Angular displacement is usucca80e /w7 juaally express in units of

  Angular velocity is expressee.x8shd(nr2 im/(p r xd in units of

  Angular acceleration is expressed in unitszs7b 5)l9cuar of

  A boy and a girl are ridini- ro6vz8y8,rlnu(m cg on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the g(ol,cn8 ymz6 -vrr 8iureater angular displacement?

  A boy and a girl are riding on a merry-go-round whic6aj1stv/d 6i7z 3gamxh is turning at a constant rate. The boy is near the outer edag36v a 7tisd6z m1/xjge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a memde c,dt6 oyi,rk; 48rrry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear sp,o8r , c4mty6ikder ;deed?

  A boy and a girl are riding rq9o0gp si,1p7 fgc5va merry-go-round which is turning at a constant rate. Th 7g 10so5pvpg, ri9fcqe boy 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 rid*wr iukx93mkiq7m + 3:qk vzf(ing 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. Who has the greater tangential acce9m w3i:7 kxfvr*m z3ik(q+ukq leration?

  Consider a rigid body that is rotating. Which of the+ ermwjn)n* y7 following is an accurate staten *)r+m7yejw nment?

  Rolling without slipping depey2kbm;3co2t9 v . h8lc2n hh :d,tcyirnds on

  Two equal forces are applied to a door. The first force is applied at the 2 rfbj)-bsf/duirfx b46+-x0ih b4we midpoint of the door; the s2i/ x)r0fwhf+bir eb4 4-x bs-f dujb6econd force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknobhflpv x-p6z366g(nx h. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torquexnf-z gp6p36 h l6(vhx?

  Two forces are applied to a doorknob, perpendicular to the door. The fcw2wgks(qd2s-c *ml0ye a r59irst force is twice as large as the second force. The ratio of the torque of the first to the torque dwmc- 25klysg(*qcsa erw 290of the second is

  What is the quantity used to measure anky3m 7uf.ke9ew/a2z- ci u5zp object's resistance to changes in rotationfpu2m- /ac37 uwk9 5ekyzze.i?

  Consider two uniform solid spheres where bot8c9 kdf1p n.gxh have the same diameter, but one has twice the mn1kd x gc89.fpass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheeh4r6 ktk+q5lres have the same mass, but one has twice the radius of the other. Thh+4lq k6tkr5e e ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheresms he cv 1b8tgxx.2.4a where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to .axg1 tb4e mcvx.2hs8that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2Mp p06z5e7basackzv7 hk:cy1r a/a-6 w and 3R, what happens to the sphere's moment of inertia about a /pz:cwe7arzk yv0-shbak 617c56paacentral axis?

  If a constant net torque is applied to an object, tbqi(aj-3 gt ozm*g.r 5hat object will

  The moment of inertia of a solid cylinder aboualws*jsf udl;x6t28kg fb(ro,9 tt 3)t 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 rtnjtz4-5p h8.k uh 7jwheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotatioktprjn. th-zh4u57 8j 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 ifcu: so y/2w)w dalv0,nclinw2o:/dal v fu0s)w y,ced plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls witho jj,qm6ci9 qi5ut slipping down an inclined plane starting from rest. Theiji , jmq9c5q6 angular velocity of the sphere at the bottom of the incline depends on

  "The total angular mome:zonly3alt n26 us ylm*(zv0wbi*3f )ntum of a system of particles changes when a net external force acts f 2n3n3t:ayoy) *zwz blil vls6*mu(0on the system." This statement is

  In what circumstance(grk v( nby0x1s can the angular velocity of system of particles change without any change in tvkyx bg(rn(01 he system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ig39qpsihasy5 .(ktm w 0nore any friction which may be present. What happens over time to tw90.s3qap5t yisk (m hhe Earth's angular momentum about the Sun?

  The Earth moves about the Sun ie yu6n ibc1kqd.vzpu *8km207n an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the .d 708q 1cny6z pkeibu 2*muvkorbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pu pzja;r;jso6)lling in his outstretched arms close to his body. What happens to his angular momentum about the axis pa6o)zjsj; ;rof rotation?

  An ice skater performs a pirouette (a fast o07z;3 wb 29 2qnbfq/ loubmtqspin) by pulling in his outstretched arms close to his body. What happens to0qu2q3b /b n2 zmfolwt;o9b7q his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his ouu)ic8 cg40rl2q n9gbbtstretched arms close)liqg9g408urcb 2c n b to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentuma*4cm j( hh t(;lifcs:.

  What arc length does the E/n:hxa gp xwjj1236 ebarth travel in a three month period in its nearly circular orwjb/ajh 63x1e :x2gnp bit about 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 q hzk.h eer,b2x80:5ebxp 3jvdistance does the tip of the second hand sweep through in 3 minutes and 45 second x 2ezb be.hhk:pvr08 xq,e3j5s?

  How many rad/s is 25 revo 67z pgg+pxay n1bb1l/lutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions )ia )ul:/d uyoin 4.0 s. What is the frequen:uud ai )yl)/ocy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. f xvs b6u/vr6.xw+ l1i The period of its rotauwi f1 rbl sxv.v+x66/tion is

  A phonograph record rotates at 4q-)fbcvr:sc. 5s :uu n5 rpm. Through what angle does it turn in 0.20 s?cq:-)r :s 5uvc.bsnuf

  A wheel of diameter 26 cm turns at 1500 rpm. How far will tbg(ex; yff i(0a m.sd**nok0a point on the outer rim mo*o bf. (kmfx0sig* t (d;a0eynve in 2.1 s?

