Angular displacement is usually express in units oic-cbmi2t8r.* y f +a-1gvrlpf

  Angular velocity is expres (u( w/mniw zlz);tab/sed in units of

  Angular acceleration is e*2-tiln bw8a2s3p s nfxpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constant a -e shwqb4;.u4x sp,qrate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater aqs wqhba4;x.4,s-p ue ngular displacement?

  A boy and a girl are ri oa4 xvk11k3peding on a merry-go-round which is turning at a constant rate. The boy is near t3xp4a1e kv1 kohe outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-rounduv2qno c,w7 9/1iaqff which is turning at a constant rate. The boy is near the outer edge, and the girl1 conuawqv2 iffq 9,7/ is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at+j.fhvb 87kkuxu znm *nkya/+n/*ru ; a constant rate. The boy is near the outeu+u /x8jn nyfa;*n/v hk*b +krm.z7 kur 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-round which is turning at a constan- 1eut7y r2 elw/d+u hiq);xamt rate. The boy is near the outer edge, while the girl is closer to the centqeywe+)dx7l 1 2m-htu /a;uirer. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an ak79x s9a9pn2 gsqrlrvhq 7. 6kccurate statem6g7qq kxlasr vs9.rpk 9n9 7h2ent?

  Rolling without slipping depdv./o,dx 19pq e4mfaaends on

  Two equal forces are appliedql,bwfx; vpz3 4 p.i;g 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 p;g ivx.w z;l,qp3bf4 exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is wns3)lrbppkff(: v 1lt n 181sapplied perpendicular to the door; the second force is applied at 30e to the plane of the door. Wsrlb38ws:f(1p)t vp l11nk fnhich force exerts the greater torque?

  Two forces are applied to a doorknob, pc3 .,85p,i pbx7c .i qbcobwaiwjjm5 /erpendicular to the door. The first force is twice as7qbxipco3i,.a pw/,jmbc55b .8jwic 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 cho515okcst 1xpghh87h0 tqi v :anges in rotation?g 5 tvoqc018:7ips 5k1h ohthx

  Consider two uniform solid spheres where both have the1wkv y7i4jr y+ same diameter, but one has twic +4 kyj17rvywie the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twi e63 2ol/:ear3ce vjxace the radius of the other. The ratio of the larger sphere's moment of iner 2l:a3o/ej6 3aevrcxe tia to that of the smaller sphere is

  Consider two uniform solv v-8/1x p 2k+vhlxmooixl6)fid spheres where one has twice the mass and twice the diameter of the othevfv +26 )ph/k -m xvxl1xloo8ir. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere hasp) w 5h hf(e9pf+/vxyf mass M and radius R. If these are increased to 2M and 3R, what p( hf+9wf5yxh/vpfe)happens to the sphere's moment of inertia about a central axis?

  If a constant net to o,1zolm z o0wz;o),yfrque is applied to an object, that object will

  The moment of inertia of a solid cylinder about,d( r4 9zm;ogh0nauz ix-,8sx5 u qutm its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of it -x5u4,qrdmtg,09;ux oanz h(im su8z s rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whi xk)ekv;ze2ewn/ 6u 6lch has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotatioxe/k 2lu6z e;n)vekw6 nal 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 slipping down an 7vyv:ymtid1 4se,us2inclined plane starting from rest. The linear velocity of the sphere at the bottom of the inclinev i4ys :,vtuys2med17 depends on

  Suppose a solid sphere of mass M and rai4o;/tuyi e( kdius R rolls without slipping down an inc(kuiy/ ;tie o4lined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net externx tet4wzp)6) ial force acts on the p) )xewtit 4z6system." This statement is

  In what circumstances can thech2rz gi1t03 )w cf ad.z(co5u angular velocity of system of particles change without any change inr ua fct(io2zwhzd)0g c31.5c the system's angular momentum?

