Angular displacement is usuallyb00igb3cgi8 b+ q s:xdgnwfx t67 tb)- express in units of

  Angular velocity is ptfs6)b 1az z6piq,y;expressed in units of

  Angular acceleration is expressed in joz9oijou) d4s ch.(t5m(70jvr5tmc units of

  A boy and a girl are riding on a merry-go-round which i */f69jfw9 bsoy8wqkr s turning at a constant rate. The boy is neaob9j w/ff*qkrsyw 98 6r the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on aebf3z(vc o iyp7::6x k 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 thc:b:z7 poi efyvk6x(3e greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constant rl)0fstie z:4 kate. The boy is near the outer edge, and the girl is closer to the center. Who has ieks4)zl0 :tf the greater linear speed?

  A boy and a girl are )dx7fup*v s5 n;khn/q riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer 7/q)d;fvs5uhpxk*n n to the center. Who has the greater centripetal acceleration?

  A boy and a girl are 06migzop 6qgfx0t2t .z4ni;db7uu) hriding a merry-go-round which is turning at a constant rate. The boy is near the ogx2g0;md u6.60ozf7pqht niz 4u b)i tuter edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rot;raa v-e,c cikay h0b0u-ye9k761nf wating. Which of the following is an accurate stat i0c 17 r0ybe96;nyf chaaev -,-uwkakement?

  Rolling without slippirbp ik *q.,nt;i7h/nr ng depends on

  Two equal forces are applied to a door. The first force itz,wm:kuvo (9gdtn 3*s applied at the midpoint vzowg(9m*:tnud ,t3 kof the 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 a0 qva h .y9r20l0:tb 5kzkmptk door at the doorknob. The first force is applied perpendicular to the door; the secklv0:0 tpy50ra zkbt. 92hkqm ond force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The fic2 kga-bws2 k/rst force is twice as large as the second force. The ratio of the torque of the first to the torque o /bagk 2-kc2swf the second is

  What is the quantity used to measure an object's resistance to chang/f 76fxt vzf7kvo;v,yes in rotatiox,;ff 77k z/6vyfvto vn?

  Consider two uniform solid spheres where both have the same dr/w 5+ 7c:-nrzb jbdrliameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of ine /w :zlcj-5rbb7r+n rdrtia is

  Two uniform solid spheres have the samec44r)e as-6vbjoip - jucjj (2 mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of th)- jc-4s6(o v4e 2ia cjrpbjuje smaller sphere is

  Consider two uniform solid sph4l,llsoy l 2z54j tb4geres where one has twice the mass and twice the diameter of the other. The razgl4l yol52tsjl 44,btio 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 2t ndvp*h:j2 fac- vc4)M and 3R, what happens tv d*tp-afv) hn cjc:24o the sphere's moment of inertia about a central axis?

  If a constant net toks; q4mngo5,: b .txbrrque is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is give/oo66-joqym q ijmy f;9;ymp8n by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translati9 jpqm8mjmy; i/y-oq fy oo;66onal kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheeax-z:gismzj/ z c*6f9l of 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 trans j6m-zfcz:gi*x saz9 /lational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rollsk 9,ke2 kjszf* 3e+ka5f)nnp2c l+xmo without slipping down an inclined plan* e+ )j3spken+ka f25 ,xmk9c2nl zfoke starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an incs pz,zd5o1unipg 5.v 2lined plane starting from rest. The angular velocity of the sphere at the bo ,psng51.pi du zzvo52ttom of the incline depends on

  "The total angular momentum of a system of partixodn 40 8 40od-u:nglo*zzmrycles changes when a net external force act4o0dn -ly8r4n gx omzd* uo:0zs on the system." This statement is

  In what circumstances can the angulabznv6 syc6 5wjepm 1x-q ee8ulm9;1u. r velocity of system of particles change without any j51 z6ml1eub896epx;ym nesvq -c .uwchange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore anyp,* brpgn8 y;p friction which may be presenr;p,n8pbyp * gt. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orba 9w*-wzshtw oys qil(f4 n54c6+t )ocit. As the Earth moves close to the Sz-9*s)witwcoh ta 4qnfyo64+lcs( w 5un, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a piroutn sb:gt /g-;cr,p 4eybyetnh99-e+ oette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about ttg -e-ebngo:p t4+9bcey 9h/r,st ny;he axis of rotation?

