Angular displacement is usually express in units of .gp)( m2fyps jzk o/9f8.hh bjd1om8(zj5nhp

  Angular velocity is expr l*2u wu,0:8cu mak5skh0i*ll ms srf/essed in units of

  Angular acceleration is expressed in 8krn/,l )dq /ibv-hliunits of

  A boy and a girl are riding on a merry-go-round which is turning at a constant b 3a1ahv-qhckx */v+f rate. The boy is near the outer edge, and the girl is closer to 1a+-b/v ak qfhvhx3c*the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which i eq7dcy-9+xeu (6xvzcs turning at a constant rate. The boy is near the outer edge, and theqc-y 9x zvee+c6d(7ux girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are ridin6-mssxxrtyqt+0,4za .,u jvh g on a merry-go-round which is turning at a constant rate. The boy is near the outer edge.srh6yvtqx at,uj+ 0mz,s4 -x, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridine46id .9k rfz+o)eny;e wlw8mg a merry-go-round which is turning at a constant rate. The boy is near thmr4e8yi;dn l 9ow.)zk+ew 6fee 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---wv- mbkz7ka pi2ar2uy y8j,5 tesm2go-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 greater2z7 rsmt wbai av2j2y5y -ekm,- 8-kup tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is 8/ize:i -.k/yq-u ncws13uqumwsc4 y an accurate stateme.q/m/ns8-c3sw u- uieqw4y1:u z kicynt?

  Rolling without slipping depe; z :o0n1alz :vnee o5enew+p)nds on

  Two equal forces are applied to a door. The first fx*:;h w+w-jsl cuc) w7urxu,:o4 q kjborce is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to t:wqc;rwb*:jj4xs , 7u+) lhw kxc -ouuhe door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the dyc z2m ay l dn)sf0;33rj*paji0yp*sg8j q- r8oorknob. The first force is applied perpendiculas;jlgqcdi203ps)j jymrap z88y an-3* r f0y*r 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, perpendicular to the door. The first /lkm:dm81fvj) y u/ lbforce is twice as large as the second force. The ratio of the torque of the first to the torque of the mv8jb/ kful /:dyl )1msecond is

  What is the quantity used to measure an object's resistance to changes in * 4r7.fdee +nwcqat iqa*5ik: rotatione7adci nw.5rqk4 qet: i**+fa?

  Consider two uniform solid spheres where both have the same diap yq0h/ /x4:cwt j cs:lrjtoy,ywo 6,6meter, but one has twice the mass of the other. The ratio of the larger moment of inertia to c,yh,ctys /pox q0rjy4l/ w6 j6o:w:t that of the smaller moment of inertia is

  Two uniform solid spheres have the same m)8jafv*0siio o(-rj .xj9/ h4aldps rass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere ij/s8fp0 hj(-a)xvj*rlia oird o4s.9 s

  Consider two uniform solid spheres where o /eumc-hxc,: qne has twice the mass and twice the diame q:cc/,xeh-u mter 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 1 lw(r( ljcqg89bxygai2d92 +xu jly:M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about +j (l aggldx9jw 2ub8crxy19l yq(:i2 a central axis?

  If a constant net torque is applied to an object ,orv1*ja sd3x, that object will

  The moment of inertia of a solid cylinder about its axisto(m;u7/y8mpwd)a jg is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic ener am(8 )t puwygdj/om;7gy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which hm;mvlip *v (muc - 3m5x+,),jgfez yvias a mass of 10 kg and a radius of 30 cm. What is the ratio of the;v)uy m,p3-mmfv c,jxiv(+ ile g 5*zm 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 Rk sy k/f 0xdxg* 12*noc v,;vck0yn(qo rolls without slipping down an inclined plane starting from rest. The ydck/00s n (o;2kxn*q*ocv x vk1g ,fylinear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere d3+vx6v8om.e ,zcer mof mass M and radius R rolls without slipping down an inclined 3, vxdvm6e8.em orzc +plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a(p)yv njpeb 8.vaz 28o net external force acts on the systemn )2o8v(vbpp e.ayjz8." This statement is

  In what circumstances can the angular velocity ofv-u:sm; yjkepytem .2 ie1 w-6 system of particles change without any e umks-y y6 ti:2;je- wem.vp1change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any/8q rdjx6yfdui 9b.5l friction which may be present. What happens over time to the Earth's angulr58 f9/d yl bidq6x.ujar momentum about the Sun?

