Angular displacement is usually exprs n2cm ;) ls;yyd3dhianr++k,ess in units of

  Angular velocity is expressed in uni t.*bn1(mdtl jin o9)cts of

  Angular acceleration is expresse gisac;)8z33y y:gux ed in units of

  A boy and a girl are ridin(3wb3 n6ejgsz g 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 cebwzjs3 (n ge63nter. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is ttw/35 ,eytc d u3kk+zburning at a constant rate. The boy is nkwyu5t,dk ze3t+3 / bcear the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding oqqw6xdd dw3x;: rurj1r. +yo/n a merry-go-round which is turning at a constant rate. The boy is nea r ;qd:wdo6r1qyr+x.d/j uwx 3r 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 7. 8iboj d,p xiqvk 29(wt:qjgmerry-go-round which is turning at a constant rate. 8do2ivx (qji7 j,b9t:qw k. pg The 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 riding a merry-go-round which is turning at aj-p7me x lzi a. qq)zfzrta7v338t87a constant rate. The boy is near the outer edge, while the girl is closer to the cent7 3at3 7 ae8) tq7vqm.azi8 pzzjr-fxler. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatin 00+imswqtt4a g. Which of the following is an accurate st0mqtsa0 w+4i tatement?

  Rolling without slippgdfie s+stsv f2; g 8v7(w+s.ning depends on

  Two equal forces are a hm * zq4v-qt9sfl5e8epplied to a door. The first force is applied at the midpoint of the door; the second force is a8vl-q*e 5h4f qt z9esmpplied 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.;gbpi1 atx l(v* njtw3( ;q *njqt0m(zao*n0i 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 greatem g tx;*z1v;*ab0((t0*lq inowjnq3 apint( jr torque?

  Two forces are applied to a doorknob, perpendicular to the dooqd( 2eummo: 6tr. The first force is twice as large as the second force. The rati e t6m2:doqmu(o of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to ch vzor-0(vt*8)cblzp 8rkqdy s;e,s: s anges in rotatiobdc zr z)(pke,:yrtss-88;l*0 vsoqvn?

  Consider two uniform soli5+cvdxyau d0fj :q/5xcs a*. dd spheres where both have the same diameter, but one has twice the mass of the other. The ratid./x5*0sf5cu jd avy:dx+qca o of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mas e3l 2zy(/aely 4saw3w3ambd2h 9hpl-s, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the slha( e2l3zpy a-h4l w92y3wmb3e/asd maller sphere is

  Consider two uniform solid sphwxbn 85(5w wjgeres where one has twice the mass and twice the diameter of the other. The raw8n 5gw5x(j wbtio 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 (pa(-s 4w -rql: bpx1hua v9bh+je kf0are increased to 2M and 3R, what happens to the sphere's moment of inertia abo(eh ubh(-xp+kw a4pv9jq b fa-ls :01rut a central axis?

  If a constant net toz m/tmoms s803rque is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis c hlwtr-2ky-ayp(:acouyn,r.-/v y) is given by 0.5 MR2. If this cylinder rolls without slipping, the ratic2la -.nowyvcy)rpytu /r-,y hk :-(ao of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheemog5; 53dlib(i8 o ui2w :etjhw9oe .pl of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of .ob(5oi85u egwtholjei2:i3p wd m;9the rotational 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 r2vpkb*46qfo kp6)s9 e kpaj1:gu+ jleolls without slipping down an inclined plane starting from rest. The linear f)bjupo* p:pk41keq es9j +alvg k266velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down ann2 +8kx etb8ho inclined plane starting n ot8+b ek2xh8from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum, ofues+iys+ p as0y(.x q30bm of a system of particles changes when a net external force acts o3+ums0 qyyesis,+a 0bp(. ofxn the system." This statement is

  In what circumstances can the angular velocitm-pf+*- s8aum/s lvso y of system of particles change without any change in the system'sv8ss *ls/om- mu- ap+f angular momentum?

