Angular displacement is usually express in unih : xk.h+y7j/3cimfyuts of

  Angular velocity is expressuqg t-y:vqdl( 8voqzih jh. b5r+24 2ced in units of

  Angular acceleration is expressed in units 3jmrh(pgy*y4 sfw (rh82aas 7of

  A boy and a girl are ridinpp20 erfj -6b8z b5:gwl(0rjzxv nj8eg on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacejzw0p5j8 rgz86 (rbxn2 0 :b jepefvl-ment?

  A boy and a girl are riding on a merry-go-round which is tukcixgt8s)j, ykhrl+o7/ (uc2 rning at a constant rate. The b /( )s82gjhixrukoyl ctc 7,+koy 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 riud.lw.d g,4g rding on a merry-go-round which is turning at a constant rate. The b d.dlgw,g ur4.oy is near 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)c )tq,i( 48q3aqe ls gji/htu is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater c(jg3q,e h ca)ltti8i su 4/q)qentripetal acceleration?

  A boy and a girl are d+ pozz- )*nsev1q 3apriding a merry-go-round which is turning at a constant rate. T1)vopap +d-se* qz3nzhe boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which k:u),nsnsq e0of the following is an accurate stnqs:u,e0 k) nsatement?

  Rolling without slipping depeniy n 7ldo)d0p.rwn:+ dds on

  Two equal forces are applied to a door. The first fo/fel9 lkm 5ho+yvw:s s+:dmtsioum)/v1x/l 8 rce is applied at the midpoint of the door; the second force is aps+i /1oul: m: 9hl5few 8lmsotdk+ x//v vsy)mplied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob.r8*eq * f*5 mcrvbk+tz The first force is applied perpendicular to the door; the second force is applied at *t*5qvkzr emf8rb + *c30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door6ij btebff4 /2. The first force is twice as large as the second force. The /24tbbefi f6j ratio of the torque of the first to the torque of the second is

  What is the quantity used to measu3t,o 7b t5e a3nyjyfa)re an object's resistance to changes in rotati3ot )y5 tny7b3ae,fj aon?

  Consider two uniform solid spherego21x 9 2uwqkts where both have the same diameter, but one has twice the mass of the other. The ratio t2 gq 9o2wukx1of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the samy+:w8 b. vvsnse mass, but one has twice the radius of the other. The ratsv.s:yvn bw 8+io of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid sw91 :rb.p s wdb07zlal r7,urrpheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of in as,brr db: p77wl 0u19rwz.rlertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased )j4cy zdao8)wwn bw;)to 2M and 3R, what happens to the sphere's moment of inertia about a central axis4 w8cya)))wb zow n;jd?

  If a constant net torque is applied to an object, that object w i tn-1f6qnr(jill

  The moment of inertia of a solid cylinder act(nrk s:;c8q:g exu 1bout its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of masi420:c eggaxus 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 ix402 ucga:egthe 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 R rollpyq/*ng12j+) fvhof cs without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of/phq vfy)g cf+1no*j2 the incline depends on

  Suppose a solid sphere of mass M and radius R rojpi j08/-fh prcjbi vdym/-/wfi2,7ylls without slipping down an inclined plajf my2yi-pd,8hc -f/7 b/0/pvwjjiir ne 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 part o8+ds44lijwe icles changes when a net external force acts on the system." This statement 8ld+wis4 oej4is

  In what circumstances can the angular velocitubamzk:y* rf ksk( 0-:3,w)h1zk by kwy of system of particles change without any chabwk ys*:-hzkzfk )uy3,kk: ba1r( 0m wnge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which ma8;ls awjj llw; .urbmfi4a2 7m) faf;4ujyu1+y be present. What happens over time to the Earth's angular momentum awj af;8rf 44sbl;;w1 u)y jjuiulaf.m7m+2labout the Sun?

  The Earth moves about thevtgu0xc1 1hy*wy+ 5ff Sun in an elliptical orbit. As the Earth moves close to thywx1ffg tycu0+5v*1 h e Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hisl47fddk77pznei /oz v9/tij0-+ zuv n tqu .6s outstretched arms close to his bodyzjfop-9uzi7 z0+vkdtvn6/s / qe.d7n l 4i7ut . What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outsubt erycf m9; 68lrw ad7*p,h4tretched arms close to his body. What l 4dwh c;rpt,rbm9 au ey76f*8happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling qts3dws/h n :8 :/gonein his outstretched arms close to his body. What happens to his mnts:g en:3 sdo q//wh8oment of inertia about the axis of rotation?

State the law of conservation of angular momenkl,n*yj;ad) wtum.

  What arc length does the Earth travel in a three mon6cim4.h k,nksth period in its nearly circular orbit aboutki.4mhs,6nkc the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has su5x sx:wnqc;; ( kxl-a length of 0.30 m. What distance does the tip of the second hand sweep througqwnu: ;;(l cxxs-kxs5 h in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute e:fer5g(3 exts quivalent to?

  A bicycle wheel rotatfy+op8mh0 oce.ulm6 - es uniformly through 2.0 revolutions in 4.0 s. What is the frequency of them m-luhy.8o60+ fpeo c wheel's rotation?

  A pulsar (a rotating neutron stlg6*o r:s ombzr(o7z 0ar) emits pulses at a frequency of 0.40 kHz. The pero0r7z olbm gs6(ro :*ziod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0./m2bum-.nz/k hf pyx-20 s?-pf hmby-/ukx .n/z2m

  A wheel of diameter 26 cm turns at 1500 rpm. H xkj)59u( m-f-bx*.mv jz-en iporo,qow far will a point on the outer rim move i) x9qrj pbxomuo -vm.-5jnf-ez,k(*in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 2n-jxwj jwhfl1 dn :4(in. /ods. What is the average angular speed of t1w w/2-hdjn(4dx .ljjfo ni:nhe wheel?

