Angular displacement is usually express in units of a1 o/186e8 tfyspsf-rl(qada

  Angular velocity is expressed in u/8u;pr ibyq9wb. tz b8nits of

  Angular acceleration is expressed inc zdaesg 5o-ys yor1x8 p9t4 87i;rpa7 units of

  A boy and a girl are riding on a merry-go-round which is turninum)4- rb8b 5)zvg3y .3m wjjax6rrjp: hkua 6xg at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angj8 )x)hxbky43gbm6rrupu6 j5a- jz.:3wvra mular displacement?

  A boy and a girl are ridingmudn i:;o)-5 ex sfs7r on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, as5 ufr n)oi e-:7;dmsxnd the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merru2ae2i, gqf5 t6wuiv3 y-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to thewaq5ifu gu2e, i3vt62 center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant*+mm o r/jrk:t rate. The boy is near the outer edge, while the girl is closer to the center.t:mm*/k jr +or Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is /: krvy80 orsqsi7y: co* qkx4turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential ac o :ksir:y4c/sk8q*0voxy rq7celeration?

  Consider a rigid body that is rotating. z*ift clo);w 7 Which of the following is an accurate statement?)z;t* floc wi7

  Rolling without slippincqka8.o s95deg depends on

  Two equal forces are applied to a door. The first force is applied at the miak71c5m:hbuve+n:l g - q*levdpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicularq - n+c5:e ak71*luh m:elbgvv to the door. Which force exerts the greater torque?

  Two equal forces are app3+ wnvlhzsar;b-7u e txoe 846lied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 3 wtzru elno;86b-v 3he4xs7+a0e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied trz1*0w v5 bkulo a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the z*bkr15u 0lwvfirst to the torque of the second is

  What is the quantity used to measure an obje3kt1+ hq +oyvx-e5a.cx g p*a+ dshdj7ct's resistance to changes in rotation?yg ax3-k + vpj*ax7+h +o d.s51qhetcd

  Consider two uniform solid sphere*l6h0g6jm u*r aj mxezs3 ri27(qh+ wns where both have the same diameter, but one has twice the mass of the oth7jnu* mqs2e *r agl6h3(r+ 6z0 xijwmher. 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 j9hutp04vhn9g ;lzp1e:( c rd has twice the radius of the other. The ratio of the larger sphere's moment of inertia to thalch pr:949g0he tz(p vd1;njut of the smaller sphere is

  Consider two uniform sol gj,k o+i3k5tnid spheres where one has twice the mass and twice the diameter of the other. The rat k j5tokin+,g3io 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. d.; /ubfqxw4zo sa -9yb8 f+bx If these are increased to 2M and 3R, what happens to the sphere's moment of inertia aboqf+wb8 .94oyb/fxzb-as xu ;dut a central axis?

  If a constant net to5 z936edaxjbqrque is applied to an object, that object will

  The moment of inertia 7r3gjqrj /.nz of a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rota.q/r 7 jznj3grtional kinetic energy to its translational kinetic energy is

  Consider a motorcycle bl d y3/s09s(tk1y.qgmuee 5 fof 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 kineticbef 0qsemd tuk9 1 g/y3yl(5s. 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 andhvf 9/ytr;h9r radius R rolls without slipping down an inclined plane starting from rest. T9 f;rt/ yh9rvhhe linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping dowt oid; 2e*j7+q7gacdpn an inclined plane starting from rest. The angular velocity of the sphere at tto 7ji2 7c+ga*dq ed;phe bottom of the incline depends on

  "The total angular momentu n z.swp,..dhem of a system of particles changes when a net external fohd e..s zp.n,wrce acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles cv)pthi*kz) +8vfbz whv92 e/ohange without any change in the fk8)+*i bvo)zvtw 2p/zh e vh9system's angular momentum?

  The Earth orbits the S edt10f+b/3 dhhkst y-d-;eh nun in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the S-/n- hs0dtddhy f1tee ;bk3h +un?

