Angular displacement is usually exprl3bjnc 1t7 bn-xfse wy0vut7/ :)p:vu ess in units of

  Angular velocity is expressed in units ajpu;tfa i).g)3*sk xof

  Angular acceleration o2oh3zki1 *1okz-a kn ef5kiu+ z-h.f6jnk y0is expressed in units of

  A boy and a girl are riding on a merry-go-round which is tury(-bhj2pw h (8whlwa)ning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Wh 82ahwhl(hwjw)- (y pbo has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constal82cb:d* p hvbf);e/utt-hh 9c vris. nt rate. The boy is near the outer edge, and the girl is closer to the center. Whv);.f up/eh*v is8:hbd t c 2l9ch-btro has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning/;ex 9i ,nhvep 9fziq1 at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who hasif/ ,nz;hqe1ep 9vxi9 the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turnifnf:pu88qi4a6)f ng m.um; tsng at a constant rate. The boy is near.nui atsnf)ff mq4p 8m 8g;:u6 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-rax-k6 vqahn /,ound which is turning at a constant rate. The ,/v qxa-k6anh boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the1j 2x+/waow vwflt 54f following is an accurate statf 2j/5vww+ofwtlxa 14ement?

  Rolling without slipping depends o2o 1ev/pbt3c5 sl7bckn

  Two equal forces are appli*9/ cyi ,0pyqlzgd*gh ed to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greag0cyy*,pd9 liq/ gh*z ter torque?

  Two equal forces are applied to a door xphdwmcol,0.u- m0 m8 at the doorknob. The first force is applied perpendicular to the door; the second force is app ,h0pu0wm dl.-ocxm m8lied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, *rkp:me ,ah ;3g l nm*zqvp*3kperpendicular to the door. The first force is twice as large as the second vk:3kp;, * pm*a hzn*qm3ler gforce. 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 resjb0s )/ 0k)z/+u8u gbnd,/riodndgxdistance to changes in rotatid/)nouk /bd ndbd8i+)sx0z/ jggr ,0uon?

  Consider two uniform solid spheres where both have the same dia w6br hkkx wt,hn-y t/+ew/mvc:+2qi 1meter, but one has twice the mass of the other. The ratio ov t/hrkiy1q xm/+2hw-:kw6 cet,nw+bf the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, m+83j8eqm5ui/4.h.4oqtyq ghx u y3 nxuj o3ubut one has twice the radius of the other. The ratio of.me uu n3 8qu yyqmh xit.+3ohuj4 jo38xg4/q5 the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solytr,/*7 lv uwwid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment ofrv/ w,7t*lwuy inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M anon 3 (zvh9pg)bd radius R. If these are increased to 2M and 3R, what happens tonhop 9zv3)(g b the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that obqs+41 ev df(nmdw e*0t:sc tf)ject will

  The moment of inertia of,gz:yil xm *)/ticeo r3q(la8 a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its tra et(:z83yl/ iglqx) ,*i aomrcnslational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which ha*uv;f0; q b1hjz90hge mnkalfl9l z-)s a mass of 10 kg and a radius of 3v )uk0zzllh 90;1fg*9lmfbqa e-;hnj0 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 p cptzl wq/,1m-2h)zpradius R rolls without slipping down an inclined plane startinp 1c p)/lz2qtzpm,- whg 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 inttm-s43atdbyh4 + zl 2clined plane starting from rest. The angular velocity of the sphere at the t3tdm+sh4ay -bz4 l2tbottom of the incline depends on

  "The total angular mor6 **tb9.sfrr e9elrd/lxte22bd9pq mentum of a system of particles changes when a net external force acts on thr2.dx*brtp *d 92 r6f9eqtre bl/9esle system." This statement is

  In what circumstances can the angularz1wdgoh3 x/8 j velocity of system of particles change without any change in the8h3o/1 gw jzdx system's angular momentum?

