Angular displacement is usually express in unitsqgz: e xz.i n -,;fg,6vrel;hi of

  Angular velocity is expressed in unitgn4o u1 pnk c,hga9sxk15cs6-s of

  Angular acceleration is expressypcxu7 k74dh3mme 1rbw7 60,4bi oj gsed in units of

  A boy and a girl are riding on a merry-go-round which is turning at an8 .(e .rp)fyxs/vgvt constant rate. The boy is near the outer en/vgvp (tsre.8.fxy) dge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which r(:93 o*pkjiaj.yn py is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. ya.(3jppk9oy* inr:j Who has the greater angular speed?

  A boy and a girl are riding on a merry-gok(uvyt/ 3bduogm 3+nkau :s7i2,* nj v-round which is turning at a constant rate. The boy is near n7i2 ku( 33 ut*:,a/no dugsv+k jmvybthe outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is tur u.;nmq wmvm(2ah1 a3ening at a constant rate. The boy is near the outuwh3mqaa2m.(n e ;v1 mer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridingt*wvnj3y d90:3 wum ec a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to t cvwtmy nd:*3j90w3ue he center. Who has the greater tangential acceleration?

  Consider a rigid body that is y8,dx -)uw oreczkz arj g-12,rotating. Which of the following is an accurate statemr,kw8 z xo--2gre z,u1yca)jdent?

  Rolling without sliplbr0 )b 01qpadq3w01y ,jpbgvping depends on

  Two equal forces are appli ttrdzme*1d- -fnp4)1zzki998l fos10rdk oeed to a door. The first force is applied at the midpoint of the door; the second force is applied at the do *o0) fn1kdrfpese zz11 o -lt84zmid -drk9t9orknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a doo76azf6 bbw/ elagte95r at the doorknob. The first force is applied perpendicular to the door; the second forc6ef aa/9 lt56b e7zwbge is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perph jhtsatq5*+ .endicular to the door. The first force is twice as large as the second force. The ratio of the torque of thhq+ j.a tsht*5e first to the torque of the second is

  What is the quantity used to 3w* 7jhhi;thsmeasure an object's resistance to changes in rotation? s*;h3hjih wt7

  Consider two uniform solid spheres where both have the same ujc :d s kw-2l8mzb8q3diameter, but one has twice the mass of the other. The ratwzl2 ub3 k8djc8s-mq:io 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 theqk( -vx j7ibz1 radius of the other. The ratio of the larger sphere's moment of inertia to7( j bz-ixqvk1 that of the smaller sphere is

  Consider two uniform solid spheres wfzbjrw a 977.uhere one has twice the mass and twice the diameter of the other. The ratio of the larger mome awb9u7f. zr7jnt of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M md)edlcgz9d.)yo p,b /p)dr, and 3R, what happens to the sphe/d,),dyep ol9 c d.drpbzg) )mre's moment of inertia about a central axis?

  If a constant net torquey*3ni 1eafthiu8w + p( is applied to an object, that object will

  The moment of inertia of a solid cylinder abgpr pce42t+.q out 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 wheel of which rk d6p8dag7+y 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 translational kinetic energy of +g 8k p7ddrya6the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and j9la a*) whm*mm(5js kradius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the s)ja9l j m5*wsk mma*(hphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls witk4 u ; 4yp;p ;2mftjfxe.gmcn5hout slipping down an inclined plane starting from res n2ujcpem;g;5 txpk;fm .4y4 ft. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular mos pbh cz.7uz( 8ehxk(7mentum of a system of particles changes when a net external fokuh xzc. (epz87(hs7brce acts on the system." This statement is

  In what circumstances can the angular velocif55sw.h kbw;i ty of system of particles change without any change in the system's angular mom5k.fi w sb5;whentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore anywqv2 8b5gh4l)m mq .ezk9jeg3 friction which may be present. What happens over time to the Earth's angula m2e 8lmh bjkwge3q4vqzg9).5r momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As(4noiel zpz9 lvz.p6- the Earth moves close to the Sun, then we nzv zl(6- 9pp.4ziolhich of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) l4*38ve ukgqo;/uk, c5owht nby pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rota5w oho;u/3tn8 ke l*c,k4vuqgtion?

