Angular displacement is usually exp(w fdw7. gn auo*3;whf1n3bdkress in units of

  Angular velocity is expressedpi ofu h;y 9(it0su;m5 in units of

  Angular acceleration is expressed in units 2jr( *mju q(;vbyr c;mof

  A boy and a girl are riding on a merry-go-round which izun,d;9ixbwth +1imx s4,* *dp axwv1s turning at a constant rate. The nzdi*+dvp*wb 1hx1iw; mx, x9, stau4 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 mp5 iu5rdeuw , zcy*4.eerry-go-round which is turning at a constant rate. The boy is near the outed u re55y4c,pwi*zu .er edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding b4cuu.of4pm0 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 greater luocb44f p0um.inear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant rb+o nf99emv .u/hb+r wate. The boy is near the outer edge, while the girl is closer to the center. Who has the gr9+/.nob 9r e vmw+hubfeater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is kcj)kvxl *x33mye*2 i turning at a constant rate. The boy l xx*i32jmevcky*k)3 is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body te2z q6o r+iy/pnp+v 0+ 3udbdcqgv.i;hat is rotating. Which of the following is an accurate stai qgv.idcenu+r0+ppobzd/;6 3 2yvq + tement?

  Rolling without slipping dependsusr mtk,w)t kf 3;)+fj on

  Two equal forces are applied to a dooru ba2r rqi6i/gnk b6/4. 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 exe/ qb6a i/r4gru62 nkibrts the greater torque?

  Two equal forces are ap-lrd8 lcq0u)- 4fmz/r4ht tf mplied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane du4fl )z-tc/rm hr8ftq 0m4l-of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the8a uoi:,ukofcu ,i -s3 door. The first force is twice as large as the second force. The ratio of the torque of the first to 8uo,a3kic:u o,u s- ifthe torque of the second is

  What is the quantity used to measure an objectd, vasne4 )ne.q+lc2 d's resistance to changes in rotation. edv,nd 24 )an+sleqc?

  Consider two uniform solid spheres where both harai 9ec6wmsavn 3o41)ve the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller rcen s39 a)6mwiv1o4a moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of 7)n4+u a4a zh9j*kwlk j;rrbtthe other. The ratio of the larger sphere'ka *zu+jjl br h44n)twka7r9;s moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twi:q:omn q:z g5hce the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that oh qq::zgn: m5of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M an*4c n,oszhd 6 8tvc oa)yk,n)wp*2,vx bkl)utd 3R, what happens to the sphere's moment of inertia about a cscv kwzb vo4xn,)8*c,d)y*ap )2 tnho, l uk6tentral axis?

  If a constant net torque is applied to an+2b rx len+kfasron+l5 7p p*1 object, that object will

  The moment of inertia of vqd5dbm,d7qnrnw,b- :qns7) a solid cylinder about 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 cidcz8 1mhy2 s8c(+a d -zsc8m-2vlom mass 150 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 m1mcld si8c +hc vszo-y22z(8 -mcda8 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 rollsg)nqq 40zab q9 without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline deq4)9a q z0qnbgpends on

  Suppose a solid sphere of mass M and radius R rolls withoutpd)mib 3j x)b7-)alul slipping down an inclineb)ipl )ux3)l- adb7jmd plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes whengxg.6h:i,( uhax yvp/ a net external force acts on the system.hgy xx.(v, /6h:ag upi" This statement is

  In what circumstances can the angula,jozwc,xns:yk.uz3xi(x 49 at up*b 3 r velocity of system of particles change without any cha,n4usw pz:xk oyxbauix,3 3z(*tc. 9jnge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fri/ di0/qsx( g6vl8rxl zv;gn 9nction which may be present. What happens over time to the Earth's angular momentum about the l x98 /isv n/qrlgzvgnd;6(0x Sun?

  The Earth moves about the Sun )ar3zd tdq-.d in an elliptical orbit. As the Earth moves close tod r tda-q3.dz) the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a piz6 orr9 firi8 g(pyg8*rouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angulap6gy*8(ri8ri9og z rfr momentum about the axis of rotation?

  An ice skater performs a pirou ,ql/(deyza ah;42w oqette (a fast spin) by pulling in his outstretched arms close to his body. W4,2;wea qo/alq dzhy( hat happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his ou ,gk9yf 5g(ycdtstretched armsd5(yg9,fyc kg close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angu 60h7 qyp/8rahsx ce+ylar momentum.

  What arc length does the Earth travel in a thre+k7bhoa.k dx 3e month period in its nearly circular orbit about the Sun with a radiu o+3kd.k7xbah s of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dispzcw8o djn;/2-r d: v.scv o6ntance does the tip of the second hand sw;cj/w8vovd zn-nd p:2cor. s6 eep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivacf+szky a6 9hxhtq 053lent to?

  A bicycle wheel rotates unifor8n-3/a zxu zxrmly through 2.0 revolutions in 4.0 s. What is the fr8z nxzurx/ a3-equency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulsest5s.)ro p:dm o at a frequency of 0.40 kHz. The srp:d5 )t .oomperiod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.v7d ;- 3u3w9yr9yihkxmjyq;x 20 drx9y q3 3yuiw-;jmv ky9;7h xs?

  A wheel of diameter 2te*v467n( c qdgkqeiew9 ff67a2ant 0 6 cm turns at 1500 rpm. How far will a point on the outer rim move in 2.1 66def t4a79qinke0qwv tac*e7f2 n(gs?

