Angular displacement is usually express in u q p*s6p/s f lzbi8d 1(u8b4jfyqt7ay6nits of

  Angular velocity is expressed in units o+worf; sm9 kcz1i1*nd f

  Angular acceleration gv f2vz /zqm-f3n5bo. is expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a o4*bib 48htd m/i*prc constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greatei cdp4tbb8 o* mr*i/4hr angular displacement?

  A boy and a girl are riding on a merry-go-round which is turningnd 368 hyk /m7zyr9hmh((asit at a constant rate. The boy is near the outer edge, and the girl is closer a9h ts6 /3 7mr(hdzy mnihy(8kto the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is 87ig o8 /toeopturning at a constant rate. The boy is near the outer edge, andoo8ei/p7o 8 gt the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridin6r4 fbsfmtut.w+/,,le t x1 drg a merry-go-round which is turning at a constant rate. The b4few /x, d1tr6tbs ,u.ft +rmloy is 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 is turning at a constanctxp1:;j;yse t rate. The boy is near the outer edge, while the girl is cect;;y:jspx1 loser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which o h+5p xbvqpx0jkc12y0f the following is an accurate st52x p+qpxb0 y jhv0c1katement?

  Rolling without slipping deh,r g8m:(paj9 v/ wkzcm6q)qx pends on

  Two equal forces are applied to a door. The first force is applied at2 4u- 35ovuest gy,ig guoue.+ the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to thvg.- o4iuuote3 g,2+yse5gu u e door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doo3l03c9h w3dh(n - hkxf khkid4rknob. The first force is applied perpendicular to the door; the second folf3(0khh-33i4nx9 cdwhdhkk rce is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first fo6licq4 d85 xzv,wa;7hfwo d-grce is twice as large as the second force. The ratio of the torque of the ffo, wcxd6 8;-dwv4ah 7lq5i zgirst to the torque of the second is

  What is the quantity used to measure an object's resistance to changes ,w i5v y)+lk2z gbwu,; :tmhvzin rotati,gi +zvbzu5 w; yt,vl)k2wm:h on?

  Consider two uniform solid spheres where both have the same diameter, bute7r( g xyum*dgl, 2+,bkxf,l s one has twice the mass of the other. Tfsxdm*bklgugl,yx2e,+ 7r(, he ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass*8bil 7 s(pivlbpb/ 0e, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that /( 7*bisle8 blbv pi0pof the smaller sphere is

  Consider two uniform solid spheres where one has trzh2 *m1ea0lu iqoprw6.i b-*wice the mass and twice the diameter of the other. The ratio of the larger momirlihb1* .2mrz-uqoa p 6*w 0eent of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and ra0icw .q19 6kioxjlpf7 dius R. If these are increased to 2M and 3R, wh0kc .6ifxi9jo p17l wqat happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to a/tb i/(sxs4qc nvob;d.okz 4: n object, that object will

  The moment of inertia of a ru r *rt28j*q*3aeann fqo;l/solid cylinder about its axis is given by 0.5 MR2. If this cylinderq3*j*2qata/ln; 8 n*rrfre uo rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle nxp k.2g rz1fh5p (vwgaj)7 lg02fv-hof mass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What (wzgf-)vl .g a2p1h 2vrp5x gj7nf0khis 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 radius xo7oga3vl2vm; 6g++l9y -kwtjj 0 igtR rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends ov-0tag +i+mgjoy 6gt2jlx7wl;3 k9ovn

  Suppose a solid sphere of mass M and radius R rolls without slipping de4pa84yc. xc xown an inclined plane starting from rest. The angular velocity of the sphere at the bot xcce4.8pyx4 atom of the incline depends on

  "The total angular momentum of)-ybqhoa gvide 1g .a,z2+ 3bh a system of particles changes when a net external force acts on the system." This stath a,zy-g+bvgeib.1 o32qh ) adement is