  An ice skater performs a pirouette (a fast 0 ukz s(4xheoy6x *j1yspin) by pulling in his outstretched arms close to his body. What happey4 hex1s0kjyz 6*ux(ons to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a piroueh.m)bglxm hh*7f hz2 /tte (a fast spin) by pulling in his outstretched arms close to his body. What happens h f.hgbmlm ) /7h*x2hzto his moment of inertia about the axis of rotation?

State the law of conservation of angular wusu-0(x k wugx0*nq /momentum.

  What arc length does the Earth travel in a three month period in its nexp 49d1s;n ttxarly circular orbit about the Sun with a radiun4dpt; xst9x 1s of $1.5 \times 10^{11} \; m$?

  The second hand of a 0g*jihz7 poz,thli i8, 7r1mo clock has a length of 0.30 m. What distance does the tip of the second hand sweep through i*l7i 8,01hjmo h zrpo7 igt,zin 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent to?wk yz (gf)esv9vgofw h ;n;+f+95q8ay

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 ot1xgrjy);7ghg. o0z s. What is the fre7gg 0t1 o)hygj .xr;ozquency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulsem p9:g*y tg cs)yzu+s3s at a frequency of 0.40 kHz. The s cgy9p :zt gyusm*+3)period of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turr*uw(bsj0* q hn in 0.20 *qur*h j(s0bws?

  A wheel of diameter 26 cm ,; yx -o3uravpturns at 1500 rpm. How far will a point on the outer rim moveu oyxp;,3v- ar in 2.1 s?

  A bicycle wheel rotates uniformly through 7 1w8uu(3z d. huvyxho2.0 revolutions in 4.0 s. What is the average angular speed of uov(h3.8zdw y x17u uhthe wheel?

  A bicycle wheel rotate, g(i g;; kgv+a,hx:62p7- s wsxxutztynceo)s uniformly through 2.0 revolutions in 4.0 s. What is the l6;hka2u7 (;v- x,ggxz ) +cnweo s:pyigstt,xinear 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 ca km0axmeur6hfq;+h x17a5 m; pble 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 minuhp6k mmu 70r x;1qfm a+h5;xeates?

  A wheel of radius 1.0 m is rotating wiy9bb,-z; tnf ath a constant angular speed of 2.0 rad/s. What is the linear speed ta,-z n9bbfy; of a point on the wheel's rim?

  The cutting cord on a gas-powere a* kin3bgm:u v2(gk k77+bijmd weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the apk:7(amvb g3i+2ki bn gu*m k7jproximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is95lr1 ub6a*q 1ug tngs rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wh9qurt*1n165g b sg ulaeel's rim?

  What is the centripetal accele f56 im2cfiss(upn/ t:ration of a point on the perimeter of a bicycle wheel off(n/ cu6stimp :2si5f diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circuvhv pt-v)f rkxt:.7 y ,2qjox(lar, rotating space station (r = 1000 m) rotate to produce akvxxtv,: y .qop7jrh2fv t(- )n artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20idws0fw++r 0j m/s.d s00rijwf++ w The 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/8f/jv9 hided69p/ck9yf m ( bsbw+qt radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static f c9tjd mb (+fqs6/9 ifbwe yp8hv//k9driction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attac g0 d5 kvwmpa+org*36bhed to the end of a 0.750-m string, is whirled around in a smooth level tabvmw rp3d56 ok+gb a0g*le. If the maximum 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 radd m+w/dmc*pv6bp +m(b jbhar-wa: (qe -:wet. ius 9.0 cm rolls without slipping 10 m down a lane at 4.3 mdpqw(6te :dm+ b*r p/-h mbj(+ae wwc-:mav b./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 s8w hf2o+ cta*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 angumnl vu;1v2by1 lar 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)6il u96gef(hn igf dd c8)w7wri4rt, tire rotate after starting from rest and accele 6(ci 4gdrlwwi)u7dr8gef,n)6 9h f itrating 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 accelerationq-hmy rzs* nm: d3b)d3 of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constant angular acce,79qmqwqig5mz xke)1 leramkq,71x 5 q )m9ezgiwqtion 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 p5 ;x+v7lux-8 k1i4q mbodiop81vm jc 6.0 rad/s while turning through 2.0 revolu uldj;m8q11i v754piv-+o 8ox pkmcb xtions. 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 over a,vvaxl7 3: qva distance of 115 m. What il3 ,x7avvaqv :s the total 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 rer)b+z9uyi :of st over a distance+bi :f) y9ruoz of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly fpkbum.w8-/ corom 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come u-mbc 8/.okp wto the stop?

