Angular displacement is usually express s 8c/0zqc9qva90a br/d,hcmt in units of

  Angular velocity is expre88v2y; ccynw cj1hv4jsew) inkj:c, 6 ssed in units of

  Angular acceleration is expressed in units :v3b9h-vg br/+qfqk lof

  A boy and a girl are riding on a merry-gom/5az6afr 6muh*hk(n8 ou4j j -round which is turning at a constant rate. The (/ 6*khrjuuf5amanm 4h o6j8z 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 at a constant rk 1i,yey8i c*bate. The boy is near the outek ey,*8ci ybi1r 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-round which is turning at a constanq:emvyzl 5o688(h(j n tk:cvnt rate. The boy is near the outer edge, (z:tm 8v56 hk(lj nyn e8q:ovcand the girl 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 a coyypa 60,t/2s uraygy7td . y(rnstant rate. The boy is near the outer edge, while the girl is closer to the d. rups7t2y/ at y6argy,y(0ycenter. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which5mb fcycd89-*poew4l is turning at a constant rate. The boy is near the outer edge, while the girl is cy b84wp9o-cc*fld5 m eloser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rot,jzwvre3nu9 +rp6xq dada8, /ating. Which of the following is an accurate statement?+ruj6 n,xrpa az 9w83eq, dd/v

  Rolling without slipping t3pdwc-g5d g r+)rn )jdepends on

  Two equal forces are a7:we;ffj t y;ct8kn0 applied 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;tt 08nc;yfaf w7 :kje perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force io;1;v,+c udpfchm.x;gdb * das applied perpendicular to the door; the second force is applied at 30e b;.h x *;,cf+g;dapudod1c mvto the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorkni mj;+,nphsn9 hn-o(h ob, perpendicular to the door. The first force is twice as large as the second force. The ratio of thei;+h9o(n phnm,n hsj- torque of the first to the torque of the second is

  What is the quantity used to measure an object's7u n 5uz4fltu1 resistance to changes in rotationzuuf lt1 n54u7?

  Consider two uniform solid sphm;6 ov1+ etrwz1a(l+vkgq.ikeres where both have the same diameter, but one has twice the mass of the other. The ratiov(l 61 ro.vi+g mqk+a;e1zktw of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mjqh2- w:kr o7iass, but one has twice the radius of the other. The ratqo r-w27k:jih io of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solidyi0 nuy,u4hj3 spheres where one has twice the mass and twice the diameter of the other. The ratio u hiy4,yun3j0 of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are inc 2 (.avfsnkm4hkmsx ,0reased to 2M and 3R, what happens to the sphere's moment of inskkvnmm x .20 (sf,h4aertia about a central axis?

  If a constant net torque is applied to an object, that object w udf/-+wt)kyv u-kikn l fp vt2o)2s7)ill

  The moment of inertia of a solid cylinder about 4na:tazy; t0pdb -;wt its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass oksw(gz1i)* :ygl351 gzxwk:yahm :qp f 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the5y ghw1kl(w*k1: y g zxm 3z)siqg::pa wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M ano 7(o t(na9fp;x,nidmd radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom o9pd;xo( ,m(afni on7 tf the incline depends on

  Suppose a solid spheb,vbq c)6i7 z 2p2,zod ,np1gtmhkl, cre of mass M and radius R rolls without slipping down an inclined plane st,)kc6bn,p,ob 1zmpdl2 czh2 vq7tig ,arting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of/j5 l/ gprm/- ih *rdkcxe+1ks particles changes when a net external force acts on the er/gjmk-i1/ +l*d5krx/sphc system." This statement is

  In what circumstances can the angular velocity of system of particl4f4kyz 4caxx ss2h,l:es change witho4z 4h,fa 4y:2lkscxs xut any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. I2q:xxce 7bxbc.f/x,v gnore any friction which may be present. What happens over time to the Earth's axc7 bf/be x2q.:,xxc vngular momentum about the Sun?

