Angular displacement is usually express in units o)hp+vs)o(, riw 9-onrspbofa c ;*bc6f

  Angular velocity is expresse( qfr u0:q+k ep,b4z rkt.i6agd in units of

  Angular acceleration is expressed in uyiay2k0f zm+hh,l3) units of

  A boy and a girl are ridin;x+/5ahgjf 40yua mgb:n3zzp g on a merry-go-round which is turning at a constant rate. The boy is near the outer edge,0a4: 5fganzxm j;byp+ 3h/ gzu and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding oni04 y:8gg jyoe a merry-go-round which is turning at a constant rate. The boy is near the oute 4ioj0g :yg8eyr 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-roun wx6kg)dk ep v897tc:4oqd*s zd which is turning at a constant rate. The boy is near the outer edge, and the gi8kdp9:*467wczq evgkox)dt s rl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-rmyf7jh y(( *txound 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 greater cfyy(mj(t*7 hx entripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at avb85 l2ic x2ihi k0e8p constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential 0hcpx88 kbel2i 5i i2vacceleration?

  Consider a rigid body that is rotating. Which of the following is an accuratd, ht*hlrf0vfu+8+j xe statement?fh+vfhl+ ,x 80t drj*u

  Rolling without slippizyuu 7/d pq6;gzo -)nyfbo8rja bw9n)i:*e :vng depends on

  Two equal forces are applied to a door. The first force is ap:imf *b .5t;*y hxcmfqplied at the midpoint of the door; the second force is applied at the doorknob. Both forb5 q;:* mh*mf.tiyxfcces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doork q(e /z8pl fy/zrel1k7nob. The first force is applied perpendicular to the door; the second fo7y(zlfq rep/z1/lek 8 rce is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doow3wr:im fck69*jynnec-j ;(zqxn-j. rknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the t. 9inej(-wcqj;3m-*fz : nkcjxr6w ynorque of the second is

  What is the quantity used to measure an objec uam/1ngjnym 8u zy,:)t's resistance to changes in rotatio,znm :)y/ajm1 u uy8gnn?

  Consider two uniform solid spheres where botaw+me nob 0go6;mp.9 8gg5pz ah 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 moment ofa;.5o p 8m g0bpemgnw+o 6a9zg inertia is

  Two uniform solid spheres have the same0)egft au/ug1 (kj 9efk1/rf1yy .n*s :exev r mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of.g( x)* e1ff//yker g1ktf0a1uevjn:s r uey9 the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice t))a6nkas 9x.z 74zcbqggn lg0he diameter of 7. b sq xzc9lz)g) a6k4ngg0anthe other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mas cm-c:w p9df+jc/d,wcs M and radius R. If these are increased to 2M and 3R, what happens to the sphere's w/ccp9c c-dwd,+:m fjmoment of inertia about a central axis?

  If a constant net torque is appliex) oks nb ,adf7sm77t9d to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given 814pl9j 8bbhdyijr /q w3kw)b by $\frac{1}{2} MR^2$. 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 ofc b7b(t9y j,ot which 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 w t9(jbo c7,ytbheels are uniform disks.

  Suppose a solid sphere of mass M and radius R roll st,n qt3ct*,ls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline det,ql3 ,tt* nscpends on

  Suppose a solid sphere of masqz7-bb9 *oq ei(fja:ms M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends oz9q(iobj *:q f7bema-n

  "The total angular momentum of a system of par-nwv--akyxnj /: 4 sbkticles changes when a net external force acts on b/sn:vy-k -xkj wn-4 athe system." This statement is

  In what circumstances can the angular velocity of system otsl zyi+,5fpjig)a ./f particles change without any i./ i,al +z)ytjsp5fgchange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which mayonue 5 j) q1hhb(qio83u3u m/g be present. What happens over time to the Ear()5h3q/1hquj ubo3mgo u8i e nth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Eafa2v 34eik:p(zuks( 1*sx(-z vln rnqrth moves close to the Sun, then which of the following best desav13s2:pskf 4qkxn-e ( nuzl (i*v zr(cribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a a8 m2-iv1rbzi;v5k gbfast spin) by pulling in his outstretched arms close to his body. What hai 2v1z i;5bbmv-r8g kappens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchwyxxas, 8.k g 9go0es69qhz*c ed arms close to his body. What happens to his rotational kinetic energy about the a8,e a x99 0*qwkxgyo gcz.6shsxis of rotation?

