Angular displacement is usually express in un r8x.c1;qpfys(w le(oits of

  Angular velocity is expressed in unitsxv0fxm 0ks58l f5 n ldgdpv)ld0 +tw8/ of

  Angular acceleration is expressed o u7q.1kx l5mqct3 x +af7qay9in units of

  A boy and a girl are riding on a merry57b7 ns e 7z8ti/z5my:1kjvxts0prcw -go-round which is turning at a constant rate. Trs5etvyxpc7jnb kzm w 1 t8i70s/z7:5 he boy is near 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 a merry-go-round which is turning atsxpdin ,k8k d:u6,.ou+oeig: a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angula,6d 8n,igxes p:uuidokk : +o.r speed?

  A boy and a girl are riding on a merry-gokp z383+yyljm xy5 z;l*n.t oi-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has8k l3yol.x5t*;zynyp 3 jzim + the greater linear speed?

  A boy and a girl are riding a merry-go-round wkb,d d3gel8 xej4t8w0be3t v1hich 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 cent 0 3jd3etb,884e1vk gxwlde tbripetal acceleration?

  A boy and a girl are ridinpq oj bb3-r; skq/q,(6efc lg6g a merry-go-round which is turning at a constant rate. The boy is near the outg/bojbkc 3,fps;(qreq 6-q l6 er edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the followingba3. j1 xma rc04h3yvc is an accurate state yrc1a3 jbvamxc34.0h ment?

  Rolling without slipping dep.z s4k x*dc)tc*h8s azends on

  Two equal forces are applied to a door. The first force is applie nx5n dmi6d q-;*av,gtd at the midpoint of the door; the second force is applied at the doorknob. Both forces are app* 5 -dq,vti6;xnndg malied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied qzv2ubho sdpl.xa:g 2 fj(r2rj ,631pto a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e p.l,pzr h so2urg:2x13a26f(vbjqjd to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, pe ge,re-/ev8x prpendicular to the door. The first force is twice as large as the second force. The ratio oegv-/ r,8eep xf the torque of the first to the torque of the second is

  What is the quantity used to w 0q.lqv-(0en-uyrd x measure an object's resistance to changes in rotation?nq0w (v0 e-lduy .x-rq

  Consider two uniform solid sphereh36tj2er jf lkt68tu9 s where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertiar l63 tjft2kuth6j98 e to that of the smaller moment of inertia is

  Two uniform solid spheres h6 b5:ojlm(y2id4d maxave the same mass, but one has twice the radius of the other. The ratio6 bilm52 4ayo:dmxj( d of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the pxox 0h-t np2: /yvq0fa2 +zjadiameter of the other. The ratio of the larger moment of inertia to that of the smaller mojzna2hv:p/ at f0x2+0qo x-y pment of inertia is

  A uniform solid sphere has mass M and ragmp m +w:fnm1f y(/m 92(uus0modk(v ydius R. If these are increased to 2M and wvn:2 g9y1/ukmo(dm (mumf +sf 0(myp3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that p eegi)v9 .(/9qw k fek*ij3chobject will

  The moment of inertia of a solid cylinder st *: j2he h3o2dt*e g 9(pra;4slhlxmabout its axis is given by 0.5 MR2. If this cylinder ro3; sdap tr*ogs9lh2h 4e*(tlejmxh: 2lls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 1hebc *4 m25 vx; 9znnz*v+ogyrtet*pkg, one wheel 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 translational kinetic energy of the bike? Assume the wh2*gh *n5tetb9 v *1ncz4v m;z+ yoexrpeels are uniform disks.

  Suppose a solid sphere of maf g cs*ep1qp;/+.tm akss M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depenkg;f*qtma+ /ppc 1s. eds on

  Suppose a solid sphere of mass M and radius R rolls without slipping down z; a7r1 v t+ysk3iof+u eru/,can inclined plane starting from rest. The angular velocity of the sphere at the bottom of they au3t,1crkzfive+o;rus/ 7 + incline depends on

  "The total angular momentum of a system of particles changes - r9*xdgx7 yhnlx5.dejt7cz, when a net external forcet jxx*g7 z-h.e ,nx5d yd7crl9 acts on the system." This statement is

  In what circumstances can the angular velocity of system of part sz46.nwc:pch /4dzkk icles change without any change in the systcdphz4:w. zsk 46 c/knem's angular momentum?