  The Earth orbits the Sun in an elliptical orbit. I8(isnfbc - )fv/m*vx xgnore any friction which may be presemb*) vv sf-cx8i /xf(nnt. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical t+zhbynxn88o 16 gctn/1 kx6oorbit. As the Earth moves close to the Sun, then which of the follow1y+t8 h zon6b 1nk8cg/6x nxtoing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretcnsy24ode :xhu m/d, tep32v, khed arms close to his body. What happens to his ang v 43e2s,2 d,hyd:em xtnupo/kular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hisi6 4l3+nsokb, k 8a ym2po,mcv outstretched arms close to hcinav 3b syo4,k m8+6m, 2kolpis body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette 0iuy+ztou2cde g k, 18:ka6jo (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotajc: 01 otez8kdao6i,u ygu+k2tion?

State the law of conservation of angular momentu ,s1ij uc5aee. l(ewi-m.

  What arc length does the Earth travel in a three month8p93umw5mye9nuq h z*a 1)et l period in its nearly circular orbit abl e91w) myhapm u*un9ezq358tout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a le6 qr 1tva ;fbqg4z4xe:ngth of 0.30 m. What distance does the tip of the second hand sweep through in 3 qxb far 41zg:;4ve6qtminutes and 45 seconds?

  How many rad/s is 25 revolutiovywn ww-qg: :qg2 zs04ns per minute equivalent to?

  A bicycle wheel rotates uniformly thrw-z/vxwa1 v+*jptsc8 ough 2.0 revolutions in 4.0 s. What is the frequency of the wheel8*atsw/v+- wv xj1cp z's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencp /zxc:wl z4a+y of 0.40 kHz. The period zzlx:4wpc /+aof its rotation is

  A phonograph record rotates 32f zrty,1t lrat 45 rpm. Through what angle does it turn in 0.20 srt ,3ly t1zrf2?

  A wheel of diameter 26 cm turns at 1500 rpm. How fave .q( + 8de3bzh;o6nnz +ec;r/xl7nr2 uze str will a point on the outer rr28olce uev/te d (+s +rbzqhzen ;6n;. 3n7xzim move in 2.1 s?

  A bicycle wheel rotates uniformly throgs. +val efyc9neq 7,q*r /y3yugh 2.0 revolutions in 4.0 s. What is the average angular speed of g7qyf3/yny le. 9v qcs,+*ea rthe wheel?

  A bicycle wheel rotates uniformly through 2.0 rek:gwqy7p,t(;ns ;a3 y5gxo v(pvx d7jvolutions in 4.0 s. What is the linear speed of a point 0.10 m fromgyx;pd 5wkyxt;j : 3v7nq,(s ( 7aopgv the center of the wheel?

  A cable car at a ski resort carries ski ;wka lqsr)6yv) 6y+aiers 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 v+ky; 6i))yq 6ws alarminutes?

  A wheel of radius 1.0 m is rotating with a constant angu1x 3zt5dcs9 yvlar speed of 2.0 rad/s. What is the linear speed of t3 s5 z9xc1yvda point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If thzw)i-7hbyw:a*er0 dx e(p3 cxe motor rotates at the rate of 20 rev/s, what is the approxraw0ex pb* e-c d3:ywh(zi7)ximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed oft kva1* nsp9t-c vtb/9p8ub aua8 fe/9 2.0 rad/s. What is thtt9- * 9ant k v/a/fp 8uvsp81b9beucae centripetal acceleration of a point on the wheel's rim?

