Angular displacement is usually express in rc s*7 xg5j5rb;yfj4 cunits of

  Angular velocity is exprebwnm-0t 7ebn 1hc * h36bbddw/ssed in units of

  Angular acceleration is exprz58.n(ja hw ;k. ssa.e ,;wgncxnzd:gessed in units of

  A boy and a girl are riding on a1si-qkh) 7u - fu5xaiu 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 gru i-7huikauq5xs1-) feater angular displacement?

  A boy and a girl are riding on a ruxw vav4 s6,ap +2vf*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 angularr2 4xfua, +a6* vvvwps speed?

  A boy and a girl are riding 6(;)ofellwz eon a merry-go-round which is turning at a constant rate. The ewfol ;(lez)6boy 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 is turni/(bn plv8ri* wng at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the gr* r/nlw8vpib(eater centripetal acceleration?

  A boy and a girl are riding a merrya0bxv4/p zf4 qler 0d7-go-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 great 47/0e0a4 zp qblxdrfver tangential acceleration?

  Consider a rigid body that is rotating. Whtar/lyk:0 pkl8f* -brumq 1 e-ich of the following is an accurate statement?t8 -r *eykkpu /1l0-r: bqalmf

  Rolling without slipping de8(- l(5ip mxjltlr 5rrpends on

  Two equal forces are applied to a door. The first force is appj6 6dy-ig+fu 6 j9q0uz l)au.4k:dduoe3klvvlied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpefjuuuvi)g ovedq3kda: j6+. kd9y46lu0-z6l ndicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the dop.dv 5wuf7th**c3 jak orknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the * p7ca3 d. h5*jtfwkuvplane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first),ibu6 gg tg8t force ,) gtb6ui g8tgis twice as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure q.ux96 nuwsiuk:2 4lu an object's resistance to changes in rotatio uni9q 6.lku2u:ws4uxn?

  Consider two uniform solid sphfb)/t-feh mtkv 82 x-beres where both have the same diameter, but one has twice the mass of the other. The ratio of-ht- b8kfmxf )e2bv /t the 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 the radiuswyq14piy;lclk3-w y; of the otwy lyq- 3w; yk4pcli1;her. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one hlv;n1w cj fm)g,0d-tu as twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertv)ljngt0 1w- ;umc ,fdia is

  A uniform solid sphere has mass M and radius R. If th* 9)+qyolf/ pxhne*jt ese are increased to 2M and 3R, what happens to the sphere's m*n) * p9xjfethy/ol q+oment of inertia about a central axis?

  If a constant net torque is applip e8u,yq*wo2mk 4zwcmu8:n z;ed to an object, that object will

  The moment of inertia of a solid cylinder,klbd -v ix50u)ep9dy gdo+,r about 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 mass 150 kg, one whee rrbc(d6 woc0o5 zm:,il of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of thewr rdmc(,6 ocbo5:0iz 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 rolls without slipping wi itegzzqcrpj6zjy.8-91tp y:.jo.b sd376 down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline1 jjp-6op39 r 6ystdt. gz: jy.bew8qz .7izic depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an / n5v,xy3full inclined plane starting lxu/n,l53v fyfrom rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a systemmr,zox, heb1-a ;.tjk of particles changes when a net external force acts on the system." This statejzt ;1eakb .rxm,-, homent is

  In what circumstances can the6 du)4 lyuy;/5zzgtyks)rw m : angular velocity of system of particles change without any change in the system's angulawtu5 y6; y ukr/:zs ly4)gmzd)r momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fri hnuyb6w 7zc z90)mt3a2i p/g8ok(ml fction which may be presen /ilbnpzk)t 3 w9 hg86 u(a02mzcoymf7t. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbons pvhgqh bpjt8+39-4 l(j,pit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the( hlq 98h+j v3 p,p4s-bgjotnp Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulli(u .8u9t dzt )kahuwr2.hhaz 3ng in his outstretched arms close to his body. What happens to his angular momentum a8 hu9z h(a3du2trhaz ). tukw.bout the axis of rotation?

  An ice skater performs a pirouette (a fast spin)lu0;xd,.ochklqny(s ) xv*9 c by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energuy 0)nlqs xo( dh9cxvcl*k,;. y about the axis of rotation?

  An ice skater performs a pmaaz yb1(6qh :irouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about theyqh1a: ma(z6 b axis of rotation?

State the law of con12aygn)pkr-,xk o9f 8a gof3 mservation of angular momentum.

  What arc length does the Earth travt4.wvbz awknh)lj /oqc ce qe/-w8 ..3el in a three month period in its nearly circular orbit about the Sun with a ra-wq83)bvhq.w. z.c jeko//na4wel ct dius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. W 3l+df beb,-aifsh q0,hat distance does the tip of the second hand sweep through in 3h,q s 0fel3 d-,ibb+fa minutes and 45 seconds?

  How many rad/s is 25 revolutions per m09vxvu( 9w 9 ,hl shkek0;twphinute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 vs)vdwf99um 5s. What is the fv9ds5)wm9v ufrequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencf;mtb jb4/ j1*p y7iashnrb 1:1w+ faoy of 0.40 kHz. The period of its rotation bs1 at*i+/bj ;yh4pnm:wj11a bforf 7is

  A phonograph record rotates at 45 rpm. Through what angle:)/nffkiw wx+1x6a n g does it turn in 0.20 s? +a)ik:n16xwn/ fxwgf

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a 6gcwyb : b)zhy5y;: tupoint on the outer rim move in 2.1 s?:) b6h;uby yzgcy5wt :

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s)tpz:6 g o s;iv5tlfzxo:3ix/4 z bng5r y6ia4. What is the average angulxn:y5v p6a t4ii 6lz4ro x;3g5z:/z stbogi) far speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutionsfg0wttg:tp bf:l04 . r in 4.0 s. What is the linear speed of a point 0.10 m from the cenl::f.04g fbptw tgr 0tter of the wheel?