  The Earth moves about the Sun i:jcdvli.q 2zs0pyo 8)zm g;- sn an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describdjvg: lmzs8;-c.y i) 0s2zqop es the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spink15u070hj g 9 8jjdknk uc1fhm) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axn 01 kjd5j910gckuj78fm hk uhis of rotation?

  An ice skater performs a pirouette (a fas-wr v;bc,7u c6a iyr72 bwrxo/t spin) by pulling in his outstretched arms close ta 6 u7cbvcb-y/w,o72xrr;wr io his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pdf aie*(lvwki, xdo b 03-zj6)b cz:w3ulling in his outstretched arms closl-fokwba 3wx(v0,bjz e cz :d 63ii)d*e to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angulvfsekx*:5 )up ar momentum.

  What arc length does the Earth travel in a tq oek)2uld 42qhree month period in its nearly circular orbit about the Sun with a radiuu 2dekqo4l)2q s of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance vub 3 g ,dyeatpn8x2v(:chf9-does the tip of the second hand sweep through in 3 minute fy,ne9ghb-uv p(2a ct3d8vx: s and 45 seconds?

  How many rad/s is 25 revoluti ,0v jz5/gt6c lu,kpmqons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revoluzkoc6ail02a ; tions in 4.0 s. What is the frequency of the wheel's2i6za akl;o0 c rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencyq svt -0e7a *iway-n)d of 0.40 kHz. The perios y7tin0 qva- da-*)wed of its rotation is

  A phonograph record rotat )( f;bvrtlzb- b+at/ees at 45 rpm. Through what angle does it turn in 0.20 s?zalb be)t-/ +f; (vrtb

  A wheel of diameter 26 cm turns at 1500 rpm. How far wilhi4t ur(pp mr (gpmbn (x9:v3+l a point on the outer rim move 9m+rb hr(3(vpug(tx: pn pmi4in 2.1 s?

  A bicycle wheel rotates unifot9zj y y3(6tfj9tg7s/kt0pc srmly through 2.0 revolutions in 4.0 s. What is the average angular spee3p7tjfy y ctsjtt9/096z(skg d of the wheel?

  A bicycle wheel rotates x2d4vn5a/i g duniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from th5v a4x/2dgn ide center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 c m82, r7skuvukm. 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 7,c2ur kmu sv8make the trip in 12 minutes?

  A wheel of radius 1.0 / njflubh x8.4wtk3;s m is rotating with a constant angular speed of 2.0 rad/s. What is the l t8uwh/ fnl;4x3jskb. inear speed of a point on the wheel's rim?

  The cutting cord on a gas9pgid/-/f 57:sowk(xqpvt p k-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximatv 5df xpp- 7/pk(o/:gw9tis qke linear speed of the end of the cord?

  A wheel of radius 1.0 m i rwc,rd u57eh,s rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the c,h dr ,r7euw5wheel's rim?

  What is the centripetal acceleratiz/rkziv aafp7+j2b; 2 on of a point on the perimeter of a bicycle wheel of diameter 70.0 cm wh/kvz; p7j+ a fir22bazen the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) mus;(wov .e- tfrft a circular, rotating space station (r = 1000 m) rotate to produce an arw;fr-(v. e otftificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of;8yw 4qcjcc8 i radius 50 m with a speed of 20 m/s. The maximum centripetal focj cw8 4qy;8icrce (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 *hhe .)i ova2 hx0zij+8heyh2radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stati 2ehoxhahzj*yhieh2 .v+0 ) i8c 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, ocy4 p a3-q3xcis whirled around in a smooth level table. If the m-xy4o pcqc 33aaximum 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 7.5n 9fnbz4nh :y* kg and radius 9.0 cm rolls without slipping 10 m down a h:nbn* 9 yz4nflane 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 acceleratiosp g ic r:2pn-d0,un4yn 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 angularhqf ( h13m4 vymo +. lowzsg5u(8cbo(r 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;f/o4ddeerq2,xgau b25 cy;c a 0.300-m radius automobile tire rotate after starting from rest andc2rxu d ;o/gby;e2q,a cf45de 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 acceleratizq ym. +yr.k4zon of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rf;hkfvn0-bvx* 7y 7 luj+juo5 ad/s decelerates with a constant angular accelerat5+h0k* jfvnul uoj b-;7xv7yfion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reachesez. qq8u j3es1 an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular 18qzq .3ju seeacceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniforu; edn o:*7 zmdsy+o7iqag0y 1mly from 8.40 m/s to rest over a distance of 115 m. What is the totaloi:1u0yds; g7d*oza+7 n myeq 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 toz).o + sep*w5gak gbe3rn:h +v rest over a distance of 115 m. What is the angular accelk+ +)v hep*3ongz5 e.brsagw: eration?

