Angular displacement is usu 666 ,mh5xpgothwf.qbjln 7ye3 im(.kally express in units of

  Angular velocity is expresse9 7ys h(qmt9skd in units of

  Angular acceleration is expressed i8 nxsm )2n:xb(gx tz6jn units of

  A boy and a girl are riding on a merry-go-round which is turning at a consty(nh/:pf(2 ;gb,u dr amlt.hxant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displamlryb u.nf2pt(adhh( g/; ,x: cement?

  A boy and a girl are riding on a merqo/ :zv k532xi zq9qdjry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to qdkj95q o/:v2 xqziz 3the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round91 1we n,6xpa6v45tplp bpbtv which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to te bxtavp15 w6bv1l4 p6n9p ,pthe center. Who has the greater linear speed?

  A boy and a girl are riding a merry-ygg.q9ngxju y1-5 lz/go-round which is turning at a constant rate. The boy i .uy yjgx1/g9- zgnlq5s 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-round which i.kd+qmyyiaw3t52 m *b s turning at a constant rate. The boy is near the outeia.w+2 5ym3mky tq*b dr edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatil(z5w,rr e.5x l4nl cing. Which of the following is an accurate statem wilx,(err 5lnlzc4. 5ent?

  Rolling without slipping depends /.v( q6b, 5htwfv wdd -e+mvzhu90v voon

  Two equal forces ared* wk3 l0d-t63 l xab:covnurbr5u v23 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 perpendicular to the door. Which force exerts the greatow6ubldrxvkb5ud3-n : v*lct3 0 2a3 rer torque?

  Two equal forces are applied to a d9lb 8b: zl(incoor at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force9cbz 8nbl(:l i exerts the greater torque?

  Two forces are applied to a doorknob, perg 6oub8a3+2qr 8todx;lok1 e6n k(bz wpendicular to the door. The first force is twice as large as the second force. The ratio8 lo1bo8uqg 2b dxkwe on 6z3a;r(+tk6 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 changes in rotr: (cizd5usxjte/ z e3 p8w/r:atio(w3zrep: j e5xi/t8scd/ r:zun?

  Consider two uniform solid spheres where both have the sam v2 y- sdwv81kzzn6ay.e diameter, but one has twice the mass of the other. The r.v s1yzad yz6k82n- vwatio 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 twice the radius of thn(wai +og 1*ds7ny 7o*9 fl;klbe zkq nds.4z4e other. The ratio of the larger sphere's moment of infk+4o;e*kzb 7o ay.is7 9(1qlnz4dgdw*sn ln ertia to that of the smaller sphere is

  Consider two uniform solid spheres whereq6*j4l gha kn7b 9)gp.4hc ho4zwlsmav0q9b; one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of t.6g9gqlwlk4bh 4a0scnb a o4;jz) m7p h *qhv9he smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are inccuz:*v liy 7a.*pgqh ps c 3ox.g47,nsreased to 2M and 3R, what happens to the sphere's moment of inertia about a central a*,cxplg7 hp.i34:g* y o.ssczqna 7 uvxis?

  If a constant net torque is 2qgdvb0d 9cbf f.k*k;n- 7jkk applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given.6 i hhwnllg2hricr;(pk */3y 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 -vzf/rv js8,w mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to th8vv/sfr- j,w ze total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls9 tn )wkawww5l9yo/pp (t1re * without slipping down an inclined plane starting from rest. The linear velocity of the sphere5r1n( /y 9w*)o t pwplt9awwke at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an h-kfq u1ezd j403rmtzqiw-5-inclined plane starting from rest. The angular velocity of the sphere at the bottomduztr05 z4q-1j3w-efmk hi -q of the incline depends on

  "The total angular momentum of a system of particles changes waj ybp/9 4j y-+jh5rxahen a net external force acts on the system." This stab4j- 59y y jaxjrahp/+tement is

  In what circumstancesk/ cpi)i//uuf/ e1fj h can the angular velocity of system of particles change without a /fuip/ u h/j1fck)i/eny change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any o- jvhx*xm e /*kh6sl0friction which may be present. What happens over time to the Earth's angular6-ovklmxh 0xhs* /j* e momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Eartvl )7ojpw+/.p pjxz(ih moves close to the Sun, then which of the following best describes the orbiting speed of px)/7ipwjlvzj .+( op the Earth about the Sun?