  An ice skater performs a pirouette (a fast spin) by ; xw7zalf8i r4pulling in his outstretched a 8a74flwixz; rrms close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular mome(w 2 awa jbqsxu7c35 vfpj5yv(-;la* )ylf6fantum.

  What arc length does the Earth travel in1-+zt ydno r5ce*g8un a three month period in its nearly circular orbit about the Sun with a radius ofr1 n-uyzc*8t go+dn5e $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a le7c+wz + pewvkg2r0r/qngth of 0.30 m. What distance does the tip of the second hand sw z+pe+rr2vq7w cwg0 /keep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions xln y/y59,uatb jpw,l9 l7+raper minute equivalent to?

  A bicycle wheel rotates uniformly thro l wji8v -t+ivf3/jp3gugh 2.0 revolutions in 4.0 s. What is theg3 vwfi/vtj3lji p+-8 frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a fre:6zhokdz .1okgfhde ( 47* hu0p* nhowquency of 0.40 kHz. The perio4o:d kwo h*1zoefkz h67h(*.hpd un0gd of its rotation is

  A phonograph record rotates at 4g md- :,,h1vzggy +udozz :/j.rtlrf85 rpm. Through what angle does it turn in 0.20 sjg 1dho:,gm-l tf.z z+:yz / vr8g,rdu?

  A wheel of diameter 26 cm turns at 1500 rpm. Hbuq53j ows sl,s mj215ow far will a point on the outer r2mso wj3q1b5,j usl s5im move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is tsx d/v)sm(s:qc8/yx ghe average angu d:x)s8v/ cgmyq(/ sxslar speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutionsehry v-/vk(fxi 2r-/3da,s wd in 4.0 s. What is the linear speed of a 2/r3rs,wfydvh- d xaik(/e-vpoint 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cabuj53kc p5x 5wzle which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast u w355 zpj5kcxmust 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 speng6m l fq)7pk/ed of 2.0 rad/s. What is the linear speed of a poif7l npkq gm6/)nt on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length 6p7.yzm m euz4-ua7tb. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the em.e4u am7ub7-yzz 6p tnd of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular spcndj) u0s 2 u+,fruf7m. 4vjpv30veiceed of 2.0 rad/s. Wh v0u4s+pc7dvf .r iuvce)n3fm2j0u j,at is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the ,+eftix ygt9wi7k75m2k +jr uperimeter of a bicycle wheel of diameter 70.0 cm when th,+m5jrxikt 7gf 9uki +e t27wye bike is moving 8.00 m/s?