  The Earth orbits the Sun in an elliptical64uj3gs koz 3:/fnw b)ncb:yc orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the Su n3 c6z3):gw4: nbsyfoubk/j cn?

  The Earth moves about the Sun in an elliptical o w0)njfb(k3bl:k45eleay p7b rbit. As the Earth moves close to the3f:np klb ea5j)yl(7 w4b0ek b Sun, then which of 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 hisz vj;lq- /qen, outstretched arms close to his body. What happens to his angular momentum aboql /jq-,;n ezvut the axis of rotation?

  An ice skater performs;l8bgsv v) in4cv)b+dy ze394tar4d q a pirouette (a fast spin) by pulling in his outstretched arms close48ibv bz;dd3 v nq)+4etvlrscy a4g)9 to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast uc6b3k,e)7wcrd- zi aspin) by pulling in his outstretched arms close to his body. Wh)back 7 d-ic z3,uew6rat happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular moment)je:)mmsz 6/nl pia( yum.

  What arc length does the Earth travel in (;cqb4 sv/ee9wd9iy8 n ugxm1 a three month period in its nearly circular orbit about the Sun with a radiusesmi1u9gq v ( 4yexwbdcn9;/ 8 of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance dol9exbi,ur3t:m j; x4zwy)n.f es the tip of the second hand sweep through in xrex3bzt4f)w; l.u m,9:njyi3 minutes and 45 seconds?

  How many rad/s is 25 revolutil96 9jpn cpjr 4o,v lm/dxoy34 kv3pb,e(psm)ons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revoluv*qp3u vb7mkk +kvv99lji2 1qtions in 4.0 s. What is the frequency of the wheel's rotatiopm 12qkl9u 3v *k+vjqvibk79 vn?

  A pulsar (a rotating neutron star) emits pulses atupekqtdf9pk:6 *.7ja a frequency of 0.40 kHz. The period of its rotation i*7.kpua epjt6 :9fd kqs

  A phonograph record rotates at 45 rpm. Through what angle does i9-o9pox )cfmbed20g wt;t mj :t turn in 0.20 s-2bgd9)we 0 txjm:m o; ftop9c?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a9x7+5y mvq.y j2cu i wrun+7tb point on the outer rim move2qwxy9ujr 75 im+7+ bcy vn.tu in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 2xpa:;pe5y voo o1m 5cgk 0zu64.0 s. What is the average angular spgvy:azc po6x o2e5kp; 0mo5u 1eed of the wheel?

  A bicycle wheel rotates uniformly throu2d+-n d yqdt1w7 uw.mggh 2.0 revolutions in 4.0 s. What is the lin1 dd +wm2qw.-7ntgy duear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort car*e h t)d,8ww-2tasctm ries 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 cabltt*ha,wte-)s m 8cwd 2e car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/aqmu3. ae w;y0s. What is the linear speed0yaqwe .3m ;ua of a point on the wheel's rim?

  The cutting cord on a gas-powered wbu7vu vi5)*q) /yvtjlaqscwwt2i /. ; eed cutter is 0.16 m in length. If the motor rotates at the vb.)iu wl)v5q uci*j 2/sa qtt/yv7w;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 of 2.0 rsnb5 r3d (fjc;/ xyxk9ad/s. What is the centrs n xb9xf/d;rj5k3(cyipetal acceleration of a point on the wheel's rim?

