Angular displacement is usually express in unitc houjw/ b1q: .f8ui*vs of

  Angular velocity is expressed in 9sw -qb)eqv 94sk4fipunits of

  Angular acceleration is1 xag+dj x6ek1n;vo)8 qp)nya expressed in units of

  A boy and a girl are riding on a merry-go-rounbtf1 8ahl h5j*d which is turning at a constant rate. The boy is near th8lh1fh*5j t bae 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 constant c*t2 gtiqq1jyrpm763 rate. The boy is near the outer edge, and the girl is closer to the centc*q p6gmjqtr 7y213i ter. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a rpb0iumo 5ao2 4 c48ciconstant rate. The bbiomi44c r0cp o5 u8a2oy 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 tb m bv7 thrlrgf.+.fir0b73) a merry-go-round which is turning at a constant ratebt trr7f.b0mrg.)7bh+vfl i3. The boy is 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-o bv,nuv7 8ff6round which is turning at a constant rate. The boy is near the8u vvnfb76,of 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 following is an accurate s- iq9.pkdpm:u( 0qii6ez kvzo40d ;attatemendizqmk- :;(9uopzd6ivt q4p. 0k i0aet?

  Rolling without slipping depen 7vh.03wg lot0in 5wdfds on

  Two equal forces are applied to a door. Th lbqw jy59(d4vrj6dv 9e first force is applied at the midpoint of the door; the second force is applied at tjw5vdyq(r49jl9 d6b vhe doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are appp(w .o1qgtp/+hyxnpbf/yrc v)0sr2- lied to a door at the doorknob. The first force is applied perpendgy+nq( r1t20 pfhcso/vy /) brpx-wp.icular to the door; 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 firses2 mq 7)4vhobt force is twice as large as the second force. The ratio of theeomh724bv sq) torque of the first to the torque of the second is

  What is the quantity used to measure an object'mn4 nv;kivt5wzy /qso1b3/,vqq)j s*d:4 kdis resistance to changes in rotati:3)/b nk*dk4q yvd oq,;ztjw51/minsqv4vsion?

  Consider two uniform solid spheres where both have the s 2ij,mjs1 s:8b8jg ysfame diameter, but one has twice tj 8g2mss1b,f jyi8:j she mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but o8et u .6bts 8;9rz9r (wqzppcone has twice the radius of the other. The ratio of the larger sphere's moment of inertia to.;ut8 (wbq6szrp8 cozrpet99 that of the smaller sphere is

  Consider two uniform solid sphereorbsf6(-84yb0 l w1x k b-8a()sqnripfuh:jas where one has twice the mass and twice the diameter of the other. The ratio of th8(suxarkhb1 -)s64w yjn0p:8f(l r bb-foq i ae 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 increasem z )n2vv ehg3hy( 70ma a 6jkh3p)9ehotn5)ttd to 2M and 3R, what ha9h5 2)mtotk3v v)yjt 3e(hn0hh6e )a gnpa m7zppens to the sphere's moment of inertia about a central axis?

  If a constant net torque is 28wz/0t md;xv3jv 5 mp /h,oxvn2foqbapplied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MRfkxocez5)6 sr t0 w+6r2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to x5wf0e s t ocrr)+zk66its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has ov7k ug9si)q21dlye so -48eoau1slhb-0 mn8a mass of 10 kg and a radius of 30 cm. What is the ratio 0) -n1ubsavs yi8g os2qll9omue7-hdek o4 81 of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of 8 jb0,hp ;ai(h9nawhdmass M and radius R rolls without slipping down an inclined plane n8h,(h0 baa hw;j9dipstarting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere o6 -*/ mcwlztlt0x0 nzsf mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular0z0lc-s/m l6*txznw t velocity of the sphere at the bottom of the incline depends on

  "The total angular mo/d5 +hpze ds2smentum of a system of particles changes when a net external force acts on the system2h5psz sdde+/." This statement is

