Angular displacement is uq8ihrvve8g9k +8 p,uxsually express in units of

  Angular velocity is expressed i4d68 hy c(kpqca)0idx n units of

  Angular acceleration lnq50b4c ezs7c bxd j:x;g, m6 4f0hzeis expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constant 5he m*ma*t/oykx( js ,rate. The boy is near the outer edge, and the girl is closer to the center. Who hao/xh,ymst5 *a(* je kms the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant a xi;rkgo3hmn8+aj a+.sk9*(5wf hq yrate. The aak 8j+f3 wxh5*asyi+9rqk.gh o ;(nm boy is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a s8mfpoo ddr-5:g 4ix0merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the gir8xm:i0 ro5odf-gp4ds l 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 9kuu jde1s- 1 g3o9zwbconstant rate. The boy is near9ogju 39suewk1- zb d1 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 6*gv9w tmp v)7:noezbw*ym 7hat a constant rate. The boy is near the outer edge, while the girl is closer to the cengzw**nmbm6eov w7y t :7p)9 vhter. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accur8 uey4 qec5qt*3pbgp .ate sty. 4g e8ebqp* pu5qt3catement?

  Rolling without slipping depends ojsz/:hc v om9,uq8gj:n

  Two equal forces are applied to a door. The first force is applied a0y srkqs zay-) hcgp2 g*8lc5,t the midpoint of the door; the second force is appl csqs0rayg-,5ckyh gp) 28z*lied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to jbyuoy62 d;e5 a door at the doorknob. The first force is applied perpendicular to the d5b26y j;eu doyoor; 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 fi u,2 ul(duole)rst force is twice as large as the second force. The ratio of the torque lou de l),u(2uof the first to the torque of the second is

  What is the quantity used to measul ec0uhx6px ;,sp yayjp4894 mre an object's resistance to changes in rotation? u, p0jp4s l;9xmhyc6x p4eay8

  Consider two uniform solid spheres where bot lw.7w 0eqx,yt5xv t:dh have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of ine.lw0:w5d 7xqt ty e,vxrtia is

  Two uniform solid spheres have the same mass, but one h3uv :hdx yv,p9a.blp7rik jt713 ec4jas twice the radius of the other. The ratio of the larger93ipa7p, d7kxjlht1:v v3 4cuby e.jr sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice thyf58s p2c59qw a)e0kc ksv (fee mass and twice the diameter of th(v5p s0a) 2eyc s9f8ekk fwcq5e other. The ratio 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 are increaecwz g+h,jc +)8yjq: fsed to 2M and 3R, what happens to the sphere's moment of inertia about a central h cwfe 8z+jg:y j)q,+caxis?

  If a constant net torque is applied to an object, thjw1w31g 6m.pz ;jazi/v2zi khat object will

  The moment of inertia of a solid cylinlbm2x3, fyjc07 kj,xs der about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the rat2c ,j 7sxybxj,kfl3m0io of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of masspgwl*d 8y(m7 w4gh j/g 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 kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the whe/p8yhw *wg( mgg7jld 4els are uniform disks.

  Suppose a solid sphere of mass M and (xqlz n:/*b klek1c,t radius R rolls without slipping down an inclined plane star 1,ncqxle/*k(tzb:k lting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mascm8yignrcve453d : c+ht w0x2s M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depenv im3dn 0c2:r gw +txc548ycehds on

  "The total angular momentum of a system crp )v)t la* xpj)w+4qof particles changes when a net external force acts on c4ppvqa wr)) jl+ t*)xthe system." This statement is

  In what circumstances can the angular velocity of syste0bq7s3oh.+krawh li3.g zqa+xt r r7 *m of particles change without any change in ther rr z o*3.sa70kqqh3iab7h+lg txw+. system's angular momentum?

