Angular displacement is usuallywt ;w2q99a uxh express in units of

  Angular velocity is et60m4pnnsg, q xpressed in units of

  Angular acceleration is ;i q/u nds. s/5xac(o m;mgp63w,ggarexpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constix* 3agoor9 + 7m:h;ntrh b3umant rate. g: mo 3nr7i3r9o bu+x;mh ah*t The boy is near the outer 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 turning at a cokay2z0t+gw;bx 6 7tie nstant rate. The boy is near the outer edge, and the girl i 2xite7b tz+ykw;0ag 6s closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-gok0b -;g z3kczt.yupcg 3(n(bm-round which is turning at a constant rate. The boy is near the outer edge, and the girl is n0kgb(kczu3(m.y-ptcg bz;3 closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round wh +2cc8vfmri-:wwim 6ke r:zx;ich is turning at a constant rate. The boy i - ;2c:i+8xzmirkv6 wrefm:wcs 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 whic38e (qgog9 aal -nwonq;4 6zgbh is turning at a constant rate. The boy is near the outer edge, while the girl is cl(9a-;e6olgnqggn3wob q 84 zaoser to the center. Who has the greater tangential acceleration?

  Consider a rigid body +b /93lqloxet gt,d71ad2a;o30lqu9c oz zzr that is rotating. Which of the following is an accurate statemendq1gc,b9o 92o;oz zl tza3l7rd3 +xq tu0/le at?

  Rolling without slipping de* oa n zt8bpnz+y:a1h+p,eb b/pends on

  Two equal forces are applied to a door. The ficmw7hbg7 af73u,ver1 rst force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perp1m7 f wa,g3 hu7cre7bvendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is apr0gl u;ajc5i p;ot(3 zgyi6d:ino).iplied perpendicular to the door; the second force is appliti doi.yc;5g):n0gzj op3 6iur; al (ied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the dowq6ok8x-q rgd+.jy x7 or. The first force is twice as large as the second force. The ratio of the torquey8x7 wkg+-x6 q.djoq r of the first to the torque of the second is

  What is the quantity used to measure an object'0 y(hmk7+48 gw a)hptldsjl)vs resistance to changes in rotation?8gk ld74 ha)my0hj(wps tv)l+

  Consider two uniform solid spheres where both have the same diameter, butl;ghi5jwggx x4 +wh 2- one has twice the mass of the other. The ratio of the larger moment of inertia to thahgw jhx4lwxgg-+2; 5 it of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, bzerz,p2vldk+zvr* -zxw b 4,7ut one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere l-*vr z7z4 dzbe, pk,vrwz x+2is

  Consider two uniform solid spherebps py71x v01x:+jgs:jju5 j fs where one has twice the mass and twice the diameter of the other. The ratio of the larger momxup01 x7b +jsjvjy1 :s j:gf5pent of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are in02so1g1vtb8srdf:x.l pln h 9 creased to 2M anglp r 0sonbs1hl.8vt 1x9d:2f d 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that qzt- mbt,u48 q6g jo2gobject will

  The moment of inertia of a solid cylh-w41i qg b)tm ch oovy93ya k0*nqcb s1,ur,+inder 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 kcohi01v )r y-bqq94wuahsg1 m+,*bc3, toynenergy is

  Consider a motorcycle of mass 150 kg, one wheel qi(v8a/rr0 rqof 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 kinetic energy of the bikeirr( aqv8qr0/? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippi./, ej3hxhiu3e (zwxn ng down an inclined plane starting from rest. The linear velocity of the sphere at the x/ew3h.ejxi , (nhu3z bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withtt s( /,u:mdmxout slipping down an inclined plu / m,txm:td(sane 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 chan:(t pg6y qt,rpz- j z+/hvdnl a57wz3lges when a net external force acts on the system." This statemelat zr6t qyg:pz-j7w3,+ d(nvz lph/5nt is

  In what circumstances cp2v2el+k ::t* acs; jzdmih7ran the angular velocity of system of particles change without any lism:depc72v2kz *r :j;ath+ change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction wh3 m,8ryd 2ij*v8,ufmp wly j;gich may be present. What happens over time to the Earth's angular momentum about the Sm8yw ,mpy f 38v2gur ij*;,ldjun?

