Angular displacement is usu h7x1zr/edz bd73b4-,t0alob d cc1zqally express in units of

  Angular velocity is expresselpbe( aa;ge-uh;53z4 x2kke yd in units of

  Angular acceleration is expressed i pbrv ffpvd:/7gf- /0in units of

  A boy and a girl are riding on a merry-go-round which is turning at a cons-0 bps u*twdkgvfd8gu9c +( p,tant rate. The boy is near the outer edge, and the girl is clu wvt -0kg,98p(c+ bgs*dpdufoser to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant t)npy9( r0y.r4 codre ratedr9r(y4n to.r) yp0ce. 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 are4 wznj zrx7y54 riding on a merry-go-round which is turning at a constant rate. The w jrzz y74xn54boy is near the 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-,1tga2ea ftu+ 7 (tiqx xryq1-go-round which is turning at a constant rate. The boy is n+ tauytq1(r -a7xq,i xgfet12ear 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 constant rag; )hgy..h07y u ypz;vr n,wibte. The boy is near the outer edge, whil0hv 7zibgp w.hu;y r;).ygn y,e the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whi-c+ cahb;g c0och of the following is an accurate statemen-o;0g c cac+bht?

  Rolling without slipping depends onl c(h7ffwvc0gpfx2h; 6ya*pd x- f;n3

  Two equal forces are appkq89m3y6ss g r1iztu 2lied to a door. The first force is applied at the midpoint of the door; the second force is stq1k r8s 2 m6iz3ugy9applied 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 doorknob. The first force is1,c fbuxr yti wq/z5 xe23*)5kx d4xsbco 4;ri applied perpendicular to the door; the second force is applied at 30e to the plane of the door. ,qxfcsy 1t3uex2zi4 crd *rox5;b4xk) i/b w5Which force exerts the greater torque?

  Two forces are applied to a doorknob, 35q)snz po0va/d.z mvtdh-:e d u59wiperpendicular to the door. The first force is twice as large as the second force. :d0uh- i)dv./vwemdaqz nsot95z3p 5 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 ref 3 s.wow6vmk;sistance to changes in rotatiom6wo;vws3 k .fn?

  Consider two uniform solid spheres wherh1g9rgv6jn6 se both have the same diameter, but one has twice the m1h69rvgjgn 6sass of the other. The ratio 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 r ,xl+i0lz0bc twice the radius of the other. The ratio of the larger sphere's moment of inertia to th l+,0lx zrb0icat of the smaller sphere is

  Consider two uniform solid spheres where one has tw * ge9.qcsxa5hice the mass and twice the diameter of c*e5 hxqags9 .the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these x78he9,ad5q rou buh ,are increased to 2M and 3 db ,q hur59ao8u,e7hxR, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object will l n44az rjsom)7bn8qw. 7t8dq

  The moment of inertia of a solid cylir b9hhu2t/5yyre:y )0 fwtuk7 nder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotatiou5y7 rrw/b90 tfyut2 ke hhy:)nal kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel -embpvy-g( ( r. t6ecgy,;lpnof 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 translational kinetic mpt(;vp,-.b e-gy g(r ly6cenenergy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere ofx1q/ ;3gxpdsy mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline dey;p xs13 d/qxgpends on

  Suppose a solid sphere of mass M and radius Rawbp7(,zmvd2rd gcy1h7xk 2/ rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline (2mby1kp ac,/gzrw2ddx v 77 hdepends on

  "The total angular momentum of a system of particles changes when a net exterivy:ckef3 /+m))x0a it- qkpf,vjs9h nal force acts on the system." This statai0yvq e/9xjtp+ i m:f -k 3,)kfcsh)vement is

  In what circumstances can the angular vcx ,myhel a,, o**9* s jc:pd3hagw.ptelocity of system of particles change without any change in the system's angular mowsg yc :,.hl *pa9exjpma*th3do,,*cmentum?

  The Earth orbits the Sun in an ebh-(2uw 9ktjj -)ox t *uzqur0lliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular mo2k t9jqu-o()xwtju- hzu 0 rb*mentum about the Sun?

