Angular displacement ih*i-tdppbr8f6 h( x a7s usually express in units of

  Angular velocity is ex(gan5su-fn1befn td 7x0 l pj+5.j, ybpressed in units of

  Angular acceleration is expressed in un4wuna98bkn k(z)p1dqits of

  A boy and a girl are riding on a merry-go-ro(rq(:g3dfa snund which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to tn(:ad 3qr(gsfhe center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-41ykl pvbc263t ma;ncgo-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 the2;n tkby43 l acv6mcp1 greater angular speed?

  A boy and a girl are riding on a merry-go-round which is+ hg8 cu)uobb-(4 id0r a)fcft turning at a constant rate. The boy isi -du)c+cbf 8(t )har0fbug4o near 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-roua lm8b mal upwhti 73/r0kd(08nd 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 greate0l p3/alk80 maduw7mbhri 8t (r centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant ratek)-o1ab vg,y e. The boy is near thev-ayoe, 1gb )k 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 th)kqh*5bt amp/ e following is an accurate state)bm tqa k/*5phment?

  Rolling without slipping dependh e*gtk0m 51fts on

  Two equal forces are applied thzv j i0dl83d9o 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 t v3j8l9idhd0zo the door. Which force exerts the greater torque?

  Two equal forces are applied to ajb +p;do v +ga19/ligm door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the planealg1+ b;dg9 +jom pvi/ of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firs/snsfgt7 bnw899 7la et force is twice as large as the second force. The ratio of the torque of the first to the torque ognfsn s l t8/a97e79wbf the second is

  What is the quantity used to measure an -k:aoml7kjn 1f+2exh zmvx khj;10iru g6b0( object's resistance to changes in rotatio0xa1ve6uhokx+mnkf12m0jbg i(:h z;lj k -r7 n?

  Consider two uniform solid spheres where bqyv5scq 8k j:e4bw: +goth have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller m g54ceqsqj:b8 +w v:ykoment of inertia is

  Two uniform solid spheres have the r,*zd0+o, 9 z /wcwajoh-xu mcqr 4hc;same mass, but one has twice the radius of the other. The ratio of the larger socodu9cjx w/ac;h,r- m h * 0,+zqr4wzphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres wherer xj6mwui3;c:x+6hlf one has twice the mass and twice the diamex3jlr;:+fixumh 6cw6 ter of the other. The 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 increaszir3.a szi 3+c7q8w,d.k roc ned to 2M and 3R, what happens to t +w zcir3sri.z3co ,.7kdq8 anhe sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object will* kiiq5lty ,yo . a9h(7rmi*3o feem;o

  The moment of inertia of a solid cylinder about its axis is given b51o5*c sedjvdy $\frac{1}{2} MR^2$. 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 which has a ma0 qd/y e+msh6pss 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 en 0 s6ydqmeh+p/ergy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rol.1 j+ai)vndqx-grrp7ihd6g hye.7* sls without slipping down an inclined plane starting from .r+jpeq.i rn7h 7vs1)gd h a-6*d giyxrest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R 4g ./0u1vhmf rpcb mcr9;vbs, rolls without slipping down an inclined plane starting from rest. The angular velocity of the sph9/ 1f.vrmvps 4hgrmc0 ;c ubb,ere at the bottom of the incline depends on

  "The total angular momentum of a system of particles chaf,p h6eh.vpn-o02 bcpnges when a net external force acts on the system." This statementef2 6.vc-phbpo,0pnh is

  In what circumstances can the angular velocitemm,(h v*rp/i , gp+fdy of system of particles change without any change i,fm p/ m*h +rd,piev(gn the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit.sbvh vy.bn 993hz64jz-m 5iaz Ignore any friction which may be present. What happens over time to the Earth's angular momenhhvi9n63zsz m 5 j9-bb.va yz4tum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth ;8vuikubs ; fh* m6zcgn4/oer i 2km5*moves close to the Sun, then which of the followingi4or;kz2u*g*nmfm kv u8e 5s6c ;/hbi best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstr0 iz)8vc y vmi)s)57pg)6fe it(mma moetched arms close to his body. What happens to his angulsimi)c5pv8 zve7 ())t 0m ymom)if6ag ar momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pull6zsmqt -86gqa /plkg0ing in his outstretched arms close to his body. What happens to his rotational kinetic energy about the atkl qps8-6z06qa m/ggxis of rotation?

  An ice skater performs a :od7nk)q+ meie *w cv)pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his e :nei ck m7d)w+o)*vqmoment of inertia about the axis of rotation?

State the law of conservation of angular momehwvej 56/yj)kpd*ye, ntum.

  What arc length does the Earth travel in a three month period ee;7n :rc8+y.uhtx qd in its nearly circular orbit about the Su+ 8 7nctxy ru:d;eehq.n with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has r)oim s42/bifa length of 0.30 m. What distance does the tip of the second hand sweep thr osmi /42frbi)ough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutionsme;/ uyh7zzd. per minute equivalent to?

  A bicycle wheel rotates uniformly xfu4me 72gv(ilqgg:-4nvl o; through 2.0 revolutions in 4.0 s. What is the frequency of the vi og gf4e;qm7l(x :v4ung -2lwheel's rotation?

  A pulsar (a rotating neutron star)t 9.da vz(bn(2a8 tiynyx +k9t emits pulses at a frequency of 0.40 kHz. The perik. y vd yaat9n+9tznxti8(b2 (od of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle doe.(t0* nbtjk +j 6shqj flb5)vks it turn in 0.20 s?(n*tv tjb0h6ql+fsjj5. bk )k

  A wheel of diameter 26 cm turns at ;twuuf,k 0/j c1500 rpm. How far will a point on the outer rim move in 2.0,u/t; cuk jwf1 s?