  The Earth moves about the Sun in an ellipt, m a kgh4qk5k-9lsoh9ical orbit. As the Earth moves close to the Sun, then which of the fok- ,shag9qohlkkm 954llowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pired d0io8q bi98ouette (a fast spin) by pulling in his outstretched ad9b qei8od8 0irms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrclm5ce25*f mz4sz mg,v uh9x2etched armccm4zusvmm52l,xghz*9e 25f s close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a piro)sj , i a3*ruu2t,1jiqv7zzm huette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his mome2 jtjmr zus,*i zqu31),v7 iahnt of inertia about the axis of rotation?

State the law of conservation of -no 71cfevhvke+o-cs 56 64 bmamc7u zangular momentum.

  What arc length does w/spot)gy a-y /9/te xthe Earth travel in a three month period in its nearly circular orbit about the Sun w/9-s yx/)/ po twyetgaith 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 t.c, -gnhvhz p.nnj.1lhe tip o.p- zn1lgvj.hch.n ,nf the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per ke ahn g+7ic60y+t,0lag d(me minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is n:ql8o7yc kqj-x dg 69the frequency of the9qycn 8lk-:jq6gx 7o d wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. T1ut6 2ucxrrc7a8s( efql z+c9he period o2z s78+qr ulr9atf(u c6cc1exf its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn4wj vllgq2k ;/w7* gbo in 0.20 s/; olggwjv7qw4 k *lb2?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will mdr f;b -pt7j3a point on the outer rt;dr jfmb3p 7-im move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thdl*j 2-7tihcpa 99s )g(c/ne k:msq xye average angular speed of the whee7dje2x)kncc/q9* -sg 9m hily(s :pt al?

  A bicycle wheel rotates uniformly through 2.0 repp ll.q-yz;i)z-sk 1 mvolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of tlkpy; lp1 -zq.z-)mishe wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whi r c09el++cplnp79nogch moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate prl ec lp0n9c+g79+o nfor the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m w*tmm(09faurg lq-1 iis rotating with a constant angular speed of 2.0 rad/s. What is the 9mafrwl*i1q( 0gut -mlinear speed of a point on the wheel's rim?

  The cutting cord on a gas-p o jk 0 wb(5m87ph(rra+myn-da1* r/qmck4 mgjowered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speedg r 0w+*kb(jr-81naj7 qo d/pymmrmcmk(4h5a of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angulafoe w3 +/-qygfr speed of 2.0 rad/s. What is the centripetalfe wqyo3f-+/ g acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a mcan1a291h 1e2gdvin bicycle wheel of diameter 70.0 cm when the bim 2dc9nhavg1i 121nae ke is moving 8.00 m/s?

  How many revolutions pe5z so*,vxgtf uwx/so3.6ehuurlm 3n jj * 5s3;r minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravigx vu wx zsul35mfu,3r63o.t* js;o*h/j5n s ety of $9.80 \; m/s^2$?