  The Earth orbits the Sun in an ell*0 e-) ri8mpgklzg; eq9(g+*obrzgm jiptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum abpko;0) ge9jbi-z m8ge *(+qmgl r*rz gout the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth+mfb3d)mt2p7 g7t8 dpug rz0w moves close to the Sun, then which of the following best describes the orbitingpgu7wmdt g3p m2)0r+ztfb d 78 speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pullk5nb3h-l-tzf 8rjoc iqy; (.sing in his outstretched arms close to his body. tcbk h8 5-(lno.-fi3 qyzj;srWhat happens to his angular momentum about the axis of rotation?

  An ice skater performs a piq62qw b*2r9p::nfdafmmv( l frouette (a fast spin) by pulling in his outstretched a f m2r9*nlp 6qvf(q:dbfwm2a:rms close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fae wrgol*-*ap scr il:i tgr56 7n3bfn6hby0:9st spin) by pulling in his outstretched arms close to his body. What s ri t-:b3**cg6 ne9rpafh0y o5illbg6nwr:7 happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum.0 f)aahcl2( tr

  What arc length does the Earth travel in a three month period in itzda aj9 h304lbs nearly circular orbit about the Sun with a ra0z39ha b l4djadius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does ch5m6wp 7u;gbthe tip of the sh7w mg6 pbuc;5econd hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions i,v j;ek1qd9vebn*4)4za if( qvpaz( per minute equivalent to?

  A bicycle wheel rotatesgarxrc;p; : b3 uniformly through 2.0 revolutions in 4.0 s. What is the frequenc;:ra px;3rbcg y of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at ef07:nl3l8y2w,9lj bluhxhs a frequency of 0.40 kHz. The period of iw lhnlh9:3,7xy ul fe2s 8bj0lts rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0fc63,rs -9+zgjli 7zl+uaa a3vhz1un.20 uzhslcaf r 7lv93z-iug n 6+13j+a za,s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far wilg-)(0 t67qf eqw/nwn uf ili6fm-9ci ll a point on the outer rim move in 2.(--0 /utn6f fil7wfmc g)qiwle6i 9 qn1 s?

  A bicycle wheel rotates uniformly through 2.0 revo,e u wc-mp0+n8 cuj1wmlutions in 4.0 s. What is the average angular speed of the wh-m8wemn,cujc+0 pu1 weel?

  A bicycle wheel rotates uniformly through 2.0 r,(tv7r8, mkp3httaw ievolutions in 4.0 s. What is the linear speed,v ttk8(a irh,wp 3t7m of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 p jj5m /x9bvrpde2a0 og5f *ss e,my7(km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuminggdp9pbeao /0 mr j( mv5fy,2*js5xe7s 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 rotatq2mawm9v p3/ging with a constant angular speed of 2.0 rad/s. W/v9a23gpw mqm hat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed culw* htwd ( /ev)g/td)ti6www;tter is 0.16 m in length. If the motor rotateg6/) w h(/d;tvwdtt w*iew)wls at the 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 ofn v5mb9ouxrse/t6k 7jy)y2m5yl )-ty 2.0 rad/s. What is theox5s5kn7emul y /r2by6ty))v m-t9y j centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point 0hs4 pa cd(dw-5puqo;ol9 *aqf 2eon;on the perimeter of a bicycle wheel of diameter- o; plqp ea4w9dc5 foanh(us02d;oq* 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutionslx 70 uw6hl7lj5 p(tdolie18kc son(( per minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificialhe5lx8w (lt( 0s1 (o cku inlj7p7od6l gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radi z1.ney2uf.gc,zrli1 u4 d f2a; on-ihus 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictinuif 211zif;cl.nyrha . e2z-g u,do4 on) 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 3 7-v,lhava3id:m scku iq97rm with a speed of 20 m/s. The maximum centripetal force (provided byv7 9iudka: sh3lqmc3 a,rv7i- static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attac* inslf.x(2 wihed to 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 speedfiiw . ls2x*(n can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rou teh.*8 gpo+blls without slipping 10 m down a lane at 4.3 m/soge .h*+tu bp8.
(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 wig )t9,*c c,edchr+ scjmr 2c1vth 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 with a constant ang r32v :ap;kpf q7ar:zqular 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 autqutkpb gl4 )21ti*w1 qt56hfgomobile tire rotate after starting from rest and accelerf 4g*1 tqpwg)k1hlt 2q5t6bui ating 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 ang0axkqy)n9 /efular 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 aclx; ,f uw)veixee:2.ymh;l. lpo- n5nceleratime5-x,louv.leh; :x .if)p y nl;enw2on of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest ls0raas3 ,arnj gs2+80au41kpgm qe5and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the wheelpsg,a8n50gq2as10js l ekra3 4ra u+ m?