  An ice skater performs a pi it3o7s ucm7/ wlz5s,irouette (a fast spin) by pulling in his outstretched arms 57s s iml,uz3t7i /wcoclose to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a piut1(edb ur/(d rouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotation(/e rubt1(ddual kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (ammrf5 -k(4 7 2cmnjv /apm m7s9i4qmpo fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rota54 jamqsmr/m4m(7 fn c pkvmp-7o mi92tion?

State the law of conservation of angd4nk4ckz2ad(9p ksr(lp.ntx87gn : kular momentum.

  What arc length does the Earth travel in a three month period in its nearly circtzz(vhk4po(908uc qb(i c ss *ular orbit abo9vq so(40zu* sph c 8iz(cbt(kut 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 distance does thexkqzz*ekt5yp1v24r x,x /z 7g tip of the second hand sweep through in 3 minutes and 45 secondst,vy grzkz /17qex*z 2xpk x45?

  How many rad/s is 25 r,7kizonv0djg,9ut-ek)r o jmqf9, v+ evolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whhk6h3e b1ex9z at is the fh3xeh1ke b 9z6requency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits puls :f/ak iur:/(n(ft6n9bl t tlxes at a frequency of 0.40 kHz. The period of its rotatiot rt fx:9ufalblk(ni:nt6/(/n is

  A phonograph record rotates at 45 rpm. Through what ang q /ia2fpe77ywle does it turn in 0.20 siwa2efqy p77/ ?

  A wheel of diameter 26 cm turns at 150ttc 96 6dc9,jynim9zkr :vm/+r myx7d0 rpm. How far will a point on the outer rim move in xn6 y+/ r9y vkitrczmtm 7c9j6m:9d,d2.1 s?

  A bicycle wheel rotates uniformly thro1fbn37u,fniv ugh 2.0 revolutions in 4.0 s. What is the average angular speed of the u3ifn fn17v ,bwheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.gs*pqr, 4d (bm+ay,(x/kzik z What is the linear speed of a point 0.1 zm( ar*kksqzb(,d/ix,gy +p40 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable 2tz vyubk/t(1which moves the car is drivek(tvt uz b1y2/n 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 constant angular speed of 2.0 ra (8q)ylon8ma cd/s. What is the linear speed of a point 8c8(alonq y)mon the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.1ebz /m8(pr/dp 6 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximapz bprdm e/(/8te linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2tq5vc/t0 dyw..- bhyjp-1j cy3)grb v.0 rad/s. What -bth5gwvyc).vrc/j1yqt0d -pjby3 . is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration ofefp3v z:y0y *hcr;e94qg*jyr a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike*r;q0y 4:h3j pc*yrzy9 v feeg is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circul0vd6 bs zqp ahx9uel*d .8tl+ovn)k 20ar, rotating space station (r = 1000 m) lvl2a6e. zhn 9kpv+)8xo b0tqd *s u0drotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curveqwmd25lw.e cvqq(+u7 of radius 50 m with a speed of 20 m/s. Thw wqcqu (l5 q+2d7vme.e maximum centripetal force (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 ray;ms53eo,(oqyctm*o dius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fromq o3eco;5s tm(y ,*yiction) 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 st8 -d1wpp fxgc*ring, is whirled around in a smooth level table. If the maximum tension that the string can withstand iw1fd - xgc8p*ps 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 rolls without slip8z*s su2- qwyv/a (fypping 10 m downy ys8vap/ 2q* (f-swuz a lane 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 a2h o85u k6dmpe 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 wit9v q7hd/ec z+5z26sbz nd+ijuh a 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 auto am: o0 se/bi5s2 lcvxo4x.pl2mobile tire rotate after starting from rest and accc5mb2/x.0:xs e l4olai osv2 pelerating 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 accelera33gug:/fmx 1huuqgkj qiq 145 p+7ev ition of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at pxf+yt n l,k4d npt6wt7-: )hose(h1o20 rad/s decelerates with a constant angular accelerat n64kn+e(7t o, y)ohsdtp:xl1-wh pftion 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 s5tyv;kv-rk,r:0crj (q lx 0u while turning through 2.0 revolutions. What is the averagul t-y;,xv( c:50 j0rrrqks kve angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 .i5 ;:dbbo5r6z h4sko 1 -ra fhdh:hyem/s to rest over a distance of 115 m. What is the totf1.h:bh- e r6o iods5z;kdb r45hya:hal 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 regi.6k8(3nzwk2 z yhk9fzp 4tzst over a distance of 115 m. What is thez 3h 9 64knk8fkpg.iz2t(zz wy angular acceleration?