  A car is negotiating a flat cf 7au 7)w,huorircular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force r7wha) ,ouu7f(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 circ;w-rxdi wi;q ww7162qtslr* kular curve of radius 50 m with a speed of 20 m/s. The maximum ceqi7wr w -q2 t ;lswxik6rw*d;1ntripetal 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 to pjl/0ct: d 8gzthe 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 250z/j d:t8 0lgpc 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-u:22 asix sj ds+mr hj5;/jj5yr f9ht 9.0 cm rolls without slipping 10 m down a lane aty fh arui/r;5jx+jds tjj-sh :59s2m 2 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 3cw) stx 3cyi*lh-un5acceleration 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 a4c i0cbkmawiu46 odxvh+567 ry/.wql 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-m radius au cbclk.tih4yksl+ 3/dg,fd5d/x+j(r tomobile tire rotate after starting from l3,(chc5jigddt.klkyfb/s +x d+r/ 4 rest 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 haf; zadzy4 y2+z1qhlq5* nq np9j08nz cs 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/ rm/va 8d7z(8v fnj-ijs decelerates with a constant angular acceleration /jjnfr iz 78dv-8( avmof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from e 1skcf54mx/n1s 1s(fyok v(s rest and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the aver4 osenf 1smfcs(k/1v1xsy5 (kage angular acceleration of the wheel?

  A wheel of diameter of bpgf y6 (3v /puay01iu68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of rev0yb6 p1ui (agyp3u/ fvolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.-7isk6:lbc dsz0mb 9 h40 m/s to rest over a distance of 115 m. W-zb7sm cks dl9i0b :h6hat is the angular acceleration?

  A wheel of diameter of 68.0 cm slows fh552z pag 6wcdown uniformly from 8.40 m/s to rest over a distance of 115 m. How long dpcf5 wza h5g26oes it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotations9k74 4n n ns1lpt+k k/pdq(zlal speed of 3600 rev/min. When switched off, it rotn z+sl k/n4d14k7pp9( kls ntqates 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 red,:7v h( qdrhequire tightening to a torque of 90 Nm. If a 30 cm long w: d7vrhqhed(,rench 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 t90hq:.b fvede o 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 .9q0h bdfee:v $53^{\circ}$ to the wrench?

  A wheel with moment 3,:nq0 w q 0rku,pzywbof 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 origio/et1ikh8+h fn, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of i+8 hetko h1/ifnertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought jlco 47a(ll.kfje z +sru5*8d-ddk5z 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 of radius R2 = 0.50 m exerts a force F2r7jl5eoa -zddf+*u k.j 5c 8(zsll4 dk = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 ke *f x)wyw9/kc)eenw t8:s;mmg 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 of radius R2 = 0.50 m 9ks t;/ywce mef*8w)mwen: x) 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*. -r/l9wj (e8dtmh jyll1iz e 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 i rllej-l*i/81 .( eymh 9zwtjdnertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be:3 felj 7fds-r a ring of radius 30 cm and mass 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 wheel achieve, as e-3 sfj:fdrl7suming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped anli 3*es(l0ks round a frictionless disk pulley of mass 7.07 kg and radius 6l0lnsk (*ei3s6.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frwhleq)62 :dgz/lcig j;gvx (0ictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the massdw6:g jcqzg/h2 lex (gv);0li?

  A rotating flywheel can be used to store energy. If it is required ty 0(p cabup(u( -dncxa3w m-r+o 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 i9mxyq2f0 d*t inertia 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 rew7s w wm ,5d1abw72qtbst and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plaam2wb,7b wq5wts 17w dne?

  A solid sphere of mass 1.0 kg and radius j zk2aw2)a;pp5a q :l hps(k8h0.010 m rolls with a speed of 10 m/s. How high up an incli 2papkwl;a85) k(aph2sjqh:zned plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released qt/ga.+ kae.los5f/mfrom rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance q sgl a/tem5.+ko/a.fof 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolljiq 0t7 xu p7w3a.o.o7bp2mjbs without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia o i0.77mu7pj3bw qj.ox 2obptaf 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 changes by my5 pl cp5pb3h:j(h7m$20 \; kgm^{2}/s$ 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 m1.2h i.o v0dei+6sztf9l f,y ;lmjd rnoment 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 u7 gmg f6s 2(emb8jpk)jdmy)ct76p e 2a moment of inertiagf8 ps2)g7yj(ee mp7td m66ku bm2c j) 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?