  A cable car at a ski resort carolmjex 9(4n.t ries skiers a distance 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 trip e.ltnm94 jox (in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2/n iap3on0o:b.0 rad/s. What is the linear speed of a point :o /p0inn3aboon the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in 5 aj,*i2edw7,n a wczvlength. If the motor rotates at the rat w52 e ,jnvw*a7i,zacde of 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 o:gp 6de3wll d;/i ,jxangular speed of 2.0 rad/s. What isw o llxj3d:;/pe gi6,d the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of aja lg 8*d6y+st 0pkl6f point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.06pf 80d kg +tyla6ls*j0 m/s?

  How many revolutions per minute (rpm)3et cz-s 73.rxq o5eat must a circular, rotating space station (r = 1000 m) rotate to produce an as5xerc73e. -a ozqtt3 rtificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m +e qj0jhui7/j with a speed of 20 m/s. The maximum centrq/7eujjhj +0 iipetal 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 of c +er qbu2e2m320 m/sre3qc2b+mue 2 . The maximum 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 strin8jid b;0q ugy:g, is whirled around in a smooth level table. If the maximum t qj;8bg i:dy0uension 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 slipping 10 m downmvyad i/32 pu( a lane mpy3ud2/ai v( at 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 rzb 4xi(g9l-0fn 1jfvacceleration 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 acc c 12i3gez7mbfeleration 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 dz.*lznna5v h k*6lx, rotate after starting from rest and k*lx5l z*za ,h6vn. ndaccelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerationxd hxgm:0wbw 93m.4rz of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotatingsre1 b1i bod d la.,).;+ljlze at 20 rad/s decelerates with a constant angular acceleration of1ols . r1 dl+b;e) bz.ilaj,de $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 r0levr2 3 4tz2y ntkif,ad/s while turning through 2.0 revolutions. What is thevnl24ye2 3i,zrkt0 ft average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest o mk/ 72fl.gonjver a distance of 115 m. What is tl kjg.no2 7mf/he total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of (u2zk gpyf4;/dke8ex4 ny m(8fy4vf l 68.0 cm slows down uniformly from 8.40 m/s to rest over a distanclf4uk (kn4d gx pm8/yfzv (y2feye;4 8e of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest oc;+6m mjywi l m.5oc*nver a distance of 11 jw+ml.65mmoncc; *yi 5 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboradl4tpj(u1z; * -jvs qstory rotates at a rotational speed of 3600 rev/min. When switched off, d s-u t(4pj;*lq jvzs1it rotates 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 torque of 0,u:;yv7 zc nomqh.bq 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the mz,y:o v q;qc7b. h0unforce required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening6i rl, 4iui:6nuew*m e to a torque of 90 Nm. If a 30 cm long wrench is used, what 6r6 lnm,*ii :e4wueui is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inez *i4 bb2bj.pertia $3.00 \; kgm^{2}$ 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 1hipv y/x1b8 gat the origin, mass 2m is at x = a,8 xhig1p1y/vb and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis tnrqs (s9ut(cn; fg e7b:g 6nh2hought the center O. A rope wrapped around the 6fner:q(un(hg ;n7b g sstc29outer 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 10 kg is pivoted about a frictionless8(t6odq /5;.dhyz0blv .ulkkg8 zcb k axis thought the center O. A ltz /bu vh .6 0c8kkl.dgy 5;dob8(qkzrope wrapped 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 heldp6 m fnqh9g89x in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleratio nm9qxfgp8h 96n 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 :q:-cg yagx2hu2 qs/ks1kb(i30 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 kx:q g-k2qaig:1s b(c yuh2s/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 arotnu2 uuw0v.q8 und a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acwunu8v. u0q t2celeration of the pulley?

  A 1.53-kg mass hangs on a rop had p.3a3g/kpe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.3p . phka/3dag0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store e33moe5cgu -ui ah( )4nce z9spnergy. 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 inerh961g gctl:i k 4uac)rtia 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 kh7u,su* 2)s0uto ym2bxjjrz +b+ m (qsg 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 reaches the bottom of the ,tz2m yjxs 0b(qs*ub2su+u+ )m7jhor inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 mk uahy z0x3s/s-p0f9f /s. How high up an inclined plane h- s09 syffz3pkuxa0/ can it climb before coming to rest?

  A hoop of radius 0.50 m and a ma1 5vw;8*0/j v zmndl.dvqdvtyss of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distanjqz* 8.t0ddvdlw m1 v5ny;v v/ce of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm roll y xcixfkq s:/m;h6;dc.uz53ls without slipping down a 35e incline that is 7.0 m long. Assume it started from xx3lf ;/c dscuizk:;65ymq.hrest. 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 change1sjoc6,gjc0t9 lp7b cs 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 moment of inertia+pcg 5d:qo+k g 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 rotatins 3ot/ tvypgjl *7gu4rz5 4hx6g at 5.00 rad/s with arms extended has a moment of inertia of4rgs uj7 o zgtvh5/x3tl *46yp
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?