  A bicycle wheel rotates uniformly throuve 2,uh5 wff7h,/lhyk8gd0ba46gcpg gh 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from th7gvy2b h,gh w0a465glf/c8, ek udfhpe center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km.86y-)alk3hub -,jkzof k obb/ The cable which moves the car is driven by a pulley with diameter 3.0 m. Assumb f-8,ku )b/lzk ho3y6ob-a jking 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 constant angular speed of 2.0 ra*k7p. kk5gvju d/s. Wha*kpk vu.7jgk 5t is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weec0to.z 8fw5)hfxda s- d cutter is 0.16 m in length. If the motor rotates at the rate osftoc ahzw)x8. f5-0df 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed9)alhex 4dc1yg9 mno) of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's oy)xgh991 lcnad e)4m rim?

  What is the centripetal accv ,0e7 olrld-a(5yxomeleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike om- ,ea5 v0dll o(7ryxis moving 8.00 m/s?

  How many revolutions per minute (rpm) z+ezgjj1vb7y)7sl ew xn8w 56 must a circular, rotating space station (r = 1000 m) rotate to produce an artif 7jgl6ve7x+1wz w bjsye) 85nzicial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular j-g ( gswu. rx:6ajt3cvg,nw2curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stacn,wvr g wg:ju.-(2 sxta 36gjtic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a fla;0nzd*r pb ,p/ag,sgf t circular curve of radius 50 m with a speed of 20 m/s. The maxim zf a, 0b*srgg,;dpp/num 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 string, is whirled a(i4v/aee e q;ground in a smooth level table. If the maximum tension that the string can withstand is 250 N,e /e4i v(;qage 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 slipping 10 m dow8p 0n.kalum,sn a lane at 48a mk.ulps0,n.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 acceleration ofbuqxgeuaq)e3:w.,/ za9v0 n s $4.5 rad/s^2$. 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 angulary*fl8ht.sov w9*oy( o 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 ae: swr93wc8w-r6asft d0a 0u tfter starting from rest and accelerating at a constant angular accelwtd06a aw9te crr 3s: sf08w-ueration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has anmh;wwy, hi2+3,t efmws(vf :n 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 with a constant angular acciz8j:9lll;a tx2eq3 vkm,+e heleration 8;2mzel jle tq ,:iv9hlax 3k+of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reachu izh6ipb z- *8txr3lp4dn -;ces an angular speed of 6.0 rad/s while turning through 2.0 revolutions. *rbz6lip; 4 3 ncp8-tdiz hx-uWhat is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rcqy* of9h42sqk w qzczaw-5 8ub:fi6.est over a distance of 115 m. What is the total number of revolutions the wheel rotates in com5-h za4i8ow*bcu q qk:fqsf269wy c.zing to rest?

  A wheel of diameter of 68.0 cm slows dowv*udgvf8x8 3el5p d- bn uniformly from 8.40 m/s to rest over a distance of 115 m. What is dplf3u* 8 vedb5 v-gx8the angular acceleration?

  A wheel of diameter of 68.0 cm slows d+*njl. k 2w5cj yki,mf5 u1nydown uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it 5 yiy2nm+n1wcdkf,* kujl.j5 take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600cy-:e-vtidx jm7 w:.o qw,5o p rev/min. When switched off, it rotates 50.0 times at a constadx.q v-ewomw-5,:7 :cj t poyint 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 aab3busbm 93 7h torque of 90 Nm. If a 30 cm long wrench is usmh9ubb73ba3s ed, 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 a torque of 90 Nm. If a 3*lpec -(bs k;g0 cm long wrench is used,e;l( pk- gb*cs what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia /tuh 0pkhn)2 3vvke*o $3.00 \; kgm^{2}$ 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 iq d*rr( bh:7 :gvovse7+bofu 4s at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about thede 7 :+bubh4vof(*rgqv ro:s7 origin?

  A solid cylinder of mass 10nrpl)m1 io) t8 kg is pivoted about a frictionless axis thought the center O. A rope wrapped aroup o))ilr1tmn 8nd the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10uk css2vbj;0d/t h29v kg is pivoted about a frictionless axis thought the center O. A rope wr;vds/sk0 292hcbv jutapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 helhvq60zc,w2oh(n4 o ngd in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is releao2,6 n(czn 4hovw0 qhgsed? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of rad* qik8a,zck/l ius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a forqac* 8,kilk z/ce 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 around a frictionless dydh0t5ot /9ytisk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the p/tyt 5 dh09toyulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of2upb8 pit gt(cxkd*5; mass 7.07 kg and radbi t5(px;2c8 p*ug dtkius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required tmzizt01:c : s rqa-e4n3b6eseo 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 inertiaky; vq7wag a4 u+ *-faj8kyig9e9sax8 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 rest and roll oyfl;nn)x(-i s without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it rf)-loxiy n(;neaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s.rw0we;k):zw05nss3g j dzj8t j + wo;p How high up an inclined plane can it clisw zg03zw8jd+;swj0 t:n5 )jporwk; emb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releasei r8 vz,)p-elt00zhq ad from rest and allowed top0)8eqz alvzh-it 0r , roll down 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 slipping down a 355iu(t mkh+j4 p9,hh qpe incline that is 7.0 mh49mhuj( 5 pt +iq,kph 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 momentum changes ba3u sn3me0uex95 a i;hy $20 \; kgm^{2}/s$ 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 moment of inertia o, l0 znwv(-qkngf (d,hf $5.0 \; kgm^{2}$ 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 adwo26we/zm(3 i b ,oykt 5.00 rad/s with arms extended has a moment of inertia ,ezo/omb2diw w6k (3y 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?