Angular displacement is usually exp :w)hr6iwf4oe ress in units of

  Angular velocity is expressed v 3ffo nrvsk-zq( 0-kf j556 8kmxihy/in units of

  Angular acceleration is expressedbo7axc -q 0s;getx+37 (av-trqqa-sppr0v e6 in units of

  A boy and a girl are riding o8a4z yjd5;iy dpje6znt w,qi gu-1/)rn a 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. zrtezq ndya4p ii ,/-;j)85d6gu1w yj Who has the greater angular displacement?

  A boy and a girl are riding on a merry-gopj k(fzs0xus h4+*j7 dlvy/7h-round which is turning at a constant rate. The boy is near the outer edge, and the h7/*jsh7 kf vu (0dxjzlp4 +sygirl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a co1b*dqdw8tit;d5)d q/mwz:v6fv)d jbnstant rate. The boy is near the outer edge, and the girl is closer to thd d5b)*/)b1v widv wqdmtj:dz6fqt8 ;e center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant p h2fhjqf8 -z6o,z*dsrate. The boy is near the outer edge, while the girl is ch-z8 qps , h2ofzdf6j*loser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turningh*-sf:j 2 zab cc0fv-j at a constant rate. The boy is near the outer edge, while the girl is clozjvf bhajc-s -*c2f0:ser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that isbx,cd lwfve xal*),rp e)sm d/))j4 .d rotating. Which of the following is an accurate statemenm/a,e f ,xp)j 4)d *.ldbxrds )vewlc)t?

  Rolling without slippingkxwz7all .y awbam06l(/ u-:g depends on

  Two equal forces are applied to a door. The first force is applied at t.nz wed:r+k+q:ha 7kc : se,yvhe midpoint of the door; the second force is appliedk ,s7v+ :qr +czyawheekd: .:n at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is s 61hyn)jzo7yr crxvz60/e5og.i tw9 applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the grea5vhi0cr1ntg xzwy6z jo)eor.s7 6 y9/ter torque?

  Two forces are applied to a doorknob, pekmg;b.,3 eoa qz6i69spo9fkkji6 ,i krpendicular to the door. The first force is twice as large as the second force. The ratio of the 6i,fpikbojk q g .9o ksa6,k96i3em;ztorque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in rotx xs n, 1zv);x 4ooo)g;gwa(dwatiwsx ,)4z; ono ggax1wd;)xov( on?

  Consider two uniform solid sphergpr* 82lit.ro es where both 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 smallerg *l.r2 ti8opr moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius ov.unec zm:rl.0h9w7c f the other. The ratio of the larger sphere's moment of inertia to7 m uz nclhv.9wr0.c:e that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and f0ah a/a3e.w:zl ngv,ule 4 z8twice the diameter of the other. The ratio of the larger mu4al lw geh,fe azz.an830/:voment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increabwek7d/y-al v9ku9ve bk 42j-sed to 2M and 3R, what happens to the sphere's moment of inertia about a -y b97k9e2ek -ladvw/4bk vj ucentral axis?

  If a constant net torque is applied to an object,+ya 0himajc 4- that object will

  The moment of inertia of a solid cylinder about its axis wt85y;,t;*(men nvb4 ooc; sgj6ckd d1ntco8is given by 0.5 MR2. If this cylinder rolls without slipping, the raticdtt ejt,*c(58sgw oon4n n6c v1;boym8d ;k; o of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle obm* 6u2ovyl 0* gc5txjf mass 150 kg, one wheel of which has a mass of 10 kg and a r* 2 5*uc0o tmbgjlyx6vadius 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 wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippin 2*62.0vq- ccc onolhnxibym kz )5wa4g down an inclined plane- zkhoi 6n 2*.4ln)cocvcw xym5b20a q 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 downgt6 h *u;mfo/yanvz y5b;30ba an inclined plug;vzha53o/fnb6 *t ; b 0amyyane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a systee;z9y o(b/t.a(0 y 0qwoovkkmm of particles changes when a net external force acts on the se00akmyw/b (q .kt vz9o o;yo(ystem." This statement is

  In what circumstances can thktf: q;x00 dwwe angular velocity of system of particles change without any c0wqkf x;w0 :dthange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any flzz fxjw(zit22 ,/-nwh+bf kxyd1.(j riction which may be present. What happens over time to the Earth' t. ff(dw1zjxlwnyk/ ,bixz2z+( -2hjs angular momentum about the Sun?