  A bicycle wheel rotates uniformly through 2+kof)*pef h d6t5h3nf.0 revolutions in 4.0 s. What is the 3p f+h)h e 6*n5dkfotfaverage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0kr zcc48dg; 4 x f6rx zx,+kydv;6rf+i s. What is the linear speed of a point 0.10 m from the centerx,zr+;x v;6drxfc6 zi44kfc 8d kry+g of the wheel?

  A cable car at a ski resort carrie;c8yueg ,d-g0e3 y zjes 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 cable car to make the trip in 12 m ;ec8du0zyegy- 3gj,einutes?

  A wheel of radius 1.0 m is rotating with a constant angular speediph4run 1+v bqz6,4ri of 2.0 rad/s. What is the l+qv, rri44hznb1i 6u pinear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed clh/j)b ju:: alc (y.pod4vc w4utter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the encv pc( :d/bua y4j.jlho:l) w4d of the cord?

  A wheel of radius 1.0 m is rotating with a cj(utz 9,wov:t0fw e7x onstant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheeeo0z :(vtu7 9,jwtwfxl's rim?

  What is the centripetal acceleratia- q wm/zm5x7gon of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when thamx/qw mz-57g e bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotati 3gc- 6ccv j3xtf822;tqzv k:.cbqfykng space station (r = 1000 m) rotate to produce an artificiaq3bc2:vyjzc.xvtk 8f62 c;qt k fg3c-l gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve arrc:0175ae 2vcny3qyk1bf g of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provi0q5f y1b372ya rg1k rcvea: cnded 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 rad+zscq jwa,l1*iox4 n6ius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static n z1 w,ax46*cqj o+slifriction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, att,m6m fhn*ut *tached to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tensiom*m,f6*hn ttun 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 r, ndt9 fopd6u1dj9 dbz4s8pcf3boi31adius 9.0 cm rolls without slipping 10 m down a lane at 43 bdfsfp9j93,1 udto14bd do z86pcni.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 acceler9mwk*lfun/j5qpf 6.n ation 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 rd e:hw, *hf76z:d ahmconstant 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-mr3v byhiuela9fx 415s 4d0n7e radius automobile tire rotate after starting from rest and accelerating 7vhr49naubx3ee fsidl1y 504at 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 lqi p- 7jy m))di2yp9aacceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s/lwan) /oi j2p,aa8s/imt6 nb decelerates with a constant angular acceleration ofan o/ta ljbi8 /,m62i/snwap ) $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rd8rhqa.0m9i z est and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleraz9a h qd8i0m.rtion of the wheel?

  A wheel of diameter of 68.0 cm slows down unifor5a dw:sqex 2py;rkcp6*gfl8f thi 3/1mly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in dc6kpifs3t2;fw8l aer/ h*5ypq1xg :coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly fromfra omj (k/8/m uqwy3y81d hq/4)hi ky 8.40 m/s to rest over a distance of 115 m. What is the angular a1ym)/ m f4/yrai 8qwhd(jkyqkh o8 /u3cceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s l23on*gz.5t h ootuae);m,v, r mxwe8 to rest over a distance of 115 m. Hohg3tl *xve)a5me z8o r;n2u w,o.,mtow long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/rbt 6(io+ v+ vqx))mfbb9p r;zmin. When switched off, itb)v;xp( foz)rrqmib+v+ t96 b 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 ofhr)7 s,t+dos; :bhhto 90 Nm. If a 30 cm long wrench is used, whatt:b7osh h); htr,os+ d is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require (p ydg8ftyh-g)ot(1x 0zhy v7tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnzhft8 yoht 0 7y1g(-yvpxdg() itude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti+: d pfq4r;p/q wx0wvza $3.00 \; kgm^{2}$ 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 origin, mass 2m io4dadjq :lspp7 9j k,/s at x = a, and, mass 3m is at x = 2a,:jq4ja kpol9d ds7/p. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictge(.r0s*ptlevms3w t s4r k. +ionless axis thought the c k 0*4e pslr(vs3twstgmr..+eenter O. 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 10 k, ey y7tz8i: tpc9*aagg is pivoted about a frictionless axis thought the center O. A rope wrapped i8, pa7yyte:*z 9agtcaround 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 rodjysnv8(9ax7g c+xpsb5;g3 m2zm nnv7 is initially held in the horizontal position, and then released as the free end is allowe vy82pzm ja+s7(75nm;xbg x3s 9gvn cnd 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 toyg9-i r3zz-cp n9i a5b be a ring of radius 30 cm and mass 1.5 kg. Neglect i9 py-- n3br95cazzigthe 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 slipping?

  A 1.53-kg mass hangs on a rope wrap u8er6 2ps t9ya0kzm:3if tgk8ped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whaa6z: r 803upgymik9tkf2et8st is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of m +ocq/w( 8kc4eo* ooqkass 7.07 kg and radius 66.0 cm. What is the aok o +q4ck(w e/oq*co8cceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requirww q8ur)xyw;w l045ja ed 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 yej h p5lp;7rq q48oz/inertia 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 sta)bw ul4w:av d8rts from rest and rolls without slipping down a 1.0-m high incl ul:ww adv48b)ined 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 an7s9 7o5z53e faiz f;aroi/ms ud radius 0.010 m rolls with a speed of 10 m/s. How;7 so9zue 75i5/roa ais3ffzm high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mam.q1r yu.it7f ss of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m t m71.uiyr.fq?

A solid sphere of mass 1.:6keager/ v)k5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given :6v ee)kg/akrby $I = (2/5)MR^2$.
(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 jkjl36z 9u0)pjuie : *xyyy( tmomentum 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 u as;*2mqw*2z-zlqes 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 extendeddzal6/.bvi)m oe3 r :x has a moment of inerti/vdb 3e6mxlzi. :ra o)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?