Angular displacementkd *rp++ p )dgh(r7lgq is usually express in units of

  Angular velocity is expressed e-y; r*mjhu3gin units of

  Angular acceleration is express0 5n/b,cdsmxp2t ( w texqp(-ded in units of

  A boy and a girl are riding on a merr mxz7f(hdz( xk/r4ce :rae8(ky-go-round which is turning at a constant rate. The boy is near the oudr/4e(7x:zxa(h z ck (fr ek8mter edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turniad*pzwjc+30 ja p u6bbl.x+jbau:x9* ng at a constant rate. The boy is near the outer edge, and the girl is closer to the cj+ *6azp9x*balj. uxa:3b p c+0dbjuwenter. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-roundtwc qp7w0 .jr1 which is turning at a constant rate. The boy is ne.wjq w1c rp07tar 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-go-round which is turning at a constclqn3vc :ige3 )tq,:c ant rate. The boy is near 3cqn c)lge, c3iv:t: qthe 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 coaxfwn360 qa5l840mm nhajt3 gnstant rate. The boy is near tftag 8n4nh maxqw 6l 33m005jahe outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the follow0rlmrt f 8p9hob9 (hz5ing is an accurate state( lozrrh80 f 5bh99mptment?

  Rolling without slipping depenzcywl3eszs: 59e-m., e(utpsds on

  Two equal forces are applied to a door. The first forcezi8 d(r(z0ufb 08mapa is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are appbir(z(u00 pza m88dfalied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door atgyrq41va 26)h mwuw5q the doorknob. The first force is applied perpendicular to the door; the second force is wv4m) uw 5aq 2h6y1rqgapplied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to v 1t5ombp*x l8 .c4.c/ytlhnsthe door. The first force is twice as large as the second force. The ratio of the torque of the first to the v c hm t*8sn.yll.b45otx/cp1torque of the second is

  What is the quantity used to measure an objecqm3 lw3:dr/szt's resistance to changes in rotatiqsl3/:dmr w3 zon?

  Consider two uniform solid spheres wherd dintr.b6,:ze both have the same diameter, but one has twice the mass of the other. The ratio of the6drb:tndiz,. larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice.lstkg4w/b8 3 ad 6lsq the radius of the .tb8l4s l wsk3agdq6/other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where onezae nacf-od gr:0:hm . dx:.eg +fx,8w has twice the mass and twice the diameteegfh0d .8gc a zrn:x-,::.o+maf wd xer of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere hawj8+1f* azpn bs mass M and radius R. If these are increased to 2M and 3R, what happen1 an+pjb8 wzf*s to the sphere's moment of inertia about a central axis?

  If a constant net tor 5-loe)bqch r4que is applied to an object, that object will

  The moment of inertia of a e6gyns4gtvxp/65cbf ig,e k) o d* f,.solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic ene4g*6 fits e d. v)pybgxk 5,co/6ge,fnrgy is

  Consider a motorcycle of mass 150 h+ 5crvzf 5 p/ifh.fo5kg, one wheel of 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 kinzho fihp ff +5rv5c/5.etic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of smqz(twcfbu;8 1g )g 8mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the spheremg8g ;bf)(c s1wu8 qtz at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down f ppj :3sgd/c9qt*lfseu v f,2 -h7,tian inclined plane starting from rest. The angular v/9u,*2hv c:fstq fi3fled p,p g-tj7selocity of the sphere at the bottom of the incline depends on

  "The total angular momentum ljkk:ux0g,8/ixvh7p: ey:wp:b a r .j of a system of particles changes when a net external force acts on the system." This s rpi:bvg/j e8yxxu:,wkkha p lj7:0.:tatement is

  In what circumstances cr.tlmy4 fynl hu71.6c6*sh naan the angular velocity of system of particles change without any change in thhn.hn1s*u.6y6y4 rmllft7 ac e system's angular momentum?

  The Earth orbits the Sun in v pj/t3dexw 7hz*y4v ,an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the d7yzt*vhw,/pv j3 4xeSun?