  In what circumstances can the angular velocity of system of partipza( n:vg:- ylclhd7/-evk3ncles change without any l-e hc/v:kznyl:a3 7(p dngv -change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore z7ql -+nim7v4. xyl byany friction which may be preseniymqll.7-yvn4z7b x+t. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves cb*6 1dxj*esq close to the Sun, then which of the follo1b j6sc**dxeq wing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by py(qo*f;63i) a;c4kd) r eyx dw npex8culling in his outstretched arms close to his body. What happens to his aa do py;kc r(if e)y*deq8x3 ;w6x)nc4ngular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spiny7a 0hmt 8r;avu)loo+qa h het8 rx1s67p) xk/) by pulling in his outstretched arms close to ohor/v6s7 ;la amx0x r)ktq1 uypt)ea7h8+8hhis body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouhq o t:zm;-xv*ette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis m-:;v*qxhz ot of rotation?

State the law of conservation of and/ ,tv om21icblp7r 7hgular momentum.

  What arc length does the Earth travel in aa,j1p 6coo r xxg(m om(1/mzpsr5hu57 three month period in its nearly circular o(5c(1hmz7ro p mo5m1 uog6ja xs,/prxrbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lengrrzgr2 ) .2d.4 oxie;pdzj b:lth of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 secogdrd2brzl2x p .:i oz.4j)e;rnds?

  How many rad/s is 25 revolutions; 2vfvc:zhzc 3cm 5ab 8;m9oyq per minute equivalent to?

  A bicycle wheel rotates uniformly thr8 /t8up sdtkm;ough 2.0 revolutions in 4.0 s. What is the frequency of the st /mupkd;8t 8wheel's rotation?

  A pulsar (a rotating niz mja1yqoi0*8wbx/0 eutron star) emits pulses at a frequency of 0.40 kHz. The peri/yoib1x0j8 wm*0izqa od of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle dousj2sd;y l,5ypulfx x1:f2 c4es it turn in 0.20 :,ull2p fd14; ysu5s2f x jyxcs?

  A wheel of diameter 26 cm o:n 2qm+ ds:uedame01turns at 1500 rpm. How far will a point on the outer rim move indu:+e0qa mendm2:so1 2.1 s?

  A bicycle wheel rotates uniformly through 2.- 9oao ybr2(dd azet9:s4z+pr hk (6jp0 revolutions in 4.0 s. What is the average angular speed of the whee pk 9z:(breays -zro(th4o 6d9d+pj2a l?

  A bicycle wheel rotates uniformly through 2.0 revolutions in io(00kr pwyuo k8p 1p2i;)tkr 4.0 s. What is the linear sppupii08yk wro;r2 1t)(ok0k peed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance od i;v:zwpgnw*d* i (ans:0hd)f 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 * *hspdw)ad:g0inw(d: ;nivz rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotca9 z(;bm+rj;g6keus ating with a constant angular speed of 2.0 rad/s. c kbrm;eu 6+gj(;sza9 What is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powerep1 heupkgn0 ze: 9/by-d weed 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 the end of the cohz-b1 kp9n /egu:y0perd?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s.jgrss,nl39jx,)p w 7 e What is the centripetal acceleration of j)n9gsjs ewp3l, rx ,7a point on the wheel's rim?

  What is the centripetal acceleration syc 52nsyf928w )enjx of a point on the perimeter of a bicycle wheel of diameter w s5s)22yfc8 neynjx 970.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circujnoqopwcs) 2dj * *u3;rfj6v.lar, rotating space station (r = 1000 m) ro *jno;fd2jpc )u*v 6j.wr sq3otate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 2u9* sdminx)i9m) 2y pr0 m/s. The maximum cmi2 9x)m usr 9pin)*ydentripetal 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 )p zs5p2 hyx*d4atyy+ of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction)yh*t )sd5a2 pzp+y 4yx is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attachedh8asr(cl r1 i7 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 the str( 7alhsr8r1ci ing is not to break?