  An ice skater performs a pirouette r 4bsdb cen umr.taj98,dzh b02y**j1 (a fast spin) by pulling in his outstretched arms close to his body. What hb rb.sjjuyabdc 2er *zd81,t9*n mh40appens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs az ,mar*glq1 v3y hcxwa/+tfyw55),l f pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his momentaf y,)5y /ftl+3*g xw r aq,1vhm5lczw of inertia about the axis of rotation?

State the law of conservation of angular momez;-2u x+ dz0pb.igt2yle4 bl7rp -m tintum.

  What arc length does the Earth travellu ek/su7rx+ kv 4z;2c in a three month period in its nearly circular orbit about the Sun with a r2kl;se7r x/zuku+cv4 adius of $1.5 \times 10^{11} \; m$?

  The second hand of a 3md gcfaa( koq6i5,6h clock has a length of 0.30 m. What distance does the tip of the secon(6,f3io hcq a5dgam k6d hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per lb7:qhp 7fq9nhwb q*;minute equivalent to?

  A bicycle wheel rotates uniform wy jti 4bqa-a;tv0wf)426twc ly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rowtajbfi4 6-2yc ta4wv )0; wqttation?

  A pulsar (a rotating neutron star) emits pulses at a frequexve 7mx65d2 eal,ja; sncy of 0.40 kHz. The perv2a6e;7al xsjm xd5,e iod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it tuianu s j;,buo r.qm8qe/a.p4nw; 4sp 2rn in 0.20 sjpoqp; s,uwqamias8. / e 4 .nu4n2r;b?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the z3ea7ppbqh( )rba1y;jv. )nvouter rim move in 2.1z1bpyvr 3a;b. aq7e)nphj ()v s?

  A bicycle wheel rotates hjx-pzcpp75 pev+ ( 0kuniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of the5 -p k+x0jep7c hvp(zp wheel?

  A bicycle wheel rotates unio2onu ra0nyo6e16vt( formly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the cente 261( 0uroanvo eo6ntyr of the wheel?

  A cable car at a ski reso wk(xf4h4aa tmq(/n6wh enc jm:11pl; rt carries skiers a distance of 6.8 km. The cable which moves t /1;(l6w am(ph1 hfkxtc4q anjen :4wmhe car is driven by a pulley with diameter 3.0 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 or5 ;p1j zwkfq: ce99uaf 2.0 rad/s. What is the linear speed of a point oujfr:1pz9k ;5c9ae wqn the wheel's rim?