  The Earth moves about the Sun in an elliptic zph,/g)qjd1 xal orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed ofj,pxqh )z g/1d the Earth about the Sun?

  An ice skater performs a pirouette (a fas)h qc u2-aw5s9s6gvllt spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about59lgs -cwah2vsql u6) the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in 5 h; vjp)tv qw0uw+me4his outstretched arms close to his body. What happens to his rot m04vp+w wu5;qv ehjt)ational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spik0f,gg;ijfj,e ht x:xf9d k00 n) by pulling in his outstretched arms close to his body. What hapej:,9fkj,0igfkx;fd 0h tx0 gpens to his moment of inertia about the axis of rotation?

State the law of conservation of ang rjnezek 9-hoj;o 1fntz 9bqa6-9 ,)szular momentum.

  What arc length does the Earth travel in a thh ) 9mv doxr u1h tw9;b1q8l0/ojh3vkjree month period in its nearly circular orbit about the vj)krd/vltuhbx 83 wm0;oh1j9 hqo 91Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock hp6x)18 p :qxyp(vjtnpas a length of 0.30 m. What distance does the tip of the second hand sweep throu 6yv:)j x 8tppp1n(qxpgh in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equgrlwc4:f/ h g(f3eit7ivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions inom+c* /m1vu5voq6 m1-m cd fkoda62p t*tu az9 4.0 s. What is the frequency of theu1damv vm5t2uc/o c ak 6t-*omd*+z1fm9p oq6 wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHzj0((-vn arqyyvn7z - lfbt7fl-zz4/g. The periot fbg4n z-0 7y/r(f z(z7a vy-lq-vnjld of its rotation is

  A phonograph record rotates at 45 rpm. Through wh fha+uu/ty lo a(o/).hat angle does it turn in 0.20 s).u(ah lt a/+h oyo/fu?

  A wheel of diameter 26 cm turns at 1500 rpm. How far wil( .l n*sm1layxlgba 29s+ri2fm7 z sx;l a point on the outer rim.7r9a bxf;s2x mzi lgl*m sa1(yl2n+ s move in 2.1 s?

  A bicycle wheel rotates uniformly tt qz8w m50 )0jlqmswl)hrough 2.0 revolutions in 4.0 s. What is the average angular speed oflt)l q0m s0 58zwmwj)q the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. fkj 8xigy0n12o;a7ez What is the linear speed of a point 0.j;fngxyi80 2eok1az 710 m from the center of the wheel?

  A cable car at a ski resort carries s a.ar 1rhb/ewb2fn epl0zz22j1z4 5yz kiers a distance of 6.8 km. The cable which moves the car is driven by a p20z /e bwyrar2za1jzpzbn45l e2. f 1hulley 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 angular speed of 2.0 rad/s. i+18,zy 5 ptidn9bbqw What is the linear speed of ad,ni5wip1+8byqbz t 9 point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16bn .ez0- co8c+zci 5peyv7xz6 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate l xc+ep.cz nz oy 8-065evbzi7cinear 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/s. 6dyz51lnwbu1 What is the centripetal acceleration of a point on tw1bun1y 56dz lhe wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a ee*uojnn;/ g(r elto)2( n3vlbicycle wheel of diameter 70.0 cm when the bike is moving v el;)n 2r *e lguj(no(t/3eno8.00 m/s?