  In what circumstances can the angular velocity of syska+k bz.dhnc9s)x 8;h tem of particles change without any change in the system+zh.x9kba)sknhdc 8 ;'s angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignorgh2vyrm6 + .u;vrqv dy1-z mg-e any friction which may be present. What happens over time to the Earth's angular momentumz-1r6hv.gq+v vm- rdg;yu2 ym about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth mx (q3ht20tp dqoves close toqq3(2tp xh0td the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performwe8*4 wzinr.zl /vj7 d/mue(ls a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens wz/m .e 4l inwjl7e u/d*8(vzrto his angular momentum about the axis of rotation?

  An ice skater performs a pm9f hcyhp n-++1 q7yvpirouette (a fast spin) by pulling in his outstretched arms clos7ch 9nqy pm- hf1vy++pe to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spint-+. kt ov1h:x4 xbqdd) by pulling in his outstretched ad v-1t4qdxxok+ .h:t brms close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular mom*2z avnt6 j5c 5:dwbh0a :rnbeentum.

  What arc length does the (rp2+p2 uhq;5 jxzm2d2f :d:bw nqbrjEarth travel in a three month period in its nearly circhq(jw md5;u2f:jz2xpd :brpr n 2q +b2ular orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.03ge4t d ijsp630 m. What distance does the tip of the second hand sweep through in 3 minutes 064gtp i jdse3and 45 seconds?

  How many rad/s is 25 revolutvddd3tjh;5so(wa x. ph2u : . vs ziz/5.aw(jlions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whathu :qs;zp8.as is the frequenczq apu s;.h:s8y of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequen9me(ad;sj* f)v2 ar2wex)z ohme; ey ho:8 )ldcy of 0.40 kHz. The period of its rotatioemz wel9x; )mj;2 afray )o(ho d2)eh*8s: dven is

  A phonograph record rotates at 45 rpm. Through wlw/z-j d/)ezb7pz, arhat angle does it turn in 0.20 -zedlpj/wr /ba7z ),zs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the ou5 py9 dakb 4qq+prg:i7ter r4 qq+yi5 p:dp79 akbgrim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 rexu if (y30n 5l5xop3xok 9rfo3volutions in 4.0 s. What is the average angula9olfi3 3pno x50rofyu (5k 3xxr speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revoluti37. *;tfyaut/ o.,8rxg -gh e hn2qf csf4pksnons in 4.0 s. What is the linchns 8e 4fupf n2fyt qgks;h t.-.*gr3x /a,7oear speed 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 km. The cable whica(kv61 o 1pfgyh(fst:h moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fastpa1hfy1:o6g s(fkv t( 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 i* hpj s:jku2;ld 61lqrad/s. u6 qds jjillk12:;p h* What is the linear speed of a point on the wheel's rim?

  The cutting cord on 9dclsmg.hyt,n jbd 8ib7c0 yrbv6d 9** r6.jxa gas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate lin .*x6.sc* 8y9g0j9d i7 ybrrt nc ,dbhd6mbjvlear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a cons(tb q(lzhu/-y vo8. xdtant angular speed of 2.0 rad/s. What is the centripetal accelerationu.tyqlvzo (/xh- 8(db of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perime (xcxw3jh1: n tba0c ,mphkg13ter of a bicycle wheel of diameter 70.0 cm when the bike is c g ,j13 mtcxa(0k13:nhpb xhwmoving 8.00 m/s?

  How many revolutions per minut/+rd r +6hyur, +hjrdte (rpm) must a circular, rotating space station (r = 100r6 jdr dr+huh +,r/y+t0 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular cu+ 8pbzt 8sk,cndil,4hnf;9 oy rve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided byk,,n+; dpyt9 8cb8h lz fi4son static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat cir+/h q, 6jv:hwc/byucj1 fm oc6cular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fricti/w /:qc 1jch6ycj,ombv huf+6on) 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:q/24sf sp5 unetyq(e, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear y/sfeq : 2qn (54supetspeed can the mass have if the string is not to break?