  What is the centripetal accel ).hxq- f .uy4nznpck6t , ,;8q)4xdfjimqhwa eration of a point on the perimeter of a bicycle wheel qfwpfnxzy xjuk,4ad4)qt qn ) 8.m.-;ci6h h,of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circulacpdu0f3hipds( fv3 ,, r, rotating space station (r = 1000 m) ,fc0vd( sp f id3hu,3protate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/s cl,qb 6. luiz;o.h0as. The maximum centripetal forc ll.o q6sui 0bha;cz.,e (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 with a 5a* /o3z hoszee1 gbw4speed of 20 m/s. The maximum centripetal force354 w1za*hgobo/eze s (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 st/: ptlsk6 6+8tm:v u nmhpww.iring, is whirled around in a smooth levem w p t6i8luk.tpnsh+:/ 6m:wvl table. 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 rollczr/l6 s;8ls(( h .(cktffkgls without slipping 10 m down a lan6(.cgfls(; ct(shlfklk zr8 /e 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 accelera( prxsp)oo1i,dpvijtd *88:ution 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 p0kb za2sko9rn5(;1n,-xumn /qnf a qa 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 af;w7shko e:g xcjv(h2 /3t ;zcqter starting from rest and accelerating at a consth:37 cvtwek;gzc;x2qo (sj h/ ant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular ac4a wrm+, ftk;qceleration 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 angdl- x9g r zed(0ho5vv+ular acceleratd(+ - dre0 x5z9hvglovion 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 while turning8-yfz +fg2 qybukd,qnb0 d3d; throuddq0b;fbdqn8 z 3fy,+-2kyug gh 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ov2oi 7sjc qi)o0er a distance of 115 m. What is the total number jq7ooi0 c)is2of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down+6gpds tm2 vo9a/glc8( - /7er ynfmed uniformly from 8.40 m/s to rest over a distance of 115 m.g/gnl pmve(my/ad oe 9+c - 6t27f8srd What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unifor:udqm er8.*zi mly from 8.40 m/s to rest over az8ur.edm :q*i distance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational sb +ss, jmce; .-rawc/ipeed of 3600 rev/min. When switched off, it rotates 50.0 times at a constanc,js; +e - c./mrbawist 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 Nz: 5gelgl np00m. If a 30 cm long wrench n0l5pgz :e0l gis used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening cq58p*woapc p/ dy s;:to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when tdpwcs*:oypcpa5 ;q 8/he force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o/xkghn/7 ow+t*y reg+; maf )nf 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 hdw7bt *f/mz1 m is at the origin, mass 2m is at x f 7 bd/z*htwm1= a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is q hschjbs. 6 12ff8hv1pkx676yug3yxpivoted about a frictionless axis thought the center O. A ropugyh y 7jvh kx1q6 66bpf38 2xs1cf.hse 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. (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)l1b tw :fvqga;n11ou 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 duonf1gt)b wv;l:1a 1qoes the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hq),v ,7rnj bwp s1jg:dinged at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. Wh1qpgr ,n: b,7d)jvwj sat 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 ringuk5iv-0h ,nll13 lszg 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 tangentially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming1nli v5,zgk 30l-ulsh it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped jkqw3(w;;pevu/ 8c n earound a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm/eu 8kwv q3;w;p(jcen . What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rodub(;8a*:1wavp tx hupe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mwtd8hb au 1v:xp*u a(;ass?

  A rotating flywheel can be usef) 0pyo)tn;x3zn5ddw0kh i ,ed to store 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 ine+qzhv 6e,ho:)fkr,f*eg r0 cl rtia 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 0.010 m starts from rest and rolls witnatu,x1or5x: *vpsxg/gb0 :i hout slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the g/in tb*r :ax,1xuv op5s0xg: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/s.6w17,g4/ cpjlf4l-astvlf n w How high up an inclinedgf p4ws- aw/,c1f7l jtn4l vl6 plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg i dvf1x.1 rv)bnr /n,dxtl/x b3s released from rest and allowed to roll d x bt3/fxrl/ .1v)vnn,b xr1ddown an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls wri(:cope1 us-ithout slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a s :soe- (1cpriuphere 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 momentumn*jc, hh3am1 f 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 oev dee-itdlx20..ye (f 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 53 ),qpkdzlem le (2nm-il*i/s .00 rad/s with arms extended has a moment of inertia ol)eis mzqin32ll /(e *,dp-mk 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?