  The Earth moves about the Spa aih1..bet9 un in an elliptical orbit. As the Earth moves close to the Sun, then which of thei.hpae9. at 1b following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pir z whe--en0l37ohl5 qw,dl4gu ouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the audh g lo hwqn3-l-54,zele 7w0xis of rotation?

  An ice skater performs a pirouette (an1l(s i b llt;m,ai+:cas u,28+h ylpe1xsq p, fast spin) by pulling in his outstretched arms close to his body. What happenss1 i :xc( ;e+alapqlm +ub,8pt s,1ynll2,his to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fastje- pz5 qp jf24b,h+vr spin) by pulling in his outstretched arms close to his body. What happens to his moment -p +,2f 4pjj5 vehrqbzof inertia about the axis of rotation?

State the law of conservation of angular momentwm .i/pgmqfou;7j r9/um.

  What arc length does the Earth travel in a three month period in its nearl7p9/vkxp+ qe :gv-4 qka; l8brg:aw bhy circular orbit about the Supk/p v8a4wqv79;xh::k+ gqlbrg-ab en with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distancengfcg*u4u8kpzf -/c89fj5 z x does the tip of the second han cf-k8x9g4 5cz/guzp*j8 uffnd sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutionsu/p*co01e0m)eet8yzys*uije t 35 dp per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is jyej 0syr cmh2+;f:5yt- nh. ethe fhmy02 :nf cyy;rt j -e5+sehj.requency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequef( m5w3z7ssv:+lap ig les;*zncy of 0.40 kHz. The period of its rot *szs les: ag3(ilm7zpf;w5+vation is

  A phonograph record rota sg8ccuks3/p )tes at 45 rpm. Through what angle does it turn in 0.20 s/ k3u8ps )cgcs?

  A wheel of diameter 26 cm turns at 150nnsgbr++,zpr w7lzpr; 5q -* z0 rpm. How far will a point on the outer rim mnbl +gqp p z w*zr,r7+;szn5r-ove in 2.1 s?

  A bicycle wheel rotates uniformly thrj9l6khl .yyq 7ough 2.0 revolutions in 4.0 s. What is the average angular speed q9.k6yy7 lh ljof the wheel?

  A bicycle wheel rotates uniformly through yu ts,8lxaix.fa os w0ks*bw-3,qc; 3x* yh)c2.0 revolutions in 4.0 s. What is the linear speed of 3;fayklxissu*boa* 3xc.8t xy)cww - s,0,qha point 0.10 m from the center of the wheel?

  A cable car at a ski re60w,cmb jo05kbmn.9j vzuo m(x7fc /o 6zon d1sort carries 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 must the pulley rotate for the cablemnc5 6d /u n.o,z16mjjbz(o0 o9c0xfbmw vo7k car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angula4 p::zbmtelhm r*,uo7 r speed of 2.0 rad/s. What is the linear speed of a point on the wheel's rim4t7 *:l:m ,ouphrz bem?

  The cutting cord on a gas-powered we-8 ,kpr ((fyn/s wf nfjuufss3k5.v 5red cutter is 0.16 m in length. If the motor rotates at the rate ofv8jnff-,p(srn/urus5 .sw3 f 5 fy(k k 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 wb*qfx bsl5.s5 6ul- za constant angular speed of 2.0 rad/s. What is the65 bs.u lwxql5fs-* zb centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycl 1ipggb0 .)ml7g /slu-wgq axwvv3 q,7e wheel of diameter 70.0 cm when the bike is movingvw ,1u)/3xl0.vaqb7qiwpg 7m -gsglg 8.00 m/s?

