Angular displacement is usually express in units j f3jxfyu/ q3x, rsk3,of

  Angular velocity is expressed in/qxd zgow :,ug8mpm ,+ units of

  Angular acceleration is expressed in un yar:g;0jaw +0fpn39he;dk w9ac0a1 am tl6xqits of

  A boy and a girl are riding on a merry-go-roun --h4qmccd/bfvk*x p4 d 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-k vmq4/ dcx4cf* bh-preater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a c6 lw(e7ec 4 q8m4myzhionstant rate. m6 ih8c ewzl4q y4e7m(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 ridinggwsa5. i6no mb(op f9( on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl.6(bw n5m ao fisp(9go is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-rouwog025r jne *qnd which is turning at a constant rate. The boy is nqjn w20re5og*ear 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 merrb 5jz3r2 umvco, mg.u5j enn16y-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 a,j5ncb 536gj2em1omnruu .zv cceleration?

  Consider a rigid body that is 1k6wc7hs veh/ 5q4h9 5yxandh rotating. Which of the following is an accurate s51s y4whh dhah6n5v ceq/97kxtatement?

  Rolling without slippau: y+xt dqcaw1g2 ow5lk-a7; ing depends on

  Two equal forces are applied to a doorb2mb 1sanj7)+ hnw(ge . The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicu7 1a+e2nnwsj) bmg h(blar to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at )v)u m9obzh0v the doorknob. The first force is appli 9mzvh0o)v) ubed perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, pee-tiqj:vug wu5e*0 a*rpendicular to the door. The first force is twice as lartav eq05ewg**uuj-:i ge 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 resist k20tpw5xd;2 85ppji iffw q,wance to changes in rotatitwif0w5; 5d,8wfp 2px2jpkq i on?

  Consider two uniform solid spherein 72y v3d(cvgs where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to tdnv 7 igv23cy(hat of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of, 1xqb f0m0ube the other. The ratio of ,1f qu0 0mebxbthe larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid sp.2beymv)oagf 49g npi88h1 o yheres where one has twice the mass and twice the diametergo1 yf.8e)9 yp82ai bo4gnmvh of 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 are increased to 2M u3lx k7ue+3n7f,nz tjand 3R, what happens to the sphere's moment of inertia xuktznj7 l3uf,+e3n 7about a central axis?

  If a constant net torque is applied to an object, that object wila *6af+do-o*;rjl t/ m yeg/eul

  The moment of inertia of a soli5z d;t,w iz8ydy9ut.td cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of idt.t 8wzti5zd; y y,9uts rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whino /zp(:s ibfaj6q k4*h4-ta ich 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 the bike? Assu: jp 6iht/i4q*z skf4ba-n o(ame the wheels are uniform disks.

  Suppose a solid spherj/)kv0hr f*lqe)+ h sae of mass M and radius R rolls without slipping down an inclined plane staej vhla k)qr)0f/*h s+rting 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 wizca/6 k4x2mu kthout slipping down an inclined mkuc4 a/x6 2zkplane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentumwaw:c(7i9e.ue tch71g4 ij jd of a system of particles changes when a net external forjw:1dcij4e i cwe .t7ugah7(9ce acts on the system." This statement is

  In what circumstances can the angular a2r6vff3m kf/n) plg7velocity of system of particles change without any chafl/ 3na r2gm7pf v)k6fnge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignot b*kc.j81itb; xn3 kf9ah .nzre any friction which may be present. What happens over time to the Earth's angt81.i * kjatxnbk.9;z h3ncb fular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orb: 3lss) bpo2,2;r sjow-fblgl it. As the Earth moves close to the Sun, then which of the followow,s r;b sl:b2 3gflps)lo2j-ing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pn1*;*lj ;fui9 f4gj) vkutx apulling in his outstretched arms closu if)kxu;vj na 1*ft4*;j9lgpe to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performka:tc6 l nzv;2s a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy ac; n6 avzkl:2tbout the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstre(ta48 tiwl (antched arms close to his body. What happens to his moment of inertia ta( w(lt4na8iabout the axis of rotation?

State the law of conservatiovb 1dp4(v tf qg.n.nn0s /mp(en of angular momentum.

  What arc length does the Earth travel in 30 u tgxgolc/a 2b+ j0ommo9fi:uc:l.a three month period in its nearly circul3gtlcjiu 0+ 90:l:m/goa 2 oub.c ofmxar orbit 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. ,0m,j-c6kz ba(gm 8yi rpk.d h What distance does the tip of the second hand sweep through in 3 minutes and 45 a(zj.di,k ,0pm hk6-y mcr8gbseconds?

  How many rad/s is 25 revolutions per minute v* /aw hby z34(gg4fqyy9udp- equivalent to?

  A bicycle wheel rotates xx5-1rj* (qreyu jb,g uniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheej(*jgyb5urq xrxe ,1-l's rotation?

  A pulsar (a rotating neut2n 35 n7ugxcvq6rwid 0y,mb7yron star) emits pulses at a frequency of 0.40 kHz. The period of its rotat7u6nqr 3mbv20 ndw7,i5 gcyx yion is

  A phonograph record rotates at 45 o vnyen :rf+kva4thr;o( :3i.rpm. Through what angle does it turn in 0.20 s?yr +t(non vv3;horfik.4::ae

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the oute mhz0tu xtws f,+rhe2+2nwy.g: blo9,r +z +,,fnob0wygth: m.sre2 29lx htuw rim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. +w mgje4:;wmjl0bh o7 What is the average angular speed of the wh0e+o7j hw;mmj l: gwb4eel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thedw)7npkru n 79aw *ih* linear speea*i77prn*nhw )9k wu dd of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a y/o-n n+ohvb9distance of 6.8 km. The cable which moves the car is driven by a pulley with diam ob9o+v/ynh-neter 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 ang,m yd vd+bu, di02k6tf. q y.:egd1ufxular speed of 2.0 rad/s. What is the linear speed of a pointd b+u.x1udg: f i.y,ed2yk 0,fvdtmq6 on the wheel's rim?