  A bowling ball of mass 7.5zs z4;brv v.(4far.nhg b+g4q kg and radius 9.0 cm rolls without slipping 10 m down vzg 4.a+.v 4f;(4qrhrzbg bs na lane 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 const7 jaip -jqm6vqy; pdj01q 2i:tant 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 a constant angular acceleration of0qrdn eo ,r2gusjj2)*3xsp+w $4.5 rad/s^2$. 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 startin )u1 +sb9z8ceuvh8c sag from rest and accelerating at a constant angular a1bch )c8+8aezss 9uvucceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration s+q w4+evmcp 8*nubv4usn t0.of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotati,avx;: jmjiw1 ng at 20 rad/s decelerates with a constant angular acceleration ofj;j wmv 1,axi: $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches a gijncr*qfe+d, ;(lt/1yv l1xzpnl / 8n angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleratio1r (d*tz/ ,+ p/nj1ncif; xy8lg lvqlen of the wheel?

  A wheel of diameter of 68.0 cm slo snbouz+0qd v25(vtbhlkyxn x 8;)c1: ws down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of v;)xvdn5t:2u oxbkq+1cysn8bhz (l0revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s xr (lffpoh i,5o2i30ito rest over a distance of 115 m. What is the anguorifx,0phlf3 ii( o52 lar acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ywf zk84jpp7 z,zb8u1over a distance of 115 m. jpz71p zyu8 4 w,8zkbfHow long does it take for the wheel to come to the stop?

  A centrifuge in a medical ldj,jgmm((9wv8 j jpv *aboratory rotates at a rotational speed of 3600 rev/min. When switchej(p,wg * 9j8m(vd jvjmd off, it 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 tnz7qoq: w :xz /3hdik)ightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of tw/h onx:d37z q ):kiqzhe force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tig 4xn6-7fab2sq8gkvj ,q1bm s5gaa f4bhtening to a torque of 90 Nm. If a 30 cm long wrench is used,f,-qa xmbbqjv4 7s6gb2a5 ks agfn418 what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofo/2c gp6bbm k6 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 origin, mass 2m ir1rvcl l20*f6skk ly0s at x = a, and, mas slfv rylc12k06*k0lrs 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 5-hi uydits +4) ff9bnaxis 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.t5ii) +su94h n bdyff-0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a fricco5z-h/bfzckp/ y,s861 popntionless 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 radi5np6f/b/c zpzo8ckp ho1y-, sans does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is xc 6y8lmor;)/6jlorr hinged at one end. The rod is initially held in the horizontal position, and thenx)rr l6/6oycjrl 8o;m 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 r ld aay87(,ji91oyf ip72yh acm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is a iyd8 f7aj2i7 pay1,oh(9ra ylpplied 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 jixbw1+h 8et gg 8;t3lon a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelt8g +;hwtejxl 3 8igb1eration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around d8a2nbz x.34(xmmb3zs3 gngf5a/mv ef 0mmy;a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whaz.n0e a (gs5fv3 zm/xdy3a8fmb;m mxnb3g4 2m t is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required tol a5 ah 3d8 n:tvrw 3fidt7v8s;vxh+,o 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 of vki+sf7tep sjm +auek;-- z22yy8;g z$5.00 \; kgm^{2}$ 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 anc4z0vm;pg xc m6gpt7j6;;ogad 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 ;pjg ;4mxo7 tpg 60gm;z6cvcathe bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls +b s ./mfcyklt30plou -8co9-os6xrnwith a speed of 10 m/s. How high upo9/lp8.3uxrcc f mnk+- 0ylbs-soo 6t 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 rt cg;/co9 1.dyrtbhr3eleased from rest and allowed to roll yrtg3.dtc1r9b h/;oc 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 and17d8 dgfhphhptkc8 9y bdwz427m k /p7 radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere izg8fdt 7yh kw7p7429h mdkdcp/18 bhps 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 momend2.;gavh:.uzm pu4 hutum 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 moment of inertia ofo0hy- *;mv b3oj9feyf $5.0 \; kgm^{2}$ 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 has a moment of i53yyfgg5. 8vz ysk: ponertig8y:z5go 5s k yvy3p.fa 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?