Angular displacement i/ 1t cpxm *lesd9v* g0*yvj0uws usually express in units of

  Angular velocity is eh.ctkw:(+5znt z4n*pkljje qq 9mc4 6xpressed in units of

  Angular acceleration is expre6cgn(kq3.lc kf4dra 0 4jejq *ssed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constant (,xf: rrj5ewz rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displar w:(ejx, frz5cement?

  A boy and a girl are riding on a merry-go-round which is turning at a consg *um)rnwsb1pkn7 +2utant ra 2bnk1w) r*pn+7 umgsute. The boy is near the 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-round which is turning at a constandkduuj,yn7m 4b*;:bg kcg9uaj1 q25yt rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater lc2qak*db; j u1 jmyg,:k9y75g4buundinear speed?

  A boy and a girl are rid ihtoz)nj ad+k1g ((9wing a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. 1)(wkgoi 9 ( hadtj+zn Who has the greater centripetal acceleration?

  A boy and a girl ared:ijw,mc+;gdh clq:i/ gl; 6r riding a merry-go-round which is turning at a constant rate. Thld ,:d wgi6l+/ij cm;q;: rghce 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 the fol r7ao/r(a:qsyj kh.v6lowing is an accurate statemeqs o6(rkv. a7j/ ay:rhnt?

  Rolling without slipping depe+x r+tar1 yxpeq/0c1ends on

  Two equal forces are apq2p is a7jijar7w4/ 9vplied 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 grej spra97ai 2iwv/4j7qater torque?

  Two equal forces are apjavw/ qpc.2; .)be7il) r5xfk7 g zizqplied to a door at the doorknob. The first force is applied perpendicular to the door; the sevqab 7fzie5 ;/ 2q)ck gp7l xi).z.wjrcond force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applie p7tm+60y zgbym peq1v:0 ep:dd to a doorknob, perpendicular to the door. The first force is twice vq1e:+6d pbetgm y0m7zp0 yp:as 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 pz :p3sa dbz9x* (nc e)8 )jbimy1xoa;changes in rotatiomczbsyj 3( * x)ai9dz:ao pepb 8n)1;xn?

  Consider two uniform solid spheres where both have j+vm7 ) e6ui 1csils,kthe same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia isc6u +1,vlisim 7)ksej

  Two uniform solid spheres have the same mass, fp(1p/*bjsy / yg( gmcbut one has twice the radius of the other. The ratio jfb(my(p gs/*/cg1 p yof the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one /te4br;d bw+ghas twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of thbt+d/ ; bw4egre smaller moment of inertia is

  A uniform solid sphere iz 7,9djlbs )vhas mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central b7)z sdj9vi,l axis?

  If a constant net torque is applied to an object, t (ctl+cwt hck );,5at4)vio dchat object will

  The moment of inertia of a solid cylinder about its axis is given by ok(oa*ek*7n o $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 1 vid2ud 1j94ynb6mti,50 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total b,m4 j1iy6ut29din vdtranslational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping docam s,3v( cq)pmt2l5b:7ihfh wn an inclined plane starting from rest. The linear velocity of the sphhp)bvc3fmasi:c 72 5 h,q(ltmere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipvkd e( 2o,a t13fe.ufpcdw1.eep-(zm ping down an inclined plane starting from rest. The angular velocity oft2-,ded e.ecofva p1w(k 3f1m u (z.ep the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of 9l8orvi ;tw d1d; .cpaparticles changes when a net external force actv9ap.l; 18w cr;otidds on the system." This statement is

  In what circumstances can the angul/c ivevtmj ,m*-n1f 0yar velocity of system of particles change without any change in the system's angular momentucy,tnmi1j fv-/v em 0*m?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whicho u2cg *)dlaef;7fzyg. nc:i7 may be present. What happens over time to the Earth's angular momentum aboutffca)n gl;zc7 y.: 72e odig*u the Sun?