  How many revolutions persiq1 r+mv9kklu r4y99 tgs6 ;p minute (rpm) must a circular, rotating space station (r r4s +lqp1 ; 9kgvu9riyk m6st9= 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 2 lx)6mgt/t 6iw1fo:mz0 m/s. The maximum centripetal force (provided by stati6:1z /wgm)6fi toxtlmc 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 wk4e va3 ayr:)of 20 m/s. The maxi:ea3wvyk 4ar) mum centripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached tu ljie. cwn4os :)fd4.o the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if si ..c4jl)w n:uo4efdthe string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cmdll,:4 8i dm; o2mnkpm,a8 bej rolls without slipping 10 m down a lane at4bie 8aomnj d2m,d ,m;:p8lkl 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 accelen9 wxrbe*z9 uf; dx;d*ration 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 acceleratione0;q(j1ne5nbo8gmf 0aqlw+kv 0p v3x 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 apkis (ti hbn,d6u, w42 0.300-m radius automobile tire rotate after starting from rest and accelerating at a constannswbtui(6h,dp i,4 k2t angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an an (;g wshdj9b:pg 6th3dgular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rab(llbscz 9)3jd/s decelerates with a constant angular acceleration of 3z)c l(blb9js $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 raze/uzfc +9rc8(k ht-2nq do3yd/s while turning through 2.0 revolucz2n/u -(r t93zdo ey+chfqk8tions. 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 2g;r 9gggwm))z+ ( mqk (hnevu44xmmrto rest over a distance of qrg 49e(gz v)gwn)hm ; kgm4x+m(umr2115 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 8.40 m/s to reste0v**g d w;hdo over a distance of 115 m. What is the angular accelerationdegwhvdo;0 **?

  A wheel of diameter of 68.0 cskzys)b mh(1*m slows down uniformly from 8.40 m/s to rest over a distanchsyk bz1 *s)(me of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical labx6mz4pokgq ( (zn:n8xm8 ei 3woratory rotates at a rotational speed of 3600 rev/min. When switcheg q p(n8z m:36k xoexzw48(nmid 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 9z1o vboltj9-a0 fm6e 10 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicula9tof6alb1mozjv0 1e- r to the wrench?

  The bolts on a car wheel require t5 .j8aby-*/n xgzxmwvightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnwy-.anbg j xx 8*vz/5mitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia se 6(wn;dr7hb$3.00 \; kgm^{2}$ 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 originilhq q(/)zfw96 sm/wgvt .*od, mass 2m is at x = a, and, mass 3m is at x = 2a. What iq9l w6.vz*m) w/(ifh/gsdoqts the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thon, w jrh57y0dnught 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 ropnn50 d,wyr hj7e wrapped around another 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 thought tj6zcm ) c(9 ii(pw0,+tl;pucxgx3ye vhe 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 arx(xim3 pc p jez0;ci9,c(u+ l6gywvt)ound another section of radius R2 = 0.50 m exerts a 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 initially held in then ca6/ck qgw(/*huq8er0vnnf.4e x o7 horizontal position, and then released as the free end is allowed to fall. What is the angu4uc/nkf* reeh/qwq vcx7(an0 6og8 .nlar 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 3ll mtt6ap th*e2l,eqm1 qpl+ mi)2,u30 cm and mass 1.5 kg. Neglect the mass of the a),,2+ i 3 1lumtll qpm ea6tmet*2qphlxle 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 wrapped around a friction l5v1*py-cr razq.4vla t7/xpless disk pulley of mass 7.07 kg and radius 66.0 cm. Wh4v*x- rrcla t 1l7.vypqz/ p5aat is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapp . ib+52rm1z3fvl96nsmg6bv umt g*jded around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acc+v1j nsv62.dm bgbm 9igr5*f3mltzu6eleration of the mass?

  A rotating flywheel can be used to spycsw*x66otvj*4w*mvy 0 pm4tore 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 yaec03i14s geyr7 ju 3of $5.00 \; kgm^{2}$ 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 mp,,cjrva fbf8e:t ,s uiyp+5* starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the e5*,:ia cfpvb,8f+sjytrp,u 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 r*-ljwy)bt0j zp ;u) va speed of 10 m/s. How high up an inclined plj -uwr )y0b;lj*z)vtpane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowedm e jpw4ifbwz3+j3frlde/72 6 to roll down an inclined plane. Howzfe+7i/4ldrwwejpf 2j3 36 mb 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 rol /fhw 4 u:eag,4r.v4)cecnwxup44bbhls 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:b4,p 4u4)xveh.c n w/crfuae4hw 4g b 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 momentumf m l8pu*i92(bl*msqiaj+ zd( 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 momento7bm5m8+im3l (7c-ppvkah/adb cnx6 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 wi) n)lm3nlvfr( 0chyj*th arms extended has a moment of inertia ol jf *ryvln h3)(c)0nmf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?