  The cutting cord on a gas-powered weed cul ts-yam 9pz87tter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approxsta-9yl78 mz pimate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angulaffa ,4 m,jck fb++3ihlr speed of 2.0 rad/s. What mc+i,43b,+ f l haffkjis the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a pois.36 kv :kvrtynt on the perimeter of a bicycle wheel of diameter 70.0 cm when thr3v.6ysvt:kk e bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) mr3p d:-4pfpxkust a circular, rotating space station (r = 1000 m) rotate to produce an artdk ppfx-:pr 43ificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed-r/caesok; .d of 20 m/s. The maximum centripedsr-oac k./e;tal 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 m witm.vg5 :f bqkiij b5xa9pbjxb / (w+;/qh a speed of 20 m/s. The maximum centripeta ab x.;pb g q5/bx9j imwbjq/(k+5i:fvl 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 aroxms7cc8v1si 6hp97u) 8mo uk rund in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum 7uvs csr8 kux76ohi)89 c1mpm 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 slippip vn:+jmd,jf .ng 10 m down:pjmf v.,jn+ d a lane 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 acceleratio a1f/;bgc 8nuh-tr b7r6ok*5uwu+ c krn 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 consadwao1d*,*,g k+ og.n mpflz+tant 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 startingnw60ts-rred7 : qz.7gd z,fjr,eep(k from rest and accelerating at a constant angular acceleration o7nwrs: rdef,etj-76 ,grz0k.(pd qe zf $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, andkrkrtzv a+i )+fi0h 4+ 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 decelegp 2(lee+* uq4p7dnibpr q/x3rates with a constant angular acceleratiq/e +lpb( q4rpind 2p 3e*u7gxon of $-5.0 \; rad/s^2$. 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 whin j2jty9f,z7yz 4cb)qle turning through 2.0 revolutions. Whabyz j)y2 f7cj,q4n9ztt is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slw0t0nkp0( q-t2h bpgf) 3q 4axria2oxows down uniformly from 8.40 m/s to rest over a distance of 115 m. Wh0kt rqxap3a0(op42g t0w n2h-fq ixb )at 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 tog 6dcrfcy3; sr8,a, ay rest over a distance of a,8 rs;gf ,d6y3carcy 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest(6 f8,vbmgcli over a distance of 115 m. How long does it take for the ,i v86gfb(lcmwheel to come to the stop?

  A centrifuge in a medical laboratoy8:k1*lqbdug:pw tn6qy: 4 xdry rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a con6k *xw:u tyd:l:p4qnd q 81bygstant angular acceleration 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 to a torque of 90 Nm. If a 30 cm lmkyn.5an9 x3zong wrench is used, what i5xk ynm9. z3nas the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require ;hde6it.. bj vtightening 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 applh.v ;6 de.jibtied at $53^{\circ}$ to the wrench?

  A wheel with moment of dgk)r jiepb dxm7h-51k7z,k.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 modeled as follows: mass m is at the origcs (t+-q c ut-(r3ay2/xim;o r: icwthin, mass 2m is at x = a, and, mass 3mt(( cy-ras;+o/uc: wctmxi3tqhr - i2 is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of matk9rey2wc,7 c0b,mi/ u3e w eu)p* cmhss 10 kg is 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 downwardmkb ww7ehmu0)t*ei9y, ,2pcrc/e c u3 . (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted amifdfks,*09x/jee hr to .kwitc15:, bout 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 thrsd:*ek0ctxr /m.o9eft ,,i5i hw f1 jkough in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hing ttwqe0bsa +vxj ,lw,1l5j7z8ed 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? (aj 7xvqtlzl+ 5,0jw1,esw t8bThe moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle whqah+y;l ;swnkait42 s 5t 7*mpeel to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangential7 kl*pat4is5whq;ny2a ;t + smly 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 myusub ayr7eqb 8(98 (frictionless disk pulley of mass 7.07 m8 b(7y89 qesu (aurbykg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of v)ka lkd;s(8bmass 7.07 kg and radius 66.0 cm.as( ; vklb)k8d What is the acceleration of the mass?

  A rotating flywheel can be used to storg m0, l(dtwu2 1z47bbh t2vfxye 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 iyl 5*wc+ea:zc nertia 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 0.010rposi6* . ukc mh4qc5hu+4j8n m starts from rest and rolls without slipping down a 1.0-m high inclined plane. n 6hp5rujhc8qsku m4oi. *4c+ 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 speed of 10 m;0i xeu c802mou.bs qt/s. How high up an inclin0b 2e 0itu;cs xuo8mq.ed plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass o 66 bjrvlxx7w zifca1,5n3z *cf 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it1c7b 5 *x66z fjzin 3rcv,axwl moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rollss a; nw 6dlxcw3bj 6;8hg(de*f without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertiabxlhej6c*a3;6nwddgfws 8 ; ( 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 momenttxmak,z0mspp 2()z. j-c) n yfum 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 - npz h2ocqg.k48k hq6of 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 a moment ov uek)znvxl04 *kdbb0e4t- g1 f inertia o44une bkt0kb)0 x1v -vgze*ld f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?