  The Earth moves about/2v2t1lei dusxf :m+c pqm 9st2ja(6j the Sun in an elliptical orbit. As the Earth moves close to the Sun, then wh /t l2s i1u2+ :ftpcx vmj9e2ma6dsjq(ich 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 mwwff;96g taplm1 .g *in his outstretched arms close to his body. What happens wl*gf16. f;ta9g wpmm to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a f; ay1usm1xq.mdm6 + yhast spin) by pulling in his outstretched arms close to his body. What happens to his ro. y um ;m61+yxams1hqdtational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling inw;r5z th c6l1o his outstretched arms close to his body. What happens to his moment of inertia about th th5 crw1;6ozle axis of rotation?

State the law of conservation7;utkbr-zpexqav 7s q g;-b+ 6 of angular momentum.

  What arc length does tjy8 lbpw95v5w he Earth travel in a three month period in its nearly circular orv5py58 lj 9bwwbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of ifk0k6md.3aq wo jo9p87ev .s 0.30 m. What distance does the tip of the second hand 0wsk69iv3 7aofq.ep dk.j 8o msweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minut ey h-kj9iu8z.e equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutw m/e4ecghofk56 m6b (ions in 4.0 s. What is the frequency of the wheel's rotatiome fbgcwho ( 56ke4m6/n?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kfh k-;6bmj:2j2ci6oc wg n.e yHz. The period of its rotatioick e g jf onmhcbj62.w2-y:6;n is

  A phonograph record rotates at 45 rpm. Through what angle does z j 4 ;n3jnmdf;wx6va8it turn in 0.20 z namw x6dj43;8fn ;vjs?

  A wheel of diameter 26 cm tu/i *cvv*a;dgsrns at 1500 rpm. How far will a point on the outer rim move i;/vi* svd gca*n 2.1 s?

  A bicycle wheel rotates ucq6) z 1 pnuj0q;2gfwm 2y+kcfha /o87zd1inuniformly through 2.0 revolutions in 4.0 s. What is the avq1igdf6z)w jzmuko8n a u1272ync0/; cq p fh+erage angular speed of the wheel?

  A bicycle wheel rotates uniforml l4 oa7h*ssb i5jdt*,dy through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m frot,4 s5 ia b*ddo7*hjlsm the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whict q q2bi*3yzg1,o4rpsh moves the car is driv3 2pqtz4gi* yb r,1qsoen 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 angular7a; kr o bcmj;zv;yo54 speed of 2.0 rad/s. Wha ;mz4jv;b7o5oka cyr;t is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in;eeoms e:50rlzs0nz gj ,r8c0 length. If the motor rotates at the rate of 20 rev/s, what eo j mr,;ncrleseg 80z00s5:zis the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a congt.b2m f92el3ekz )cop1z (e ustant angular speed of 2.0 rad/s. What is the centripetal u9.(f)el2o1pbzgk3cz te 2me acceleration of a point on the wheel's rim?