  What is the centripeta --a/kduue6pp l acceleration of a point on the perimeter of a bicycle wheel of diameter 70upd-e- /u a6kp.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stat houhecjm 327 16a2nk 5n,j:h+f fbrjiion (r = 1000 m) rotate to produce an artificial grave7 :j6u,jmnfk3 oh a r2bf2n5+hhicj1ity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of rad3* pic* zg/pxdh+td/wius 50 m with a speed of 20 m/s. The maximum centripetal force (provided*w+xpd 3 g*cpt/ih/dz 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 wi51*cxmhq.lqry b. v+ nth a speed of 20 m/s. The maximum centripetal force (provided by static friction) rhql+mv ..1cxb 5q ny*is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the endbvph :w;xc-g) of a 0.750-m string, is whirled around in a smooth level table. If the maximum tensi;-p cwv)bx:ghon 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 j-:g rz8hwcju4m.ye2 and radius 9.0 cm rolls without slipping 10 m down 8.yjre zjmwhu: 2gc- 4a 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 constant angular acceln u84qdhj4;uwxy :xh( eration 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 +vqrb41l3fpxh(e o i ;/mrl( rwith a constant 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.ovohh :bfwxt*4vkq7p 6f-*-b (s plc5300-m radius automobile tire rotate after starting fromfk( -wfq v 4p6lphxbc h-7so:5tobv** rest and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rei ;1i0(vjbq++x3p pz:rb y 6 1e8dnzux:a ikjgst, 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 rad/s decelerates with a coq:-i, dxz 8w lfhjt-)dnstant angular acceleratiowfz-dxjt8hdi l): -q,n 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 tgl )4z)8 g7u7hhap6fmsn gv0 speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the whee68lh 0s pfn tghuzg 7g4av)m7)l?

  A wheel of diameter of 6.5mfxi+vn t -b8.0 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 rotates in coming to rest+fx v b.5n-mti?

  A wheel of diameter ofj(3ze 7s0xlg t 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accelerationt(l gexz370s j?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over ke1c3gew i8dp38i p 8ja distance of 115 m. How long do cgp8e3j1dik88epw 3ies it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotationalwvmg, qd o5j3h 1 8swp1gr:de. speed of 3600 rev/min. Whenpv r3 ojw15wde:, s8gdhm 1qg. switched 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 90 Nm. If au lpu6gdp9o) :jeu3i w(c6moyd; *: aa 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrenc m*j3p pucue6 :;go :9ay) daliowdu6(h?

  The bolts on a car wheel require tightening to a tzs .w/0zm d-wl qvp;x0orque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forcx0.-z ;zvsw/lq p wd0me applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiaoqx)td, 9r( k;w i2dns $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeledu6m tq, 1pl*lf as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the t,p l*6qlfmu1 origin?

  A solid cylinder of mass 10 kg is pivoted abod02n24arwpbyf 4fjn (ut a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, ex way24nd2ff(0 n4p rbjerts 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. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of maqn4 kyo- o) yfrani 322vag/2ass 10 kg is pivoted about a frictionless axis thought 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 rope wrapped around another section ynk- qaaooy)/ nr3g favi242 2of 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 iss- efu8:5f bo w;1vesg hinged at one end. The rod is initially held in the horizontal position, and then released as thefobfs5v-su:w;e1eg 8 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 5 ,vgjf;csq .vmass 1.5 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 wh ; .gv,qfjvs5ceel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley ofxkc3 pg 26u9;kdxzqi-y3 v9cb mass 7.07 kg and radius 66.0 cm. What icuxqp 9b3 k6gxdi32-y z;kv9cs the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionl xt:+ uccvf;d,xy x38hess disk pulley of mass 7.07 kdx:c;u+ 3y8tf ,vxxchg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required tqd6 dki3 )*xblo 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 i6 t m+h(x37 tibkeckw6r.w +sunertia 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 rest and rolls wi u 4lcovou;72othout slipping down a 1.0v;7ouoo 4l2uc-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.enx-fs/jtp ;;ig(r e+ 0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb befe;r -pe(t;+i/sngfx jore coming to rest?

  A hoop of radius 0.50 m and a maso,yow , a+2n3y3. g v7ffhqp4l ajn+)qbqf w-rs of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertic+-2pqwn .q f,fjoyayg 3,+ vl4)ohwq7 b3fnaral distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls.0a::ev;q1s0 0pqjt dea qfk9mj6b ys without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The momqe qtya0kvq:0;pmf bss96ja 1:e.0jd ent 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 change t)z l/blq2z) 3qqu+vys 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 mom /i-nwbw91wdb 0h6eccr6 ;bfo ent 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 l w4mahga6) h b1vx58gextended has a moment of inertia x)h6a4b mv ggwh1 85laof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?