Angular displacement is ub6 wvc,5(7o86g pdo opb 9rnv c4dz.cjsually express in units of

  Angular velocity is expresnl;1jbmt x 680l *uyx (gvr*er/zc5znsed in units of

  Angular acceleration is expressed ii4g dhrd.x+1k b* g+own units of

  A boy and a girl are riding on a +6qbha.sy4ab,kkre *zg-t r: 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 the grehargqa -.6 kbt*ybszk,4+:reater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a;q,zii z a 93k,8bl.pnxr9yur constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular ua9r3,zxzb k8y.n ,p9 riql ;ispeed?

  A boy and a girl are riding on a merry-go-round which is turning atruox 6:mj7 od;tx qv2s4p* x)e a constant rate. The boy is near the out2jm ;evr6x) x:sop 7dqu*xt4oer 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-ro b126dl ekc okrc8j b.8jp,uy:und which is turning at a constant rate. The:ub8cdbl26.rkpo 1 ,j jkc8ey boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-(f5byl myr2n5)bipqet-/pm 8 round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the cenbn2pbyf 5meri mq 5-py (8l)t/ter. Who has the greater tangential acceleration?

  Consider a rigid body that is rh /n5l*8*9jqr zp ifup(ln4ih otating. Which of the following is an accurate sta i(/q9*znjl5ul 4*phr h8inpf tement?

  Rolling without slipping depeneonuda 0b 8h03 ijspy d/ot08;ds on

  Two equal forces are applied to a door. The first force i6 a))zs :bydcfs applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the zdc ))f6sa:by door. Which force exerts the greater torque?

  Two equal forces are applied to a door at theqeja jr4it xhir+u :81/vv :9y doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the j y4ex1iq jvh t::9ir a+u8/rvgreater torque?

  Two forces are applied to a doorknob, perpendijyd l6.k.d 5cicular to the door. The first forc5 .kid ycjld.6e is twice as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to chan1fxq ,h1zcf13 vsoe-hges in rotati of11exq c-hv1zs, 3fhon?

  Consider two uniform solid spheres where both have the same diamet8(b3 fq h.v)uyqgbkuo+ *ek)ger, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inf)+u(h o)u 8bqqb*ekgg.3 kyv ertia is

  Two uniform solid spheres have the same mass, baqcz806/l 5pm :wxfw kut one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of th865wkz f/cm l0a: xwpqe smaller sphere is

  Consider two uniform solid spheres where one has twic ,j* w(xxr/nyre the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertinj(xrrx,/ wy *a is

  A uniform solid sphere z a i+ke:-sgl y(.v2ltmc-5v8 pnk1d rhas mass M and radius R. If these are increased to 2M and 3R, what happens to 1:n2dyig+zp kvc s-a58vl .k-mel(r tthe sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wi(hg1w / s7hmtvll

  The moment of inertia of a solid cylivx 42rdt+2 8aliy,bmd nder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic en4,da 8xr ydit+2m2l vbergy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 1 j (d,b9w.x6mqrw2qzh0 kg and a radius of 30 cm. What is the ratio(.z6,rd w9q jhqw 2mxb 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 win8ziues;7 6oethout slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends ze usnoi6 ;87eon

  Suppose a solid sphere of mass M and radius R rolls without slipping do6+y/ hgmwop la*, e-nwwn an inclined plane starting from rest. The angular velocity of the sphere at the bot e+h-wngo,/6alwy m*ptom of the incline depends on

  "The total angular momentum of a system of particles changes 59tg /t1tpb,mj /,g /tpkoaa iwhen a net external force acts on the system." This statement 1btt,/g,pt 9 i/t5 omjgaakp/is

  In what circumstances can the angular velocitk;idjr s0nq )3y of system of particles change without any change in theinsd;rq)30 j k system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore aq9 d2tj5o0awh7 f nk-rny friction which may be present. What happens over time to the Earth's angular momentum about the7 fnq- 2ah09kr5jtwo d Sun?