  The cutting cord on a gp2 qatpeu 5x2x) q6yxp7/m5zbas-powered weed cutter 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 end ofbz 5 x)/myexa2xu6t qpq7p5p2 the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.,0m+m:p6.x lyvd ug xw0 rad/s. What is the centripetal accelerationl+y uwx.06,vdm pg:mx of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the+bsav; ).u,h amu)le l perimeter of a bicycle wheel of diam+). uuv;blae s)amlh,eter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stat1c. + 9vc ptdca1p(ebvion (r = 1000 m) rotate to produce an artificial gravity of pa9(pd1v .bct1+vecc$9.80 \; m/s^2$?

  A car is negotiating5/z qy7 n1.y7leqq myzx3 *gcb a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centry qgy1 7ex* .zq7/m nylcqb3z5ipetal 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 , jtx-2 gk,iihflat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) is i xij t-,,g2kh$1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 1-2rh,pydcyr q8 aj v;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 the string is not to bd ,hry;jpy 1r-8v a2cqreak?

  A bowling ball of mass 7.5 kg and radc65y0r; d : dxf6ek xta0kc 9ewum*+oxkdi3: vius 9.0 cm rolls without slipping 10 m down a lane at 4.3 mv; i9 m0oedxkk y:ex *6fcxd5:6 u ad+0rt3wkc/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 conluhu vmzy1( *pdg5m * ;9u;thfstant 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 consta)gn9d v wiek75nt 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 a1mdsi /gfbpxwi4 ig p):/ 0)kr 0.300-m radius automobile tire rotate after starting from rest and accelerd:4pgf) )ix0 i/swm1ibpgk r/ating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest lo +:tj8cs8 ,v1duraptta6l0 , and has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 ra7 +qdmf2 upa l/9xq* utq.7rtwd/s decelerates with a constant angular accelerafq.ua+qdr*7t2wxm qpu/ 7l t9tion 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 6.0 rad/s bg44+wz3xfh..b t- +y j7sufcbm*dz u7n1ftw while turning through 2.0 revolutions. What is the aver4+wjbdhgu7 zm .w-*zfc + f7btunb.f 4syt3 1xage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down u(,n ckd 4d;h6zfl/ joeniformly from 8.40 m/s to rest over a jd,oflez hc4nd (;k6/ distance of 115 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 v4ntlc5g1z( b m/s to rest over a distance of 115 m. What is the angular accelc vbz1n t4g(l5eration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.4i 2a bif,lyb ec0im 9;inc**:00 o vx(doyol9r0 m/s to rest over a distance of 115 m. yocomvb(*lrybdx f:9a20 i0* ii e l,o cn;i09 How long does it take for the wheel to come to the stop?

  A centrifuge in a medicsn6 enp0m8s f er0pi/fnt0,x/al laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to rxnf0se 08rmf,st p 6/i0np/neest.
(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 rea:kg (imk1rri49pk9:qkn s l3quire tightening to a torque of 90 Nm. If a 30 cm long wrench is u9 94:( a qkrskl1igrp mi3kkn:sed, 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 torque of 90 Nm. If a 30 cm lht-3 ):m)fo. we8jgxy5 hvf ewong wrench is used, what is the magnitude of the force required v) .ftj3e ) howfwg:e8xm-5 yhwhen the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia iph7)ka3jxlj9x mz.: f; ycb u8no/2 k$3.00 \; kgm^{2}$ 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 origenl 0+ka-ys6eud/uy; m fmc,,in, mass 2m is at x = a, an0+ useu;mdn k/, feylc,-y6amd, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg ihjkbe87jf- m3s pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 mehk - jbf738j= 5.0 N to the right. A second rope 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-e)yeh05vu9r8psd i rmprs -1 thought the center O. A rope wrapped around the outer radiu-v89sdpu pir5r0 h-m)reey s1s R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around 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 rfhab7lxu1tqz -t 2 4+held in the horizontal-rtt7lux 1hq4 z+a2b f 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 1xvvg6o 97ad 3v ceki(4.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius xdv ev63ak4v(go9ic74.0 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 r4rmg4p irme40 kzwp4n ++ y8mmope wrapped around a frictionless disk pulley of mass 7.07 kg and radiusrnp imm444+ km0mey+4 zpgr8w 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fri5zetj: jculqw 9q/ x6)ctionless disk pulley of mass 7.07 kg and radcq) utj9l5/j qwx e:z6ius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to sh -.tyum.s2wp(8o ydrtore 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 inertie+0s lshl h+crzwnmjob365o 352blg7a 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 an r5.e0lp8yi zo s-pzti7 c9yj9d radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed ofyyotj -ri zli97cepz0s95 p .8 the 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 a speed of 10 m/s. bx/d- xp /fy/*g,se6k .3ie gz3uexsm How high up an inclined plane can it climb before coming to restz/.3bexgm * 6 -sf 3eyx/ud,kgexp is/?

  A hoop of radius 0.50 ixdq d)5 bqq3x)gj)9 pm and a mass of 0.20 kg is released from rest and allowed to roll down an inclined5jbxp qg)3 d)d)qq ix9 plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of masui4:o lhwz:s 8s 1.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 i8h4s: :wlzo um long. 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 mxwi/ qz )o/sgj(6q op,v w;bn.tf*j d.omentum 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*7h unr8osof 9 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 moment1pd:mus3dw( d(o u6:ewhlef, of inertia o1p ee63hwofu,:dmsd ( l(duw:f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?