  The Earth moves about the Sun in an elliptical orbit. As the Earth move 90hg2sgf bs 9gun4qb(s close to the Sun, then which of the 2g9s409bgnuq bf(gsh following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by ;xzv9 2xv ,0ckbl8 ba7 gx,maepulling in his outstretched arms close to his body. What happens to his angular momentum about the axis 8x,v mcz , abe;9gl7axbv0x2 kof rotation?

  An ice skater performsvjj(rnc .- l+(vo /dyq a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotatiov(-.o(j cq vylnd+j/rnal kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstret- h8l7;8 6vtzvuwza3 qcek7nuched arms close -;3t7lqw 67vv8u az8uzkncheto his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of oebo6 ya,ck8jlpd 4uqe89; a4angular momentum.

  What arc length does the Ear1imuirf okjq2p:+ +s ;s2 5oebth travel in a three month period in its nearly circular orbit about the S+s2p2q5 o+ifobsij1u;:m e k run with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the 4)i 7ej 8-6n krtiimtitip of the second hand sweep through im6etkti nirj-8i)7i 4n 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute (k mttk;exkh r rd*h: *zx2s47 9o3aqnkng l17equivalent to?

  A bicycle wheel rotates uniformov)dcntc) x9 0fk ;gi5ly through 2.0 revolutions in 4.0 s. What is the c )cgvo0df)ti95 k nx;frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emit7u1-3ewa bluq s pulses at a frequency of 0.40 kHz. The uaw3ubqel17- period of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does egaskvu. ge +. /rbpur b1(-v/it turn in 0.20 s?bu/upbger .r(v +v-a.k gse1/

  A wheel of diameter 26 cmy( kez lrnfqq4a0.znse2/.z:( ikqx . turns at 1500 rpm. How far will a point on the outer riy 4sz qkqnl nfkx e..zi2(e/0a :rq(.zm move in 2.1 s?

  A bicycle wheel rotates uniformly thr( ezj ,g,weh8xough 2.0 revolutions in 4.0 s. What is the average angular spwgz,(e8e jh,xeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. h4z jeom0ulilj .m 5s,tv)-yid*;c2p What is the linear speed of a point 0.10 m from thsc ij - ) upl.0vmem zt2j4yold5*h,;ie center of the wheel?

  A cable car at a ski resort carries skiers a distance m wmhj8fh:0 s0of 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 rotshf0h8w j:m0m ate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating wi f: psml1*beyqru+d;zy fbki+ 4* 6ce2th a constant angular speed of 2.0 rad/s. What is the linear speed of a point on te :zcribk+f4 +s 6ely*bfd qym ;2*pu1he wheel's rim?

  The cutting cord on a gas-powered wed3h 1d 6xkrvm wo:crzf0;x/ w/ed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approxkr 1/cz odx;3:f x6d/wwr m0vhimate 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/rr -jc hxac,.k pu+j,. qzzygo43 9cf/s. What is the centripetal acceleration of a point on tzf3o9cc, .h ,pj/ja.4 c-ryqrgkzux+ he wheel's rim?

  What is the centripetal acceleratitu cw0gn 7+vlv8wp;y0on of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m/s? 80u l7ypcwvtg+;n0vw

  How many revolutions per minute (rpm) mn. kvsy(2kh uts3h)3q ust a circular, rotating space station (r = 1000 m) rotate to produce kv h3.ny3kt(suh 2)qs an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flo7zmw 5 m ,so t1*amjx1;xo8 s j7o*rdh:0uxqoat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by sx,max0zm * o5q s8*oomxj7swuj7 1r;od:h ot 1tatic 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 wy/: xezx zaa;y 44v2ugith a speed of 20 m/s. The maximum centripetal force (provided by y;4 z /2yuaa vz4ex:xgstatic friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to 1xpdjl fnxo*1, :t 8exthe end of a 0.750-m string, is whirled around in a smooth level t dtx1xn* o lx1,e:pjf8able. 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 radius 9.0 cm rol 6kexi/ xyk2x2ojug+97 j ph7xls without slipping 10 m down a lane jye2/oj+69px ixxux h77 2kkgat 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 j:juz:,avz; lwith a constant 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 wi)op9f cqgr33m:us: c kth 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 0.300-,o o4rdi;cmq1g9 ef s2m radius automobile tire rotate after starting from restrm2o f14 dg9 q;s,coie and accelerating 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 ang78 azvikwrwf45zy98 t ioy dr8 n08dde*hv5+q ular 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 constant anh rw1yz,u v7)6k2su4 w kgzy7nh;uax 4gular acceleratio6u zzruy72ysuwxkkn g14h4aw)h7; ,v n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest aj5f3zg1bi /glhm/ / uqeo40iwnd reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutionsi ozmwhb5 q1j gf/e304/u/ gli. 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 er pud+7 x;xk;nnn)f)to rest over a distance of 115 m. What is the total number of revolutions the wheel rotatendkfenu 7pxx )n );r;+s in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniforml / iq) kya*zp0k4v.woo5i x+ady from 8.40 m/s to rest over a distance5 x+a) 0awkpoio4qi /zky*d.v of 115 m. What is the angular acceleration?