  What is the centripetal as67dpx1vzc k s/zuldx e.(6 c:cceleration of a point on the perimeter of a bicycle wheel of diam( u pd6xvecx6 cz/:7l.k1sszd eter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per mda j u yo.1az)yps7o:.r3n, nxinute (rpm) must a circular, rotating space station (r = 1000 m) rotate .ay,zyp ) unxoj.:s1o3rad n7 to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve o9 5 6eeg:vll +8tok;ha(lna , wvawpbu8is)l 5f radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fr8pn5,6)tb5ah8wol :i avkvgal lew(e;l9s+ uiction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circulaxo88 j) dvk(pg qlu.u2r curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (p). q8lvpgxd28j(ukou rovided 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 string7wi51 ,*occ0 er hrn:jgd,kwu, is whirled around in a smooth level table. If the maximumngr d re:w hw 0,jo,1uc7kci*5 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 rolls without slipp.v4nocp: ctw0 ing 10 m down a c p04w.tn:vo clane 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 acceleration fg n5k4zo luhjnz(7 07of $4.5 rad/s^2$. 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 angular acceleratiade1 jqat g1d3lcq9 t abz5i.*25y,acon 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 starting frcg o,1uuqey-lqb dm /v1 s9/86v-rcvcom rest and ac1r-qqccous- ,ev 96 /dvyu8g v1lm/bccelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has ew pam 0he3 ;lz2gyz(:hgf 8t/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 decelerate lt0nt/j; ;taib:3ohes with a constant angular acceleration oh ;atnl0tbt o/;:ej 3if $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular sp7ki5/x1di v3: denzkste4)i w eed of 6.0 rad/s while turning through 2.0 revolut s:i )t3ne1idi4v5xdk /ewz k7ions. 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 )i,9rj5 u4jxb )1lekdggd muy2wkuzaa(:19mover a distance of 115 m. What is the total number of revolutions the wheel rotlzu xja:aegk15mu9( d1)m jugd,29rkbi)y w4ates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rnh(k) l/6dyl iest over a distance of 115 m. What is the angular ac l)(ki dn6/lyhceleration?

  A wheel of diameter of 68.0 cm slos h9)u*i(evblws down uniformly from 8.40 m/s to rest over a distance of 115 m. Howb(9 h*iev lus) long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 360a q/ q+2q+a+/leelumww5jx9 t0 rev/min. When switched off, it rotates 50.0 times at a constant angular accell w+muxw /lq+a2a+qqt 9eje5/eration 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. e+ zzir7t(9hlIf a 30 cm long wrench is used, what is the magnitude of the force required when the force is 7htr zi9 (le+zperpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 ou- d+ ke2xrk.v7jye) Nm. If a 30 cm long wrench is used, what is teovx y k+2 7r).keu-djhe magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of o i1k )9dtkkfg1u f(p,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 modelet4 s*v dceege(:bu.93 a1bwvld as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the e1dswv e(9t bleu 4cv3bga*:.moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pi1 lg-c3if mjl;voted about a frictionless axis thought the center O.g1lij- ;c fl3m A 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 1 -fpej v7/mbphk4oja7c.ejq *f i5i.10 kg is pivoted about a frictionless axis thought the center O. Akefp7ivm e.7oij -jcjq.4b1/af5h*p 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) 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 the horig6, v; bjyr1et p+331bzuzd iivu+i1azontal position, and then released as the free end is allowed to fall. What is the a+ 1 pzv b,;v3iyiz ad63rtj euug+1i1bngular acceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel toj) ,zgnrvh 6cl1ue ;4 oau8r6p be a 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 n)jl1zcuup8, va he4g;r66r o 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 around a frictionlessi.9fqph;kt j7 disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accetjfhi k q;.9p7leration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a e365v0xv i a2wk/tb )xgbate,z5c:un frictionless disk pulley of mass 7 b tnc: b)5w,0xv e2aiket56/3gazu xv.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to vo8acl; 1h+v ystore $1.00 \times 10^{6} \; J$ 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 ,grcd j:oma 8,b44 eaf$5.00 \; kgm^{2}$ 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 2+dg9h yo0xet)tba )dand 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 of the inclined xg d))oed ta9+tb0 yh2plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speetv*)b3pm,dvmwhu:xqpa)v/ 5x6 0 dt zd of 10 m/s. How high up an inclined pla/p) dw,zpudx*b 0 )hvat 6:xqvv3 m5mtne can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from zkj4*t1 uy6ukrest and allowed to roll down an i*4zkj 6u1yukt nclined 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 without slipptmrs7;y n1g3h ing down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a smty3 h7;s1 nrgphere 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 tfl 5l-h c01*qbi ey)xchanges 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 moonyzp((;st(m 7;) f rxqr;nvrment 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 mo36z ) o8elq g7jlxbi;kment of inertia ofo6j3xlil k;zq e)b 87g
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?