  The Earth moves about the Sun in an elliptical orbit. As -p9(ik 7fc1z 1jlqt0ne4 byumthe Earth moves close to the Sun, then which of i704fle (t-z9kb yp cqu1n j1mthe following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrpurn 35dx1vq5 qc--2em)v bcxetched arms close to his body. What happens to his angular momentum about the )rnu2-xc ec5vxb q-d 31m5vpqaxis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretf 538fq-w vn 8ajk;+m.omd ekfched afn 5m.foe 3fw8;m-d+8kaj v qkrms close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in eh k4i2 z2qs 9p)/je d.bvv8ddhis outstretched arms close to his body. What happens to his momenqj )4pebsd8/v e2di. 92zkvdht of inertia about the axis of rotation?

State the law of conservation of angu8 ;eas8d nerti+lxv +hu.w ,h)lar momentum.

  What arc length does the Earth travel in a three month period in its nearl);n* e*jtzycc y;)xkby circular ;)k*z e*y );ybjcxc tnorbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a len,qqalz 6l-3r.r89 hx xn4 3:grpifkk sgth of 0.30 m. What distance does the tip of the second h3ax k.l,3qx g- 8zi lksph4n:qrrf9 r6and sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalentk1o0- ra 6wr9ex f15/kixtxbf to?

  A bicycle wheel rotates uniformly through 2.0 revolutunq cp.lw3ixvs :(u. vt :2k.9oe+qkkions in 4.0 s. What is the frequency of the whe s 9qt :vwlu 32xiukc:+p .vok.(qen.kel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHymp+gkje a,f8lr5 3a 6z. The periodraepmga8 kj3 +6 fl5,y of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn yzx/,v mi(/q rin 0.20 xm,v/rz y i(/qs?

  A wheel of diameter 26 cm turns at 1500 rpm. lb., 09;vqzvq r xpv/gHow far will a point on the outer rim move pvb qvz.lr/0q9v, x; gin 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutionsdi-7q5-hhc yw in 4.0 s. What is the average angud y h--wchiq57lar speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. d-6p)t-n g18gb ks(dzbmw+ dvh8ol.eWhat is the linear speed of a point 0.10 m from the center of b.e-pk )gzhdw86(+ l gd8bmonvt s 1-dthe wheel?

  A cable car at a ski resort carries skiers a distance of 686qzc* 01w/a9edp n+ge odc sm.8 km. The cable which moves the car is driven by a gznwe+cq9o80d /m1s6 aep d*c 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 minutes?

  A wheel of radius 1.0 m is rotating with a conbml.k;yd -gf6bpq -/;fn8l fpstant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel.gmf-dbn;k f yp q;lf8/ pb6-l's rim?

  The cutting cord on a gas-powered weed cut /yawwct cw:2k (c:yv+ter 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 (wtk+ :ycv cc2w:y/wa of the cord?

  A wheel of radius 1.0gfgk*hmf;vwpd2bwo0 x2+4 b5*x h d/b m is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration 0p2*dxb/fo *+bwb;k4gfdh2h5w vxgm of a point on the wheel's rim?