  The Earth moves about the Sun in an ellipticpoen: 2qe9t*lal orbit. As the Earth moves close to the Sun, then which of*:n92 eqplet o the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outjp h;h0*rc)szstretched arms close to his body. What happens rz;hh* )p csj0to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outs28jm o1v,b udstretched arms close to his body. What happens to his rotational kinetic energy about the axis of mdo, 82jbu1 svrotation?

  An ice skater performs a pirouette (a fast sm3jh3arw*e)lz+h3v03 ddfwn pin) by pulling in his outstretched arms close to his body. What happens to his moment f*h3 3h wm )j03dvrw+eaznd 3lof inertia about the axis of rotation?

State the law of conservation of angular 1rv9lttso-yv p(9 b,t momentum.

  What arc length does the Eaxmjl1 re4w9 r7ge/r)e rth travel in a three month period in its nearly circular orbit about the Sun with amw7gj r e9r4x)e/r 1le radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the (el uqoo;j8 -utip of the seco u-8o(u;jlqe ond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolu io /jtv):5wvmvjq83 ztions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wx)rnx* wu9;;u9djhb mu j*c 2chat is the frequency of the wheel's rotatiodux*u9;2nm ub) cw;jjch xr9*n?

  A pulsar (a rotating neutron star) f+ cd-f+;n r0+wc u0myomsmxpx44h (temits pulses at a frequency of 0.40 kHz. The period ofrsmw+ u++ xf (; t4coyhfp0cm0nm4x-d its rotation is

  A phonograph record rotates at 45 rpm. Through what angle)is0 ukpc+d ,j.pkl4d does it turn in 0.20 s.kidc)ujp 4ds l,+k p0?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the ouk:4fbvnx3z) j(uswv (sv*q5b f)a2juter rim move z:(n2fsv))bxuj45vqsf*k jwab v(3 u in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revoluab)i /sf dd51dtions in 4.0 s. What is the avedi5dda b1/)sfrage angular speed of the wheel?

  A bicycle wheel rotates uniformly thob/ootmc,6:m0 r2x.qlp i) utrough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from t6,poti olmc:/ o2r0 m. x)ubqthe center of the wheel?

  A cable car at a ski resort carries skiers a distau ux3r2 :jk9fwnce of 6.8 km. The cable which moves theuurwf9 2x kj3: 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 consei 0k)fn m*vp.e.jsf;tant angular speed of 2.0 rad/s. What ve ;fpk)ej .*isf0nm. is the 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 2, ismyadiax/h:n1b(motor rotates at the rate of 20 rev/s, what is the approximate linear s2/(a: nxd myia, s1hbipeed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a cozzx/ ;r+,idl,eeu 3gknstant angular speed of 2.0 rad/s. What is the centrii/ug ed ;x,kzz,r+e3lpetal acceleration of a point on the wheel's rim?

  What is the centripetal accelersr/hnqex3g 3 w +( ocuo:hha)3ation of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m/ o:ux e3)rw/3+hno3(a q hsghcs?

  How many revolutions per minute (rpm) must a cir i)/enh z3.npwdf87thcular, rotating space station (r = 1000 m) rotn 73hw8htpi/dn )f .zeate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radiuhvsv-e1;de ,ce/ (ldts 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stativedd e1s;(vl c-e,h/tc friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curv mkjv63 ih3l df2cq,ewtj+qo6rm1 ,j2 e of radius 50 m with a speed of 20 m/s. The maximum centripetal forceqjdq3 2iv m 2,hlw,1ct mf6+rjo36 ejk (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached (n4, hj(inxw2t sxal;m+9nleto the end of a 0.750-m string, is whirled 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 havennm x+ xj42as;(w(l nilhe,9t if the string is not to break?