  The Earth orbits the Sun in an elli+lj r2k;1l9 )s nrvykaptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about th2rl+ ny 9)k;skj1avlr e Sun?

  The Earth moves about the Sun in anzjnr o;pthw,p/j5c8o v9bwg4w/,bo 4 elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the obpog pwhorv5 wj4, z ;n8/j4t9/cwb,orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a faslt34lp72*ge fbo;lq et spin) by pulling in his outstretched arms close ttll;f e 3gb4pl 7o*2eqo his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by phi9zp 5np1f1rpqm aw*d( gp)x3)qi4 yulling in his outstretched arms close to his body. What*hqdwaxpp3i4 pzyfir1 )1 )g( 5qp9nm happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretgc c93zx++stj;rze0x ched arms close to his body. W9++ scxc xr;jze 3ztg0hat happens to his moment of inertia about the axis of rotation?

State the law of conservation of anw-( tn g;px du6heb;4zgular momentum.

  What arc length does the Eart1av/p;hqar(by.h lr ;h travel in a three month period in its nearly circular orbybr1ah ap;(h/ vq;lr.it about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distanckq*rsqq :p*9se does the tip of the second hand sweep through in 3 minutes s9 p:qskqr*q* and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent tod- 1z cz1pybjrcs,1/6k9pox l?

  A bicycle wheel rotates uniformly thb :+i: cm.dujv*j9dsm rough 2.0 revolutions in 4.0 s. What is the f*:vsj.jc 9mdud i b:+mrequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulsesv3h1 .dc+ cvas at a frequency of 0.40 kHz. The ad s+v.3cv1h cperiod of its rotation is

  A phonograph record rotates at 45 rpmcbh6 1bnh 7 4;289onct bzyhk5u gf6da. Through what angle does it turn in 0.20 s?b5b 7k4fohag6n6zh9 bnc1ut8 hd;2c y

  A wheel of diameter 26 cm turns at 1500 rpm. eb r7fqy8g f.)How far will a point on the outer rimyf7)ef rb8q.g move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W02s pqffext7gm7 m( y0mak4+f hat is the average angular sp07q(fmkmap e7 s4 f0x g2mtyf+eed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in n(y ubj tv 397zmgm70n4.0 s. What is the linear speed ofgujynvbmmn73 07 t(z9 a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a )t*os3pxrz q /k,ayq;ot0 ;lndistance 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 cable car to make the trip nk, )q ;l 3ztsayqoopx;0rt /*in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant ans7c5jy tkv+:( , dfax( zzvq.ngular speed of 2.0 rad/s. What is the linear speea:yzxcsf qn. (v5 vk+d(,jzt7 d 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 moten2d 6pj1yfg. gca 2:mor rotates at the rate of 20 rev/s, what is the approximate linear a p.fc:nejy g2g6 dm12speed of the end of the cord?