  A wheel of diameter of 68.0 cm slows down unifo 9b *g wh;uf69tcru2 z*dbz)lormly from 8.40 m/s to rest over a distance of 115 m. What is the total nu)2uw 9 frtgb69 ;ozlu d*zb*hcmber 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:f1+ebu 2cywi s o-/gzv x3-+;eqbivt over a distance of 115 m. What is the angular acct i+y 2v -ce+:gi vuz3o1;-xeqfbsbw/eleration?

  A wheel of diameter of 68.0 cm slows-.kg(iqh3lxx down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to(3kqxl.i- hx g come to the stop?

  A centrifuge in a medical laborato6+ kfca-8 dvuwry rotates at a rotational speed of 3600 rev/min. When switched ocdwv6ka 8 -u+fff, 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 au(k. d,y2ymz k torque of 90 Nm. If a 30 cm long wrench is used, what is the yuk(k, d zy2m.magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a: 0vt3p,ov9dbh p5)ea3vxd jv torque of 90 Nm. If a 30 cm long wrench is used, what is the th 03p5 :jdv 3vp,oev9ad)xbvmagnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner qn qnl1hn)28s,p hxo3tia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mocz *57zl:t-af zmo+c sdeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What iz lma- 7stfco*:cz+z5 s the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictio5i2ica ba)xp6)9jn qqnless axis thought the center O. A rope wrapped around the outer radibq qcji)a9p 5n6i2a)xus 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. (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 thoughx0zpc (z/jtm .1q5ue ht 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 se .h(m e10p5u/zxjctqzcond 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 hinged at one end. The rod is initially heldd0dwd (nf+q m8 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 rod ddf m 8(wqn+d0about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and0-g nwxj2bd4 / rb8bra mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 2-bbd2ga4 8jw /bn0rxr0 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 wrapped aroia 4e *wbul:5rnn +am7/+iiec und a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerat4 5*7eln ca+e nriii bwm:ua+/ion of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mb0 x+hu;wu(tb+dn lriq)fm 9s0 ,v4qs.l1eh mass 7.07 kg0uw hld ne;bhbuil, ).1 txs mq9qf++s(0 4rmv and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. fl;mhs8 dp;znnhtdb *37 jrqs.*q j27 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 inertia of wf cad -xy 6mfo3v)2;n$5.00 \; kgm^{2}$ 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.w/zu5 4.c8hew4qv rh53 n jolu010 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 t5h w wq4 u.j43r8 veul5onzch/he 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/s1.w f 89pxoyss. How hip 1syx8f9. swogh up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released hf3 :svx+ xvs+from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distxhx +v+ s:sfv3ance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping n8j6d dyg8p 4udown a 35e incline 8 u g864jynddpthat 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 moment mk+: dw(nd*ux5 c5set-pwrj7a-dtb,um 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 inertiae( uo- 93hj4hdo8g db v5o5aie 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 r;qgntc,,zb p(eg7c (3afn3a extended has a moment of inertia of7z 3anfrnb caq,, t 3egg;cp((
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?