 l:vbbp*t and twice the diameter of the other. The rapvv:l0tb1b *c tio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere haw:xd+j-4q z ssblkt1;s mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a centralzk td-q+ :s;jwx b41ls axis?

  If a constant net torque is applied to an object, thfx*zcxwswg. 5f (.3jbat object will

  The moment of inertia of a solid cylinder about itb3ku-)ubn47gq g g7r is axis is given by 0.5 MR2. If this cylinder rolls without s k7biugub)gq ngr 734-lipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 k er -hm 73mk.hqd00xgxg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ehqrhgkx.md 07x3-m 0ratio 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 8 /fwcgh jkdqr;r u464of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom hf ;u8rkrw4j6cg/ d4qof the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an intey*s1v; n e/(tbwd:wclined plane starting from rest. The angular velocity of the sphere at the b:/w*; ne dvyt(e1 btswottom of the incline depends on

  "The total angular momentum of a system of particles changes whi/vcdpj jfsp:0. e,dn9 rh-g d-d): klen a net external force acts on the system." This statem ddgh9i /--scvd.j,:jkl:n pf p r0de)ent is

  In what circumstances can the angular velocity of systa/*waz(y ofb * d-8gbpem of particles change without any change in the system's ang(**pba8f/ w obzd -ygaular momentum?

  The Earth orbits the Sun in an elliptical o + oybt14ja9)1j6t .2e u isg,ndqcxmzrbit. Ignore any friction which may be present. What happens boqmy2z1t + jc9nx)s46ida je1t.,ug over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earxlfa.fk8 ep pa4:d5 0ympkha26 br+z;th moves close to the Sun, then which of the following best d a+k6.b r54:pylpk;f pxh mea8d fa02zescribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling igi, go1 fh;gf0n his outstretched arms close to his body. What happens to his ang;gifo f, 0ghg1ular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast q2* * nh *pkupzpsg(0espin) by pulling in his outstretched arms close to his body. What happens to his rotational *p n0 *pq hgk(ze*u2pskinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullv.uz(,5v4qv( fdfzpo.waox v-dd m(0ing in his outstretched arms close to his body. Wha0a. 5-xovd vfvw,v.q((4dz(dfzomu pt happens to his moment of inertia about the axis of rotation?

State the law of conservation of angularu*;h d6 lp(vg**+v uye+sdwha momentum.

  What arc length does the Earth travel in a three month period in its nearly cirl1:t i4kp mubozaj b.1d 1a99fcular orbit about the Sun with a radius9z 9jao il d1b:1bk.14pftmau of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance m ,i7tzin)wy/ does the tip of the second hand sweep through in , w/t7)zmy iin3 minutes and 45 seconds?

  How many rad/s is 25 revolutions pe r1q0 c3bsdhcc4/ti x4r minute equivalent to?

  A bicycle wheel rotates uniformly 9 7xe;b ks lno9z:e et7h4vl tc:0vzm,through 2.0 revolutions in 4.0 s. What is theh7, le:c;94 k tov 7x0 sbmv:netlzez9 frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emit d6 53ou *+bmu1ejnurms pulses at a frequency of 0.40 kHz. The period on*bd 61meuuuo53m+jr f its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turns5llu46 rldt1 5vkhjz(: kdf-aa40ir in 0.20 skd6(4- v:5ri01k sza rjuhl l 4atf5dl?

  A wheel of diameter 26 cm turns at 1500 r/ +;9+un0xw5q31 f lhjuzbmmnhqbm.epm. How far will a point on the outer rbx5zfmn9j b lu 0m+.q/h hqwu;mn+1 3eim move in 2.1 s?

  A bicycle wheel rotates u6)vuqtm), 6 welpt +ipu,o l4iniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of the6 pl,+lwi 4m tvp6oiq)eut,) u wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the71hhq ztc*;l2te6vo w linear speed of a point 0.10 m te*woqvth;7h26cl 1z from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6. bp7:n.u+imdroxu* .w 8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Ass7u:wd*.xru o bm .n+piuming 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 spee6stznyv:.b l* s(vl*0mr.yabd of 2.0 rad/s. What is the *l*.y( v6a0 lnmsbzr .bvst:y linear 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 the moto0d 0 5yk5tlsn/m u5jgfz+f a(5enkz+qr rotates at the rate of 20 rev/s, w+j5zkgd f5nlz(+5/snuea0ym q05tf k hat is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/o. g +fc68sv/xpu h6uaz9ndl3s. What is the centripetal acceleration ou+zp6 /gfxvao hdc 9 .83nlu6sf a point on the wheel's rim?

  What is the centripetal acceleratqr )5o3 oayhwnzq- g*25ri,xw ion of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 5q*5i nrqg) oroy,wwh 3 x-a2zm/s?