  A bicycle wheel rotates uniformly through 2r3-my*z kao;am4f 6xf.0 revolutions in 4.0 s. What is the average anmmfa-f34xkzoa * y r6;gular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. d qupf.8 h34c.vfhcje4q/q9hWhat is the lhu.9qdefcq4fqj/ h34 p.8 chvinear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries q4e;zdx 9cncn i4xndixsp*/n5j+* )z 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, how fast mjp e *z+cnizq9x4 nni5d sd4;xx)n/* cust the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rox- zdn4( r6gn -kb+ tu0gytac;6kshf/tating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's r- ;( a uchnn k /y-g6dgkfsttz6bx40r+im?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. nt96 emhs0 c h+n:qpw1 If the motor rotates at th6np 0+ wsmqntc91h: hee rate of 20 rev/s, what 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 2.0y hzu7 *a6zuo5jds ;x9 rad/s. What is the ho9z ysudaj5x7 *z6u ;centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimetetb7.*:id y gyzpfu;iu5yyk93p 3gf j 3r of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m/diz;g 9yuj u yfy3tkg5i37f:py* 3. pbs?

  How many revolutions per minute (rpm) must a circular, rotatij-fyf:;r u /ukb/tz(mng space station (r = 1000 m) rotate to produce an artif-k/fr(zft :/ybuum ;j icial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speebzjiu o;c6/* cd of 20 m/s. The maximum centripetal force (provided by stati/ 6joc*z; ubicc 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 mt.v2f, zxmh8 t;q2kqoa k* 4avpp)pw) with a speed of 20 m/s. Theq )4akwfpvto p8z2t kvm;x.a*q 2p,)h maximum 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 to the end of a 0.750-m string, is whirled around in6og 0p)dqf lu6e 4g4ay a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if the string is nqday646o4g lpf 0)ugeot to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls wit zy f -j6a8+8twj/o 8ztz3ohaphout slipping 10 m down a lane at 4.3yz/z t-8 j+fha8wz6oat8 o3 jp 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 constantoj-sy(1:vwmfllpx2 ) 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,n2db iv*t j9x 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 aftffo c*3mn9 oz+er starting from rest and acce39o* c+oz fmfnlerating 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,g;k q nkj0u5,pqha/l llt5) k angular acceleration 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 afl fwd 75r8v,s constant angular acceleration os,f5rfvd lw87f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/sn s /wo;i:hmm; while turning through 2.0 revolutions. What is the average an:whn/osi; mm ;gular acceleration of the wheel?

  A wheel of diameter of)9k jvd.1,yi r kg8qws 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the )jdr1i. gyvwk8q 9ks, wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rj 7(co gglh-knr+6. s+- wukprest over ak j6nopk+ cgurs rh(g-+7wl-. distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down u /x vm,5zig4weniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel vx 4e5w,izg/m to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600c wi;1 ay4 ec:-lxwk4)j whqxb0l:3w.mck1wm rev/min. When switched off, it rotates 50.0 times at a constant angular accel44: kx-mlwb.wa10mxq ww3 h1ik )wj:c ;ycecleration 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 tr ri954ao0m k2lcktafas/x9 hcha0f/ 7-o5k uo 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 the wrenc0achrtao9/aifc m4/rf90- a uk5 2h7 5xo lskkh?

  The bolts on a car wheel require tightening to a torque of 90 hwbi8 ,w2i lw5Nm. If a 30 cm long wrench is used, whalw,wi5bih w82t is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o46j6o2yv*,fz mt szucf inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modelnf( 8*qovs7/foxh zg3ed as follows: mass m is at the origin, mass 2m is at x = *vfq3f8/soz no 7(hxga, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionlesssu : m/9hjcp3h axis thought the center O.mh/:cu9pjsh 3 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 about a frictionless axis thought th3 c hc,dye.cg9e center O. A rope wrapped arouny 3,h.eccdc9g d 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 isj* i9j0foy u0p initially held in the horizontal position, and then released as the free end is allowed to fall. Wha0y0ij 9f*pou jt 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 massh17 u;xqsrf1l 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tanqfl 1r7sux1; hgentially 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 i/h:eg r5njj5 frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Wrh:ni/5jg j5ehat is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope)dktu91e r (+ht q3hvq wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of thetkhr9 t3 (1 uhq+vdq)e mass?

  A rotating flywheel can bdp,:f7npm):t jpr +sm0jp q0oe used to store energy. If 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 inert njfx.wdz iy o)4+;vx;ia 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:q db an2tu/o(eal8g1 without slipping down a 1.0-m high inclined plane. What is the spee1n:a b/ letuda8q(2ogd of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radi))ig l2sk0n/8y0zcrzf qtg3 nus 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before comiysk q/ 2 r8l3tgznz c)i00fgn)ng to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released frs )v:2ez ddk;ql q*az:om rest and allowed to roll down an incqqazz ddsl;)2:ke v: *lined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius e ne8 ;yv;fa-j15 cm rolls without slipping down a 35e vn a-e 8e;y;fjincline 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 changes by 5g(cz()ykby1+:tu 1okc c sux$20 \; kgm^{2}/s$ 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 m3;kyt;kn/aoz3q-xsc1a0kio oment 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.v.5g7ae ei5vplm;:c4( z ic7xnmwl6www6 cf6 00 rad/s with arms extended has a moment of inertia v7 gp7x w5i6:e ;lvcw46m ef mizc5 (l6.canwwof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?