  A wheel of diameter of 68l9 kv. fww1ngqf(,:pd.0 cm slows down uniformly from 8.40 m/s to rest over a distdg:n, 9 kfw.p1(wf qlvance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medicalg2 1bw 6dr tdbsnsbcy:y8i3 ; ul21(bi laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration befor2n(36;1 sbt 8:b1w cliyugb s2dbdirye 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 re)h:quwe6ugg 34t y(a equire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicu:e4 )( q3tyuuawe6ggh lar to the wrench?

  The bolts on a car wheel require tightening to7m7w)o r/dir c a torque of 90 Nm. If a 30 cm long wir c)7/mdro 7wrench 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 inertia scs m8g 7j w,a wf1uv7-t9qml6$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mode8 5tvpmg1 qg:6 pgrjhr oijo6l-)u4 5xled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What isj8 g-p j6omr51tvpq4)hog5rxgl ui6: the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted x a1i o1n;uccts (:g6-nu6vwlabout a frictionless axis thought the center O. A ropc-o( x6ugn11ts:6 ai c vw;nule 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 a5epffmvu lvu ut,0 0m961vrly4 36ihz frictionless axis thought the center O. A rope wrapped around the outer mrm viluh 1yfevu06 p930l65u,tf z v4radius $R_1$ = 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. The rod is iniprml+0a9k a9d86oz y atially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as o 9a9l ypkmdr a+8a60zit 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 38euk8v fjtq;z+0d r+q q3z6vigmijc -k9 *la50 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,k+9mdfg*z5j0-z8iqqa3r k uq vic8e; +jv lt6 assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a c 4b1ije87a1b9 c auazfrictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of thea a7 cc4ubjai1 91bez8 pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless diskg*wl7lf )xphlsg f*2 0 pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the sg7 f)g lxp0wl2 *flh*mass?

  A rotating flywheel can be used to store env-2o7d 25 hzqdm95tlcg yk.ewergy. 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 imd*vrm z14 c8tnertia 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 stjqw5v:w 9c i4cxzp. oh7o lac(,ej9 4qarts 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 of the inclined pwo9jcc q z4cx.7o h: qvwji5p4(,ale 9lane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed m7z,x 8(oypdiof 10 m/s. How high up an inclined pla ziydxp7(m,8o ne can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fo)i*-2a ipk 0ol: 3d7ipbn nchrom rest and allowed to roll down an inclined plane. How fast is it moving afterp3a7k2pd i- *oii: 0onl)nc bh dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radit )*lqek,cc (zus 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assqek(ctz* cl,) ume 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 momentum changes bo gw4,eay) 7fcy $20 \; kgm^{2}/s$ 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-zsi/;(p;zlruh1u o r h oqm:/r d47qp 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 extended has r56p(8ltx )iyjvk4r i a moment of inertia of)8(it rvyrk 6x l45pji
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?