  The Earth moves about the Sun in an ed4yi y -/s k4tpn2tej4lliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earthyp442dj/yei n 4-tkst about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hihey06x2cmt+*h*bc2ascj7icn/ nzt6 s outstretched arj2 htmaxn*scy ctb+20h*/ 6zen6c i 7cms 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 pulli p.5vxe4 e3ixvng in his outstretched arm v4ipvx3e xe5.s close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (3omu tm tt)fq7o/hh9s4-g g. da fast spin) by pulling in his outstretched arms close to his body. What happemt t9m.h-7f q 3oh/utgdgo4)sns to his moment of inertia about the axis of rotation?

State the law of conservation of angular moment3utdq 0irbfd:bkq0ao /z/nb6 h 0t6l5um.

  What arc length does the Earth travel in a three month period in ip/0lxkq5vf 2 ,*jkhv kts nearly circular orbit about th02k fqph*x/l jv,k5kve Sun 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 thk 4qpdnv7mj.g37ykm9t-e q/ ke tip of the second hand sweep through iny3j7. 9 nkt eq kmq7/mpkgv4d- 3 minutes and 45 seconds?

  How many rad/s is 25 revoluti4fv)p t o(a5-d1gs cewffy 3/mons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. c1fp r-:n)u/g nh-+coz:zdkl What is the frequency of the whn:)zrkp/u1n f- g-+z: h ldocceel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of sut80pp3 pb:oo4)dl n0.40 kHz. The periodp4tpo0sdn)lo :3u8 bp of its rotation is

  A phonograph record rotates at 45 rpm. Throuhv;r b jqdh*oa07 7:gegh what angle does it turn in 0.20 sq;hhgre7 0ovjd b7 :*a?

  A wheel of diameter 26 ,o+i/n aqi/9eeay v-vcm turns at 1500 rpm. How far will a point on the outer rim move in 2e9qvav,ieo-y/ n / +ia.1 s?

  A bicycle wheel rotates u(;hwv dx; kur:niformly through 2.0 revolutions in 4.0 s. What is the average angular speed of v;;duk x:hr w(the wheel?

  A bicycle wheel rotates uni roh.uv d(q39:zlp yc-formly through 2.0 revolutions in 4.0 s. What is the li(od lv yhq3cr -:pz9u.near speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a d;f+ o;oy wyhld1ux8 u;istance 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 triw ;yud;1o ;8hyulfx+op in 12 minutes?

  A wheel of radius 1.0 m )cj nx24xx 1sdis rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a poinjx)d4 21sxnx ct on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If :3sw8 1vip p**d(2ytrfx zaywthe motor rotates at the rate of 20 rev/s, what is the approximate linear spetw12z3pirwsva* p: f8*yd x( yed of the end of the cord?

  A wheel of radius 1.0 :agn--acpe/lk e6m -qm is rotating with a constant angular speed of 2.0 rad/s. What is the k a6pqnee/g- -l:mac-centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration owzi(d dyda uzix6* n 7w53p,7yf a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moviy6dau5x wz77zy(3i*dpwn ,d ing 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, r+ tw6fltuws r5a/7m1 ,vuy42a3n c zoiotating space station (r = 1000 m) wmv,z 73tl 4ytaf oawr2n/+51uui c6srotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of rad79u np1/bvd9aq e( cg ww )7;zk(rsrevius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fricti e;v/ wvz9g s()d9 rqb1e ukcrw7pan(7on) 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 spm b-arl2t7bxy m p4-;xeed of 20 m/s. The maximum centripetal fo xxp4 r2;-mlm7 bb-yatrce (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, atta)g9qkrc6 c3 *5 sivsriched to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum*s5)9 qisgc 36ckvrri 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 rolls without slipping3t 8t6:u oncjfzbr7-c 10 m down a lane at 4.3 mrf : z8ctt7j3nco6 u-b/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 acceleratioa:wgxy b gq5lx81cg;i ;h ,j,on 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(yftovtnmj.+1yn/y / 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 automobile tire rotate after starti w(h,vj;mtn n*ng from rest and acceleratint n,(*hv;wjm ng at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest6s7c +tf7gno /gt)c+ uqao bo7, 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 witr0 ds1 p(+jz yd((zl: psnb5snh a constant angular acceleration o0( ysj nn5ds pz+(pbrzd :s1l(f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0(v*4s2otci vy *+sxst rad/s while turning through 2.0 revolutions. What is the average angular acceleratioo* ( vt+s2xvis4 tc*syn of the wheel?