  How many revolutions per min;fp lvlmw((* .3nk ovnute (rpm) must a circular, rotating space station (r = 1000 nv;l nl m(k(*p.v 3ofwm) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of12 q bjpl6 zfw5-xhck9 radius 50 m with a speed of 20 m/s. The maximum centripj xwck-2z9 16b5lpqfhetal 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 k;ss6 +n8i,ekx xqn ti m7(4m gew+p/sm with a speed of 20 m/s. The mas/gxq xn(mn +w ,4+6ks 7pteik;8 mesiximum 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 stry7m. k2 qpnvqv, t27wring, is whirled around in a smooth level table. If the m,.2yvqv rn2wm7qp 7ktaximum tension 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 7.5 kg and radius 9.0 cm rolls without slippinhwffvr:wt-;u+rnqa)g //;*dz khbo0g 10 m down a lane at 4u/)rr g;/vbdhf:fz kq+o0;ta w-wn* h.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 g)kk(nz2 b9ml hi;r2k $4.5 rad/s^2$. 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 angule- t (w/ivpm2u.q)gkxar 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 p;7hwq5(rgxi a 0.300-m radius automobile tire rotate after starting from rest and acceleratin;qh5pi7 wg(rx g at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at red7i5km lq+ : y)k+b/yeasnbd 7st, and has an 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 a constant angular acceletahx ulh 5d cq8oh//-0ration t 5l/ hocuh 8d/a-qx0hof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest .ly0z5thh(jd3mn, /qj a pi2oand reaches an angular speed of 6.0 rad/s while turning through 2.03o,hnytq2/.j05h ip m (z jald revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40;)tb7fb 4 gdlcdu/ot1 m/s to rest over a distance of tu4o7; dg1bb/td)lc f 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 uniformd ugvm 7/4 * etaob/vum;/5jx:)btuhlly from 8.40 m/s to rest over a distance of 115 m. What iu)gut: vujh* b o45;tl7/a/bxm mde/vs the angular acceleration?

  A wheel of diameter of 68 7a.+kti3p/yloz2m x m.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. Hoylmt2k+o7paiz 3x .m/ w long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotat+n/euhbs*9 lcjqhse s q m-+*;es at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before+e*bjqs ce-s9un*s ;hq/m l +h 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 torque of 90 Nm. If a 30 cm lf ygacy q54+a3b9 2 bdyit7iub-do*4mong wrench is used, what is the magnitude of the force re gi-y*aa72 ud bb5mo4id c9qb3f4tyy+quired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30z8lu5j fskfuht10- xe)9;a i ;hw5hhc cm long wrench is used, what is the magnitude of the force required when the ;tu8x155zh90akclff huh ehs- )jwi ; force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertqp29g u9-w2b px zqnvjty3k.7ia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as folldew b-j3 i gzb+a8kn(3ows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin-d+ g 8 jabzi(3bkne3w?

  A solid cylinder of mass 10 kg is psxen3m h0 domloxik.5 hmd t 5k: 2s)*4zfp.7mivoted about a frictionless axis thought the cez5it lddkksx7 h24smo5mm mhf.0ne)3:.x o*pnter O. 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 -cxk 862bek7t z;uqlcfrictionless axis thought the 8t7c6e;uqb2lc z- k kxcenter O. 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) 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 hing*9n3uh ph):cx3 6ptrte ipu:ied at one end. The rod is initially held in the horizontal 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 r3 ::hppt9)it hix3ueunc p6*r od about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of 8u1bgk99wi8 i.riz mqradius 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 4.0muii1wiq89. 9r bzk 8g 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 aroup:krasxye . 04nd a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration xapky.s :e 40rof the pulley?

  A 1.53-kg mass hangs on a rope wrapped around w,1mw7:mrhsvx a 8th.p 17 zbfeo-gy;a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whatmvsp1 w-by x1hhr;:77e8mo zg ,. fwta is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is f lyk(f).re:x 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 inertia9kn88lokn iysk r7 (t4 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 radt )x 4,:igvetfius 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 ,tx: ti)ge4fvthe bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m ycdk/bh5,z ov ;e.zq(rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to rk,h b/cd( yq .5;evozzest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from j+o;nzt/hyu o/3n((su jjo j1rest and allowed to roll down an inclined plane. How o(+1h ojznj jn ou 3suj/y(/t;fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 1 rmcu,a lw9lx2 5mypxp7j;).g 5 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The m5l7agy; mmpujl9x,c 2x.rw )poment 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 chai i vrb81;j) pe,wqlntx)n 66znges 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 mome1ind0oz izh. .nt 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 artz0 vv46wjr+e ms extended has a moment of inertia 0rv+v z wej46tof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?