  A wheel of diameter of 68.0 cm slows down unifo1p4 ktbd3mr4c rmly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel tp r1m4t4 ckbd3o come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of3 -z y sqpj8hte4ar7m-,m/ zss 3600 rev/min. When switched off, it rotmz3rjqey7 m/s,tsh --8 szpa4ates 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 ofz99r 7t* ko,vja8db+nb-v v7i 2cbszo 90 Nm. If a 30 cm long wrench is used, what is the magnitukb+* or 9bt78anv -z97z di,vvo2 cbsjde of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require6 vjf7 .6e3aqnoon,fgc1w-;) g1oysv) r fqvc tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what 3v7rav)onye cfj6sqf,fvog.1 ;og6c n)w -1qis the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ze,cvn zotrw62.*6uw 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 m is at the origin0 njqo fy4itg0556eqx mfa( q4, mass 2m is at x = a, and, mass 3m is at x = 2a. 44y5ani qq56 gfj mof(00xteqWhat is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought 2em j2i*-ofr cthe center O. 2m*-fj2r cio eA rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought thyqd hvoy3ndn on;n0 ,l45 3s7me center O. A rope wra d,d7nno3y ;lvysm4n 3q on5h0pped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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. The6av dr5-.04g nsrtmdb rod is initially held in the horizontal position, and then released as the free va-60grbn5s . 4mt rddend 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 apgx4y8 +5:cny. hb;r7mtyqf n ring 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, assuming it rolls without slipp:py5nfg+nbmy . q;ry4h7cx 8ting?

  A 1.53-kg mass hangs on a rope wrapped around a frictionles:ovs 5vm+v9xg 1dh0 tbs disk pulley of massm 0vbsd 5vh1gxvot9+: 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrappekwglzh, x+pm 4zb(8 p9ve2c3ux+ dyx+d around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What dk 2,+u( zc438w9+xxz xmebpl+ gvpyhis the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required toj(5th;ay.sc xk8yu ;je6ua9izi2k:m 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 ofd3 z7sp4k wj0h $5.00 \; kgm^{2}$ 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 kgsmixh l,3:3z+3 8 slq7 sqgfdj and radius 0.010 m starts from rest and rolls without j zl3q3if3d+78q:hx, lssgms slipping down a 1.0-m high inclined plane. What is the speed 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 with33l vx7g 48y0djxkmmt a speed of 10 m/s. How high up an 3gdx730xkymm vj t4l8 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 from rest and allowed pm 3sc o4 qw2nswtxxfz+2+ 6-*k: jvmhto roll down an inclined plane. How fast is h+m s6+stxj2wk*-o: zwqvf 42nm 3cpxit moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping dow xc;g fe.6)rikn a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere i6ei gr.);fcxk s 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 rum0xuuc:b-n (x ((cnmomentum 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 inert j9c*m t zg (u3ywn8sh8*tl1gbia 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 rotat iuv)2*0ukr fs-dbpd5ing at 5.00 rad/s with arms extended has a moment of inerti0 kudbuv*5)ps 2r-dif a of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?