  A bowling ball of mass 7.5 6+dlyoe(z:l7ax i3 qg sp4iz3kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.dp 4i3y6zalgl e( 3i+so q:x7z3 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 t9i20m x1svm hh;c xn6of $4.5 rad/s^2$. 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 angular acceleration uw2)yhd f uew8)ml2un70gngqnx0 c*g 5rhp0)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 0.30mw9x2zk86:g) au s mdi0-m radius automobile tire rotate after starting from rest and accelerata8:)9 mmw2gzud6ksx iing 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 acceler+6sclgc.w xn, ation of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotat /d fg-a9h zs/o*:el 7bupxez(ing at 20 rad/s decelerates with a constant angular acceleration of e7 shlazg fp9/: x/eu (zd-bo*$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reacheslz7j2 (;r3rzl t sigf0 an angular speed of 6.0 rad/s while turning through 2.0(z0sl3jz 2rr gfi;lt 7 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformlyeuw ;qcc oj-v);1o rx/ from 8.40 m/s to rest over a distance1oo-;ejucwq) vc;/rx of 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 uniformly from 8.40 m/s to rest ow(hbg9 7 ask5e5/ jghyo:wai,ver a distance of 115 m. What is the an ,gj5o:k w 7hgw/(a9y5eaisbhgular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest o i awgo6e/;ba0ver a distance of 115 m. How long does it take fo6eag i/a;o0b wr the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at5oduzjd ;h.3 u /cyzz( a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constan ;zc/ydz.jzd u35u(hot 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 le 7 yaeo3e91n t3bol+torque of 90 Nm. If a 30 cm long wrench is used, w33e en+te9bo yao1ll7hat is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If e m,x3z4j7n eoy/js77j, mklya 30 cm long wrench is uje,7 emk s/z347y l7 yo,xjjmnsed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment nf 6,* jbv/ptsof 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 modmp pzk6j u2/t3+6 vzl9m t(hhweled as follows: mass m is at the origin, mass 2m is at x = a, and, maphp+tmmhzlu6 9vz/23t k6(j wss 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 frictionlesur( yfiqx5c4*s 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 radiuuxfi5r(q *4 ycs 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 m94cqgsi xqx( 0 r*xu,+tnyc(qass 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 downward. How many radians does the cylinder rotate through in the fi*n(4 xcr,x(9qx0qiqs+ yc gturst 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is +j*h k33)j;meis8 f ;h ofrwfshinged at one end. The rod is initially held in the horizontal positm8sj3jrf*h;;ifk f)howe 3+ sion, 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 rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. Neglecr3;z ghq, .razoxn v6czq2c1zad88v (t the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cg8vdoc.zzc r,x2nrah(v zqz3q8 6 a;1m 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 frictionle uaw0wtr. xe4n 6;lek4ss disk pulley of mass 7.07 kg and radius 66.0 cm. What is th w k. 6wu0;neelar4xt4e angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrappedb:cfg xqugx4;j;/ 8(p* rax2b a a4or -8szwec around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What x*c8s rz ;;gb8u/xfjbag2a 4awp(crqo 4 e:-x is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to sify2.okme e: :tore $1.00 \times 10^{6} \; J$ 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 in7.; xlgh3 ujeqertia 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 radim6m.vuu6t p 3c3uqf5m us 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the sp3mu53t.q 6 vup6fum mceed 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 spe:9awug cit.-j1 ebp;v 11xzjw cevu* -ed of 10 m/s. How high up an inclined plane can it c;jxbge:-u* iuce wv1c1z91 tw. jvap-limb before coming to rest?

  A hoop of radius 0.50 m and a a nb56p.m(qo gmass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vert qo6 5na.bpg(mical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 1qz /+newfwg: 95 cm rolls without slipping down a 35e incline that is 7wwf +:g e/qzn9.0 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 mom.8l g*:1;+sj ye tv 2c*pfxeen3 fcerzentum 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 of inertia ov2ykn:q2 ysbzc: o/ tj*x-u 0tf $5.0 \; kgm^{2}$ 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 au,7 :nveqo;c c moment of inertia ;:cun 7qv oe,cof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?