  The Earth orbits the Sun in an elliptica 7/q nfdc wf c.(;nrjnxma289hl orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the 9wn/xjq(fnh 8d.nm ;caf7 c r2Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movesdrzd+3e 4kg+pa qu /:g close to the Sun, then which of the following best describes the orbiting speed udazg3+:/ep+ q rg k4dof the Earth about the Sun?

  An ice skater performs a pirouette (a fast spinzu8oc v4dc3v8c o 9d dz5c.e9l) by pulling in his outstretched arms close to his body. What happens to his angular momentum o8occvdz.e5dvc z 93l4u8dc 9 about the axis of rotation?

  An ice skater performs a pirouette (a fast spimyvi - vyli-/qgmuzl 5 19)w+ln) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic ene/u 5 9)lv-gwy1zyqi lm-i+mlvrgy about the axis of rotation?

  An ice skater performs a pi-okq;rn(+1sx4 f yiy7hus: eg rouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about hy1sxo su7 4+q;r:f-kin y(gethe axis of rotation?

State the law of conservahk,ikebx 4 e89tion of angular momentum.

  What arc length does the Earth travel in a three month per4dnjne*py h 01iod in its nearly circular orbit about the Sdnj 1n4p*0hye un with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length o7qrn esoxiq+: v4: iq)f 0.30 m. What distance does the tip of the second hand sweep through in 3 minutevin ix)qr:4:q qo7e+ss and 45 seconds?

  How many rad/s is 25 revolutions per minute e-n j c3keea*kc e;n4s6quivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0o;.vphh- /6fe0nbrz5rh/g1bjz twlfgv8 , ( u s. What is the frequency of the wh ,fz rtejzbg;hb/-6ow 1.(0 /5unvvhhfr plg8eel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency o,o ebbs 4mb0ce/fr(6rf 0.40 kHz. The period of its rob/ 6b f0,mo4cserb( ertation is

  A phonograph record rotates at 45 rpm. Through what angle does it tjs/ )b oq hxbol-7u- w7y7ve)murn in 0.20 s? -yo77xbe -s7)q/vmulb hj)w o

  A wheel of diameter 26 cm turns at 1500 rpm. How v9ntt 3hlnpg8b () dp9far will a point on the outer r 8nbg p3tlnh(9) 9dvtpim move in 2.1 s?

  A bicycle wheel rotates unify595r+r odg ttv7yh+wormly through 2.0 revolutions in 4.0 s. What is the average angulard+ +y7 rg5vrht5ow yt9 speed of the wheel?

  A bicycle wheel rotates uniformly throuaqaj )v5 2lz*kfq.*ialz.v5m gh 2.0 revolutions in 4.0 s. What is the lineaaq )5.mq*ki 2 *lfl. avzvjz5ar speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.,2z g1ao;11 zi m0tln(ez sbfv2y5yz ,om:rpi8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must z, vl,n;b0 mi1zaig2tpm1o y52zy z1sro:f e( the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating witpa ottcys)8 c1kczkk .sv.ad7c -2c 69h a constant angular speed of 2.0 rad/s. What is c .1t7pkc2c)-o9acdazc t8y6.s vs kkthe linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed v,iz+rv:qdf - cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of ,fid -v+ q:zrvthe end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 y 6gmg4iypkdn/1bn np.*,d / crad/s. What is the centripeyb.mn k g/4p/,gi n ny16dpc*dtal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycleb vt(y2;x/,e xh 4ktdz wheel of diameter 7x4ex/dv yht,k(z b2t;0.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a cir 0m.h svut 8kkep*;;lzeas0y- cular, rotating space station (r = 1000 myea kk00 ;lvzu8*.-st ps ;hme) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50o tl ig b92sc/x*qr3e2 m with a speed of 20 m/s. The maxiqb/3x29eri l t*gs2o cmum centripetal force (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 circular curve of radius 50 m with a speed v 9 jbg85a:m:g2w aemtof 20 m/s. The maxi8b2a 59v :gtjg:emm wamum centripetal 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 the end of a 0.750-m stsb5a epsq(()ufoq -. mring, 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 the string iq s(meu5.o s(qf)b-ap s not to break?