  A wheel of radius 1.0 m is rotatkvnp/,tgyavo cq.3 :5ing with a constant angular speed of 2.0 rad/s. What is the centa oqyt5pv:n.c,k 3g/ vripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimetnrme. jtp b-. a8f:pd .v9s7.mvsb2bter of a bicycle wheel of diameter 70.0 cm when the biv jt:nbpdvre2.s. -fs7.. 8mmtb abp9ke is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rota jfe1fynk 4vj281 xxotg6i62bting space station (r = 1000 m) rotate to produce an artifjyffjo i tk8 1n6bxve2g642x1icial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed ow962asi vv 8y7bypq va9, ibr5f 20 m/s. The maximum centripetal force (provided by stata5bpa9 86vv i,iyrbqw 79vy2sic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular kzh/) 7n7bnccm2wp r7 curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (providrcwb2kh n7z 7m/)n7cp ed 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 s5 e35p:,av d( 8zydlz zwp aart(8sc3otring, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, zdvwaez a r3lp85 o8:s(tpya53c( z d,then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.ucfv -*ktrvd 460.yoh i:a 0qrjns )s.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s.sqav j )nd0ric :foy*ku.t04s. -vr6h
(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 accel8 umlddu 71pa-eration 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 ajevz5*u8y uzs)(pff5 5 v*n+.ubfboe 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-m radius automobile tire rotate after startialxxay:n-ike 1 ;j1 +qng from rest ak1y-jixa1l;n: +e x qand accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, v4 vqa72yv:4 l/n l ge9piqhf*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 decelerat h1tc d/byn.xt9p4/u zes with a constant angular acceleration uc/tz t/hy1npd b4. 9xof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from res9gi1 * c6jq) dlogsa6dt and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the wheelid*9d)6 sl6oaq g cg1j?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to restx mg+b 9:0samtff cn )6 ms0cmyk-1i8x over a distance of 115 m. What is the totalb)0fgms+n0m 6-x9: ct xmky 1mfa8sci number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniform58 rijexick 6(ly from 8.40 m/s to rest over a distance of 115 m. 5ixc(i j8ke6r What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 zj+tr,nyq;8su cvj*1 m/s to rest over a distance of 1j v1c+q,y uzjn8rts; *15 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates a7-mc;-rvsflzmm6+ c et a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 ti-rm6 - e;fcml+czmv s7mes 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 torqubo)ld t(*huf t,,u8 ob oabq3.e of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force8ou(q,o)*th.u3 b fl ta,dbo b is perpendicular to the wrench?

  The bolts on a car wheel require tighn3g:cv .llmo15h c3so2gyfi0 tening to a torque of 90 Nm. If a 30 cm long wri 02cslc3fyvl3g 5o hn:g1o.mench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ijxm 5eaj9(w n,nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as jb ,tkydev;862c 9l:brkz-wc follows: mass m is at the origin, mass 2m is at x = a, and, massd6 -r2,9 c8;w bvckytj:z lebk 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 frictionladbj b+uc ;h6 ln)e2mv .r.cf;ess 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 n.cd)cj e;6u.bf2varh +l mb;.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 a a1voxajw37b(xis 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 e7ba ao(w3v1j xxerts 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 held in; vo8wanms 6*q* ;rxhr*r(*e uxt0 zst 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 about one end is ML2/3r8 *w*mv ;exh0n rs* utxqszt;6or( a*.)

  Consider a bicycle wheel to be a0elm9ak / offxy-6le 9 ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle e y9o-el/60kxmaff 9l and 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 wrapped aroygm aj*d4h p5p3;ycb6p(sx-w8 0cccnund a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acchbn6c (x*p5 cpp4 g8w0s3ycmday-; j celeration of the pulley?

  A 1.53-kg mass hangs,+ -l;stpg u)lad-vc w on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What ist,uw+)cl v-lasp -gd; the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to kau)hl 8.fb*n d ,/pq+hb-yristore $1.00 \times 10^{6} \; J$ 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 i d-t)-o tnwstkxor1;79ac u +qnertia 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 kg0w ez 0k.ej-mf;wxnh5 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 ofn-fe 0 whk0;.emwjx5z the inclined plane?

  A solid sphere of mass 1.0 kg an +p 5p1tv/ 4h,smdtannd radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can ips+hp1dn4av ntm/t ,5t climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releas :7 p1icpzvevtya*-j4ilt2a) ed from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a4taeyap*t2 7)pvv ic-jiz1 :l vertical distance of 3.0 m?

A solid sphere of mass 1.xir f bsymv b0.,p;. ukz*h83h5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it starhkvp r.3z8b*imy. ; hb0f,uxsted 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 momentum chanesfdn(. o38 vmges 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 momei) sz0bbkj/dz2( 6k zmnt 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 5j lvxcwiu* joim0:y7d -,1q5y.00 rad/s with arms extended has a moment of inertia d-m*:y7cl w 5vxij1o,yj q 0uiof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?