  How many revolutions per minute (rpm) must a circular, rotating p,vsi46r0g e zspace station (r = 1000 m) ros46g v,irze0p tate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with aoaq0 1y;lj.7 r*pymv0 edzi j* speed of 20 m/s. The maximum centripetal force (provided by oml*e7jqap .z0yy j d 0v*;ri1static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular cg ct45:; ikyicurve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fricti5itgy ik; c4c:on) 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 c,9zf4tuqaf.h3(u6xgv u:iwcge a6( around 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 haveq9uh x f z4 tu6e(3g,awcivfagu.:6(c if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls wn d;u5 4vda4/kdh ph1eithout slipping 10 m down a lane at45kdh /u4pedah1d ;nv 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 anguj9 l-iz2kb cbrd)ms +u+;tm/mlar 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 constant ang orh+;7 mrk+ v*z)q3pq0i joeiular 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 doe(klgit+hb57lkem 6+;ex cln +s a 0.300-m radius automobile tire rotate after starting from rest and accelerating at a constam+lh lc( tnkx6;5b 7 e+lgi+eknt angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration oo* b1:8 qj /h,9czgknx.ngswsfn; fy1 f $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s:-f+ yno ct:re decelerates with a constant angular acceleration oeo -n :ycft+r:f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular spe kecofr q( :6er9tpx406+wk ezed of 6.0 rad/s while turning through 2.0 revolutions. What is the a pkq:o(6er 4frwc ek0zt ex+96verage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s (6i /fntgl lm4irm1e(to rest over a distance of 115 m. What is the total number of revolutions the wheelt1 ( n46mlfge i(mlri/ rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest q1nftoj ok0 73over a distance of 115 m. What is the angular acceo k3tqnof07 j1leration?

  A wheel of diameter of 68.0 cm w6 :nkp, gsg 9,j1yppoae i(o2slows down uniformly from 8.40 m/s to rest over a distance of 115 m.wpoiygkg1,jn:p s(ea 296po , How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rurtw 6cmc c5qn4i,6f0otates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to cwq54,u fmcnt66ir c0 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,flhdd nv4p*4l gxs7mlt(v+ u:l j1x0 to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to th+4jxd h dvx(mll*vp:gtl n lu10 47f,se wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. 6.rvz.nlb uia y/ g*8wIf a 30 cm long wrench is used, what is the magnitude of t*nbilr wg z8uya/6.v.he force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertrcb.42-,f.utaw vkue ia $3.00 \; kgm^{2}$ 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, mas7+f-m )pq +kyess w eoi g61gp9n* 9ttgjmh*w2s 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia ay9ej2 os-i6 p )e n++mg* wfgpgk*sw7tm1h9qtbout the origin?

  A solid cylinder of mass 10 kg is pivoted aboun rak.uy/ :b mjpk0v7;t 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 riy/uv jr a;kkb:.70mpn ght. 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 kg is pivoted about a frictionless axis thofke oud8 -s:ng8v2-4jhlm8s 2pwj v (yught 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-8 l82j2vgsjsn8h mo:y e 4u(-vfwkp d 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 e*pvp52ai9 hi7ml de5ynd. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acc92 ldem 5piv*y5ahpi7eleration 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 lxn*n sw)/fe3 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 sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assue *fn /)snw3lxming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of ma xk d*rk /pc24n1qicx(ss 7.07 kg and radius 66.0 cm. What is the angular acceleration of thip*c(k2 nxq /d4rk1xce pulley?

  A 1.53-kg mass hangs on a rope qe (smd6wykvo4z*n0/k ,yz0)+dfofp0gt+ b fwrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.mk 0gz qf6o(fp+tn) d ,e4sf0od +vbk0y* /ywz0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is re 9pts6g,ymx6 vgx(13(t4hw hac,amhxquired 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 cnv5 9/9yep3d p/1wo fogzr4y 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 wme syc8)l 4.gf,dtnn+ ithout slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the +nmedf ,. nc t4y)ls8gbottom of the inclined plane?

  A solid sphere of mass d:x-n,tu/nd)h*wwkt1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an ix-kdt d,*w)/t :uwnhnnclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from r l;:woaf 9toi.est and allowed to roll down an inclined plane. .9olaf:; tiow How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cxce3v o you.:ksre6h 9x/h(5ym rolls without slipping down a 35e incline that is 7.0 m long. Assume it startedokyhh e9r(xu s c./y5o3vxe :6 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 change; mqy - c,nj1 bu.;7kry6xz n+k;jijvds 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 muz1fo6o. 8. vfr crw8of 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 : wa97ju,5yxfedjjw4f 51 aoja moment of inertia odj,efu57f j:jy4 o wwx1a5j9af
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?