  What is the centripetal acceleration ofbf job46xn wxz.o l;83 a point on the perimeter of a bicycle wheel of diameter 70.0 zox. ;46fb3 nxjwbo8l cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, o+qokv)bor/df(ib5 7rotating space station (r = 1000 m) rotab7d)k5f(/orib oov+q te to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a fc e9z k*ae /h +iktu9kx*ia-nb*1 oex7-ub)jrlat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stak7xn) u*- b r-zhxitjak kbiu9 *ee*/+e1 oac9tic 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 w,po n 7w5+0i-jnqyhihith a speed of 20 m/s. The maximum centripp ,7 nyq5h o+ij0ni-hwetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attachesw9 u+v1j *x/;jqdkoed to the 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 250 N, then what maximum linear speed can the mass have if tsud +1vox9w*qk / ;ejjhe string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10 m dowk/u+xrrv8p 7 /bnk7-c3 x krqwn a lane at 4.3 3/ c 8r/n-rk xkrpwxquk77+bvm/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 6t j73 pwr i2-(fy;g2h4c ine pllhz7n ;:bigywith 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 with ::x0-5p6rtduszt jrpa 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 automobile tire rotate afb9 ,zybztmhz x0l4up6v88j ;mter starting from rest and accelerating at a constant angularhpxm6m tzbu,b;v 9jly848 z0 z acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acx.+i4de lx8euceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/i4v, s3ur+xjg ms(t e1s decelerates with a constant angular acceleratisj emt,xgr4i( 3vu+1son of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an aatxa3 806n/)boubnns fr)l: kngular speed of 6.0 rad/s while turning through 2.0 revolutions. What is thex /nr3ln8b ak ))s6 t:0ofabun average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows dnwc t40 kb76zdown uniformly from 8.40 m/s to rest over a distance of 115 m. 4cz0bdk w67 tn 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 m/s to rest0v* a9necp8ou over a distance of 115 m. What is the angular 9con08ua e*pv acceleration?

  A wheel of diameter of ev8 g w9in;n*p68.0 cm slows down uniformly from 8.40 m/s to rest over a distae g9*8pw ;nivnnce of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatwuv76y 6g z:w9v z+hnpional speed of 3600 rev/min. When switched off, it rotates 50.0 times p7 n6w:69yz+z vhu vwgat 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 requireg+c) 7)l70mzuv+ lthakubip 2 tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular t ugu7+t+lak p0v27bmi )z) lhco the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. ni wr+agbv,hiu9tv;t+a;( j 6 If a 30 cm long wrench is used, what is the magnitude of the force requiredv9;tia+wvgju, train hb6( ; + when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia.rhpwkv8(s1x8x -qekm; a-oh $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as 2zthqqn) ,gi)3nn hjlu)t:5 ifollows: mass m is at the origin, mass 2m is at x = a, an l),g2ujqtzn3):h)i 5n ihtqnd, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted jk0-7ch6av y5/k0by37r ewnogzb 8f uabout 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 downh o fv7 kbrc/unj653ag8wbyzy0-0e7kward. (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 thovgb136 )h getsi00agtught the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the rig ve6 i0sgth)gbtag 013ht. 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 hinge2f33u 4e9.nm, qlgq nq)gbsr nd at one end. The rod is initially held in the horizontal pmr2ng ) qne ns34qu3 lqg9.f,bosition, 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 1.5 kg.63wcs eqwf41 p Neglect the mass of the axle and sprocket. If a foqew 4wpf6c13s rce 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, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped arouz4th6w ,+3 vd.tcgashnd a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerat.+vcg43 ws ah6td ht,zion of the pulley?

  A 1.53-kg mass hangs on a r)jr s.2hywbo+ope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration.s+obyjw 2h )r of the mass?

  A rotating flywheel can be used to store energy. If it 28c l:) s :rlh kdygej17an*sltxn-/gis 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 inerttw q: qfm3,tq2ia 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 k k8yu25/t z0p hez0kzw 93kdxvg and radius 0.010 m starts from rest and rolls without y/k8 uzztd 2k395v kp 0ze0xwhslipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of masn-fs4xic1b* ve au ,7ks 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How higi1, xbsvk cf -47na*ueh up an inclined 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 akfjmsd7;b5z zi 9 ;d9ond allowed to roll down an inclined plane. How fast is it mo if79k;sd mo bdj9z;5zving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius pa/j b j4g4d,neily+m k;/iy015 cm rolls without slipping down a 35e incline that is 7.0 m long 0/niyj d4p+l4bk/jg ,im;ea y. 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 momentum changm ;:uxc6:g 3uld1c25 u*ocscagg+q eves 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 mge.9.y9 jz pfsnhck)q y/i8 z9oment 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 .7vi qeq r j7g9synk*7has a moment of inertia ofj yiq9 s7 v7.q7*nerkg
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?