  How many revolutions per minute (rpm) must pl07, 4x4 dypxqe* 9qeiw8u8:ijq ezda circular, rotating space station (r = 1000 m) rotate to id8x :d*q,zy p8x qew74uei e90 jqp4lproduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speedc ( :lz;7okcmk of 20 m/s. The maximumm(7:; c klczok centripetal 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 circularv62su )5x1,z kocytcw curve of radius 50 m with a speed of 20 m/s. The maximum)51wyovcz, s2ct k6ux 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, io:hax.ly2;nb qvw+( /+ ;qxr vsjxk9xs whirled around in a smooth level b o (kwly.a:hn+j ;29q q /vxs;vx+rxxtable. 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 not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slippom j2. a47o zk6kbl1jling 10 m down a lane at 4.2 bjz4jkol1m7o.l ak 63 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 withq8mf. o; ,-* h2 wsp-fi1q fqko5orpwf a constant 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 a6 g1+8:0xf1 dmpn q/lfy/ avtid d.hcwith 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-dmmd /cqy/m +/ 5hcklz8l4o1dm radius automobile tire rotate after starting from rest4lk8cym hd1/z5cddml o/m+ /q and accelerating 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 angular acceleratio2 ez nkxth w6faq+;u qdd:o2*et f:;b+n 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+mqnf+9t:i1h f r cp.mstant angular acceleratim9+m. fq+rt 1:np cihfon 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 7 q zp:wvflp+ug; y86bspeed of 6.0 rad/s while turning through 2.0 revolutiol zu8:7ybg;wp pv f6+qns. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uaxyn/:t* ;:x1 9fkq q7rlqky bniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming k;rq/*n7lb1fy9q:xy q:x tka to rest?

  A wheel of diameter of 68.0 ;q-+ dzc iws2 apdy)w9a4cu 2icm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the ang-2 sd2wc49ipqu;dwzy c+ aia)ular acceleration?

  A wheel of diameter of 68.0 cm slows doa5ks)/k2uf xa wn uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for takfa/2ku 5xs)he wheel to come to the stop?

  A centrifuge in a medical labowq9- .iwlv ,n bcle1)uratory rotates at a rotational speed of 3600 rev/min. When switched offw-vi, bl l.u9w)ncq1 e, it rotates 50.0 times at a constant 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. Ifke8e eb. 8beo( a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the e e8(kbb8eoe .wrench?

  The bolts on a car wheel require tightening to a torv3 d0 a8qh+lijque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force require8hav +q 30lijdd when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment olqf.ws)iwvdc/n-u r: ;+mw6f f 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 mode8yc y w9;al11iqk9k un4*uvmgled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m isa4 l8qg1vk*knmu9;i9 1uw cyy at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of 0rgxwr,* . 9lmp*ogtrmass 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 t,oplrw0gr*rm*xg9 .= 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 thought the ild 66e xu rsnmyg/ok0zj/)45 center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 0rgkm d56 su) ejl6/yiz4no/x 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 through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hingbwh0t b-yqwwn+)7 i9aed 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 momeywqh7tnb+a i9w0- )w bnt of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cmzvl7 0 1i)ps1 z63uncwtqqwc ; and mass 1.5 kg. Neglect the mass of the axle and); 1tqqn 7zvzscicw061p3 luw 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, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrbaj x k74 wai():1wph0vlq b8oapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratiool:akbwjqx 1 hp(07vi8 aw 4b)n of the pulley?

  A 1.53-kg mass hangs on a rope wr .:unxur:.k tgq9cjk )apped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What tx.9 uung.rk k:c:jq)is the acceleration of the mass?

  A rotating flywheel can be used to store energywmv.xea mwkd49i 7g0- . 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 in1ny( :(k0mz.)r5zk7gwzj o tl ccou fg-/ad-tertia 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 mass9; eriuoy;(p f 1.0 kg and radius 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 the bottom of the inclined p9(; pufoi yre;lane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed lve llj,pv0 4e+e a0l9of 10 m/s. How high up an i lj,vp 4e0allele+90 vnclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a massniipot 5r3c/bv:e8 q ; of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distan3r5i8:/ n cpqeoib ;vtce of 3.0 m?

A solid sphere of mass 1.5 kg and radius)(ne5duqs hd 5 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started fnh)5 qdu5(e sdrom 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 b.qvk:c8f1zlp( m 6ots 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 of( jtb ewg) lf11 )or-f6rsj*gs $5.0 \; kgm^{2}$ 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 momp*0t2x b xto6bjrf6 kv 3z6z1went of inertia ot6b3 rtfxv0x b pkjz*z6o1 w62f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?