  A wheel of diameter of 68.0 cm slows down unif k szs4:-bvj(b6lt6us ormly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in co6kss (jb z:6b-4 vusltming to rest?

  A wheel of diameter of 68g1g +r z0j 2-g ,5 k+9udkvmho-dvsslf.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accelehmsf1 s0z2 jd+k5lvo k -g-gu+r, dgv9ration?

  A wheel of diameter of 68.0 cm slows down uniformly fromo bxz+f90pvh- 8.40 m/s to rest over a distance of 115 m. How long does it tak0oz f-xhbpv+9e for the wheel to come to the stop?

  A centrifuge in a medica afob0; .thd,jr3csvv +u2-fll laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotat; sd- ofbt2uc3rhj0 v,+ afl.ves 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 torquebct;,2r 3 wrlh nd/tq1ae5 1ts of 90 Nm. If a 30 cm long wrench is used, what is the /h1t nd lc,1ra;tbq5erst2w3magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque1jyb,i /y yt6a8my *fb of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force applied at ybi8y j,f1b6*ya/ym t $53^{\circ}$ to the wrench?

  A wheel with moment o8:s4z )qt9s vt; b.bv -cwxih6da9qbuf 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;ymd8v7 nudi3 origin, mass 2m is at x = a, and, mass 3m is at x = 2a. i7nm;udvy 8 d3 What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg idfbg9)p7 isc 30tu7 iis 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 secodtgii7sbci3uf 0 9 )7pnd 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 10:8d;k *x.adye+jexf: 8. bqra4jxc ai 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 of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does the k:.*xxye a8rx :afj bej8+ddq4;i ca.cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one j,(,t5mr4m xnng 9swhend. The rod is initially held in the horizontal position, and then released as the free et ,mm4s (r,g nnjxwh59nd 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 wgx+bvd1;dvbl cr ,k +i go9/tdwa.5 1iheel to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 tv+ib91gvr1;c .b ko i dl5dxdw/ag+, 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 frictionless db +;y bu:eopf:(uvv c:isk pulley of mass:bup y+ev(cb: uvo: f; 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulleyzrcs5mn:n9z1 p e2 ch:nm) se3 of mass 7.07 kg and radius 66.0 cm. Wha3cs9zehnernm c)p5:1n : m s2zt is the acceleration of the mass?

  A rotating flywheel can(4 a i 7h:wkqtbvh33cx be used to store 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 dp k8*rhj:a a.r4km.tof $5.00 \; kgm^{2}$ 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 8ti* (3gj4ewd r5pn9e 2fcmkjwithout slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches th 5pe8j9 ke(mij4cnwt f2rgd3*e bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 yaox + +k(3bpxlwq:9k rno0v)m/s. How high up an inclinedoa:+ wnbkxk(v3+ 9opl) y0 xrq plane 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 allowedfz:,m*lg5ufkfpx// k l2 :skiv 8fr-d to roll do 2szm5if v /f,dl8 kk-r /g:p*fxf:uklwn an inclined plane. How 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 rolls without 4z h)iq 9bc o28b)vizjslipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is givenzib i 28v bzqcj4)9o)h 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 mo7 iyf(86xwxqz mentum 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 momeni+5 a 3h)lf3a i7gcnept 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//8:kbfnmk3wtwds j+ pj*jg2 5s with arms extended has a moment of inertigp+j23f 8n d5w jjkt/ksw :*mba 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?