  A bowling ball of mass 7kd q:fi b*q91igh,7xdb8kcq4bk b +2v .5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.*hx7, ik4idbkvqq8q 2cfgd :b+ 1bkb 93 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 sdl+s38ti7inq mzyts 4:k(cp*dxr ++ 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 conv wp5h 9u qd ,1tutz-+yzb-7egstant 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 stard-sj4olkl / kp3*/of rting from rest and accelerating fk dr4-o3/l* pskjo /lat a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, a92e a vfimc cy(ybh,76nd 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/sc*y* 5g1w1pchoc7xt c decelerates with a constant angular acceleration of15chowx*py 7t1 c *cgc $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from resa6148o45c u+bi wl ozwvbpjd8 6 f4yvmt and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolu +ci48vzw adm yvpb5ob66 1w l8fj4o4utions. 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 rj -l m1vj4y3iexos;d. est over a d.lj4yx e;s md-j1o3 viistance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from )23ggg zkw2p b8.40 m/s to rest over a distanck)gw g23pg2 bze of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from+.: y6f:,ca l wilpjmp 8.40 m/s to rest over a distance of 115 m. How long does it tak+:plm6ayi jcfl,p :.we for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600,3zm9goin )i8cm+f ht rev/min. Wheoi+ im czth9g),fn8 3mn switched off, 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 a torque of 90 Nm. If a05 lxrxd4 wj1gnz:cz; 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the wgz 5wr1d;l cn4xz:0j xrench?

  The bolts on a car wheel require tightening to a torqe zmc-dm;i,2vyhh1z61c /pa mue of 90 Nm. If a 30 cm long wrench is ue 1;1,/mh-zm2zcac hv ipy dm6sed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia ad/ +aa.7/ uytmz wd-ulx8frt0xt;j3 $3.00 \; kgm^{2}$ 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 k-y 8;fs4z/gk mjoxd(is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia abyk-4 /j;dkxz(g 8mo sfout the origin?

  A solid cylinder of mass 10 kg is pivoted aoqirbgpk gphh5*2:0 77uf z2ft+ /f cpbout a frictionless 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 anotherftph5 +uk/7zfp g2i c0rgq:f72phbo* 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 b/6r9 +epugvdcmo q1( 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 auob/mr eg( 6p cv9+qd1 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 initiall yjpuphl05 v-eft3e-/y held 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 about 3-pe /f0j-5ely uhptv one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and ma 9(etd m(nda2oss 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 rollm 2otdd( an(9es without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pym4kp9f j*-htt1esi)zr g,x)ulley of mass 7.07 kg and radius 66.0 cm. What is the angular r jt,ft9-yg ))*e4i x1kszphmacceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk p1 efp6ss0kk ,cac 3nq:;f;zb pulley of mass e6s,kzp;f3 kanf:pqb c;0s 1c 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be z f2/cjcq/9g 2b-yo pcused 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 inertia of 69o+4hztvjj5 d c 4mcvwxm)nya:7i*d$5.00 \; kgm^{2}$ 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 rads:jh 4pr81/tlq ;xs diius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed;48j : pxltshd/sri1q 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 with a speed :3ixiy.l3mo e of 10 m/s. How high up an inclined plane can it climb before co 3m io3yxi.e:lming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is relewfzit5/ w k/90asec g+ased from rest and allowed to roll down an inclined plane. How fast i5 skf te0w/zca+/gw 9is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rn v/ xoep2ao6g)wv.p7rux 31holls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inerti/v316 xo)a2 rwup nv.o7 pghexa 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 pxhvvr)xgs2z( ;15vgum 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 m2-j/0y tlu cnhr;l9kaoment 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 5.00 rad/s with arms extended has a moment of inert kvm o:4q;f en+amh:6dj 6nn1oia oo+16ekj hq f;ona :nvdm:mn4 6f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?