  A bicycle wheel rotates uniformly through objii.uqzc l :bn9*8jns *im2l4:v*t x 5 zm1n2.0 revolutions in 4.0 s. What is the average angb*zl5zm*: j. 9b84mn c*nxou2:i jnl1si viq tular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thxa j0ihjqc/ 7cdd //5oe l5/dqcij a co j//d70hxinear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resrw8ladl4vza r 613*ptort carries 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 inlv3a4td6w 1pl8*r z ar 12 minutes?

  A wheel of radius 1.0 m is rotating with a const1nudtk*se /)yu6a;s kant angular speed of 2.0 rad/s. What is thet u6sk)1eudk/a n* ;sy linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the rkiy7jz fi 7(nf c21,tmotor rotates at the rate ff277 , kztyinci( jr1of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/sgvkty e :b. b i63)3zmqc ak/(b).lopx. What is the centripetal acceleration of )bxtzyb( k)6 qio3 3c/.b.egv:m kpal a point on the wheel's rim?

  What is the centripetal acceleration of a point on ,a.sb8h9pfed ;t*mh wthe perimeter of a bicycle whb.t, e *fp89dhhw;m saeel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions p4z 5tt iubw t9sd7twc+o-w /i+er minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gc7id-b9wtt tw4wz+ ot isu/5+ravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 ip)uu -dlu, c/m/s. The maximum centripetal force (,lp uiuc /-du)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 radius 50 m with a speed of 20 m/s s(8ev1ffixjce 8 ;u7en:x9tf. The maximum centripetal force (provided by sf1vu cf ie;8: ejst e97x(8xfntatic 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, is whirled aroo/s+j.y r; sqri/goa1und in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the q.y/ios jrg1ao r/+s;mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping nl:talxa-iy/b/ s3lwx 7m 8h410 m down aaswmty n/xx b-h7/a:84ll 3il 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 a conqoi, 5/(y/3 5:s r lrli hspjk)a* f*g,mcbmpistant 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 constant angular accelerationwtcqe ,pi9 f.q* 454cw31qgyjpsh, kr 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*-eg ,c fbb*lr from rest and accelerating at a constant angular accelef-*glb br,c *eration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and haf*3ol pxx5 a*gs 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 decelerate0,l) uumzvlw v1a1p)k s with a constant angular acceleration of,mz 0uwa)uv)v11 lkl p $-5.0 \; rad/s^2$. 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 ,,d1ktnv 9bc 8(eeobo :kw6ks while turning through 2.0 revolutions. What is the average angulaew k1skk,,96:b ct(8eodobvnr acceleration of the wheel?

  A wheel of diameter 9t( ,rw voyoe 2nn:fv1of 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotatt, v n(1no29y r:fevwoes in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over . 4lq:z/xx-su jyut4ea dxx yzjetu l. 4q/4u-:sistance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over:a thub.n rpcn7n-p8)v ,; xln a distance of 115 m. How long does it take for the wheel to come to the stop?avnpnh-l8tr) n;c7n:. b,up x

  A centrifuge in a medical laboratory rotates at a rotational speed of 36007j0; wnx6 ob itxosro)0sv0d0 rev/min. When switched ofxo06tjs rods )n70 xiw;v0o0bf, 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 Nk(kt vdak.78vlw69ynk w2)dsm. If a 30 cm long wrench is used, what is the magnitude of the force required wh s9.a2kww 8 tv ()6kl7dkndyvken the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to 8am4 atdjeji o/ev9- 1+wk-l 71urlyh a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force applied 7le/ui jd--1hv9rmy4eaw +j8 o atk l1at $53^{\circ}$ to the wrench?

  A wheel with moment of inert8- nzfpmc8 ;mr /e5xpfi*sz)fia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modelekvh7,tghr5c3f8 dl*8n e4sfx qi4 : vfq:2lvtd as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What r*5xf474h8l d c2 qeigv:ftv s8, q3 h:kltfnvis the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless ax+uh7x7*0 pfh5vgpsuh is thought the center O. A rope wrappvf70u57+p hhxg*sh pued 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 t.s 6biv6 q;07db8(gj( v xky2tck dinehe center O. A ropeebyk08xkbjctq s ;in(6d.6i( d7 gv 2v 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 inf3v( a soi03zb the horizontal3sfi3 0zov(ba 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 one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.4 dpj-vti)haz:,-ktc i ga (9e5 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 rot4hv-iai(ak j-d:)e,czg9 t p lls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pullvvy1*,0 bl(nlxop; ycey of mass 7y0po ly(*bx;lvc,1nv .07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped ay(4j) d p v.a3k js9/yakys3isround a frictionless disk pulley of mass 7.07 kgsksdi/yy393yjva) k a4pj s(. and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If itcg6 3 avh)jialv )o.x)o/o: oe 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 o 25cxus v.zub1tfn xhl(63 7uinertia 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 starts from re3iarjj-( .rbqst and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottoqir j.r3a-( bjm of the inclined plane?

  A solid sphere of mass 1.0 kg and r3it-psdeb j c.0 g-kg7adius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb 3 7tdjis kp g.ce--b0gbefore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allo r8aqrfxl o3*0jf*pu 7wed to roll down an inclined plane. How fast is it moving after * pr ura830q*j fxf7oldropping a vertical distance of 3.0 m?

A solid sphere of mass 1.51 hth.g/n1rvj7wh21r2d wu 7g / tbqja kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m londhr ru1vthhjw 2tg2qnagj. 7 7w//b11 g. Assume 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 klhc3vyd0z70 a8 8z c(ssm e6wchanges 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 inert6,1* zxlp pzhxia 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 rotaep- ur u+t9io4ting at 5.00 rad/s with arms extended has a moment of inertia ofi e+opu-r 4tu9
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?