  A centrifuge in a medical labo8ln raax715 afp q54xj :qd9leratory rotates at a rotational speed of 3600 rev/min. When switched offndpa4 5q xer:5f78xaaql j9l1, 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 tp;3; ococ7qgdfh9i/ iorque of 90 Nm. If a 30 cm long wrench is usef 73 ogoc/q; ch9di;ipd, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a tmm zlhyu726 od3pbe 83orque of 90 Nm. If a 30 cm long wrench is used, what is the magnitlhm38bzd7p2yu em 36oude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine5my;rny pp7; v ym4twonx-niw*2c 0 5hrtia $3.00 \; kgm^{2}$ 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 is1ir9p3em3u myq anj+, at x = a, and, ma+mq j1piyen3,9 m3uarss 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thougqipjk4 b)24 jcht the center O. A ropejqi bj4 cp24)k 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 aba9x2 22edx.ic jq: mwfout a frictionless axis thought the center q2w de2 i .cjx:2x9mfaO. 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) 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 ontwyy,2 bozzhnb4h4v23* y asg3r/t ;o e end. The rod is initially held in the horizontal position, and then released as the 44yybr;22n ga othsz/z3y *,o3wt bhv 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.jndh 9s px4/uo2v-xrg q;1b,m6dy k+p 5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is apmb r v/1p jpx 4u,s-kg62ndqyo9h+;dxplied 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 wrapped around a frictionl+0qxt6 7v v-b7ktx ;u5glvf xvess disk pulley of mass 7.07 kg and radius 66.0 cm.fbv7-xt l t76qg+xv uk;5vx 0v What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley x.l qn9u8xs6 :7hnbeejn1qun -t m- p8of mass 7.07 kg and radius 66.0 cm. What is the acceleratn e-u1pqbenqm86. 7:t unnhxlsj9 8-xion of the mass?

  A rotating flywheel can be used to store energy. If it is required to stor evk:v qm.*q,:ect3mlwp:t a*e $1.00 \times 10^{6} \; J$ 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 ineu/v:ee-(b6etj0u aoi4y( i zhrtia 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 radicc52bazg uxh5*5msjwo 33i3ci,vx/ w us 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the s5bswj iwzchgx/ 3*xa5oc,v35i2 u cm3phere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with k+ak1ojr;db6n j am;3 a speed of 10 m/s. How high up an inclined plane can it climb before k; o 16bnj+r kadjm;a3coming to rest?

  A hoop of radius 0.50 m and a mass of 0.2ps33(w2 mo-8b q-eq 7zfgsskv0 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a sw-8e-qqk23o z pg7( vsmfsb3 vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 i*ubj j:xi; /a+6ni m n5/*lnir byk1xn( 1cnncm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. 6yr1iinmliban+nn:*ukj5n * n/x(ci b xj1;/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 ch27dyd5p 7bvtf:qtq +d anges 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 ines :vd3i8owd o,,m2ky zrtia 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.n6h.frt6 j rx300 rad/s with arms extended has a moment of inertia ofjnxr6frt3 6 .h
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?