  A bowling ball of mass 7.5 vxe1 y t7 89/(cwyln r/0zwm02f p8lhcpioji)kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s.jyicf 97c (hx z2nmww/rlpp)1i e/ 8o vy8lt00
(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 acceleration o2it3 *y ;a 2 gxiw);azvpef(nxf $4.5 rad/s^2$. 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 accelej84 u; rn8btvo+dhlj7ration 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 startinzp-v*ju /t; r/ymv(p vg from rest and accelerating at a constant angular a/pr(pv/vt z- ;u *vmyjcceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an as* 8oiy,s+kp qku2s 8lngular 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 m.m/o5 e q:dteqtazql2(+. d +ej0vgbangular acceleratej ota :(5 qdm/zevl+b qeqg0+ .d2m.tion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angu-iup:pc6-e(2vbip ii7ks 78 jw zbg1olar speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular 7b iwe g -pbi76(8izi1-uk jpcos2vp: acceleration of the wheel?

  A wheel of diameter of 68.0 cm s7;dsj6ji mrb :pqaa -6lows down uniformly from 8.40 m/s to rest over a distance of 115 m. What i d76 a;bs :apjqrimj6-s the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows downyr.pll4 c6 wb. uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleration?py46.cb.l l wr

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over ah ieq8- 4,anmw dis,w-miena48h qtance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotath* v*-1 7r rgbkc5tegves at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration ber*bk-15vv tc he7gg* rfore 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 yyb- xd)pr*b4 torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpen) -4yrb xdp*bydicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 puu68l3/ tudz0 sn2ysa h cd54Nm. If a 30 cm long wrench is used, what is the magnitsd4tzu02d 58l6/usacy3 uphn ude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in nsijp 7q52ct (uj2jv*ertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule wh/ 0mjoxtx b9uf+ nc)(4(rozis modeled 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 origin?o/nf (rouw j4bzmtc +( x)h0x9

  A solid cylinder of mass 10 kg is ry,wcq1iuph* f -vso9 )(1wucpivoted 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. (See Fig. 8-1.) What is the angular acceleratios wr yiofwph)(u c1u,v cq19*-n of the cylinder?

  A solid cylinder of m7lmtqk0p-i3 +fux+ ahass 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 ffaihp+q k+x-3m7 ltu0orce 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/bmy) ugbxq5m(taz(y n3vw:r+hu9 w: held 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 abomu)9:bub3/:+ wqwzta m(( nyvhxgy5r ut one end is ML2/3.)

  Consider a bicycle wheel to be a ring of4o u t1c7gkc;rq1)ol k 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 radiu o r;c1gk7okt1 c)4qlus 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 ari 2(d+5rhn wduound a frictionless disk pulley of mass 7.07 kg and radu5nd (2rh +wdiius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fri66 x27oxngeamqota *2 ctionless disk pulley of mass*mneq6ag27oxx 2t a6 o 7.07 kg 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 to store rc/i: cltg99lr+ +aun$1.00 \times 10^{6} \; J$ 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 op hjuf t* 3jyle,m)ub q1d5e7-pil7*gq /pp k9f $5.00 \; kgm^{2}$ 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 euqf3s6z+ox1 and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it qus3 o6f1z+xereaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls witi v 3(ofdua2.yu4bvi,h a speed of 10 m/s. How high up an inclined plane can it climb beforeayd b3vui fo42i.(v u, coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released frwn,d 8 rued.b*+pbwr3om rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vrb8+*rw, nd u3web.pdertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 3g +fxs3qmab:4 5e incline that is 7.0 m long. Assume it started from rest. The moment of inert ag3sb4fq:x+ mia 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 changelem-: r cuan2,y-+ uwns 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 7hk+si )cr2,cffm. p hmoment 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 wi)p-61nxgcv d w;o8bf ath arms extended has a moment of inertia offd1g;x oncwp)a8b6 v-
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?