  A wheel of diameter of 64xoaqrh s5)8n 8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 118nqrh xa s45o)5 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotw* on*hd-xx / g;veh2x7pr 3koates at a rotational speed of 3600 rev/min. Wd3r7h ngpe;x xv* /*w oo-xhk2hen 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 torqroa1e*d qb 1b n 694-pe,vfyvaue of 90 Nm. If a 30 cm lon6 f9vy* -e podrnqavab1e,4b1g wrench is used, 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 ;t:xntj.9 ,mwfrh p3 r h qraad(ifn3-. fvz4;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 at r.qnrxvw3p3;:dahafn-4(9 th r.f ; ,mjifzt $53^{\circ}$ to the wrench?

  A wheel with moment of yx1 vgqy6rk5 7dglu9 1 dc.l1ef;iwl .inertia $3.00 \; kgm^{2}$ 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, mi2e+ zj1.b(.ahg lozl ass 2m is at x = a, and, mass 3m is at x = 2a. What is the momeh+1l gl zj.(.oa 2eibznt of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought;g-u8dbvgnqbub a /46 the center O. A rope wrapped around the outer radius R1 = 1.0 m, bnug/q b6ud8g; - bav4exerts 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 mass 10 kg is pivoted about a frictionless axis thoughtn-c i6af7n9l,tydz+h the center O. A rope wrapped around the outer radius R1 fa 7dl, +n-yt96ichnz= 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 hab o era889mpeeuo.9-d0rn k5eld in the horizontal 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 a-e89aeun 0mbe8pr9o5kd ro. about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 306cs:- 8kxpc.+6s9qd wk,ttigxc 2y dd cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of2,ycdp-+ic9 tk6cxs ddgt:s6qx . 8wk 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 w. c *2 jjubd1,/fdrpmarapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerat ajujbc2pd1drm, *./f ion of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around hc os-04 3xipxh 9o,wob)ek+,k+ sog la frictionless disk pulley of mass 7.07 kg and radius 66.0 c-h ox,3s9k gchx++ kop 0oelwo4s,bi)m. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requix+g 57ee8kcvdpi0 mk8red 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 of cmg0tp+lami ,z l t/z.36gak/ $5.00 \; kgm^{2}$ 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 enl1 7i;0cxo 1gil0qkfrom rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere whl07q icgexl0 n;ko1i 1en it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls yh,zqlwdu7 - k(cx.,sr8rrn: y)2rvjwith a speed of 10 m/s. How high up an inclined plane can it climb befo8zrx h,rj):l( c7y rnwvqks uyrd2.-,re coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from resz4b85 pu8p3b tlnzcd+t and allowed to roll down an inclined plane. How fast is it moving after+u bpz84 db3 tpl5ncz8 dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radiubjqyhe8jju:ho wh /k)ps;rsj.6*u8(pu w 5 0as 15 cm rolls without slipping down a 35e injp/sopbkh;hujs 68rh.) *u(a :w0wj5jy qe8ucline that is 7.0 m 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 momenc(9p3rywf* h ztum 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 mogz1hkn)z4vi rs6+ k0 tment 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 moment of0s a5phn6 nt cn3kdh w;p4 kl5bwuo7+- inertia hwl +ntb4 nh5c;okunwd apk53s-76p0 of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?