Angular displacement wa. ,u . 4gc:8)hdfnm/lcbugi is usually express in units of

  Angular velocity is expressed in units u8h7p gfby* )wof

  Angular acceleration is expressed in unifity*mi72k1qzn -*u7cn 0g oi ts of

  A boy and a girl are riding on a merry-go-rov j(2mke2r*reog ;nj5gxeo-)y / e7ryund which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center;eo5r (*rg2e)2nrg oek-vj/ yye xm j7. Who has the greater angular displacement?

  A boy and a girl are riqoelwluq 0*+ck 13qtta/ *e3cu h+5ooding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge*u k/qle3laqo3 15 +uo*cwo et +htq0c, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round whi5nforv/mgue7 s lq ,33ch is turning at a constant rate. The boy is near the/35lm o7fr ,vegns 3qu outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a md1 xngrykw.4;erry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Whoy;gnrw1 .x d4k has the greater centripetal acceleration?

  A boy and a girl are i4jn ;9h6r ht w*wsni7wbm*d9riding a merry-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 greater d*m rwb9nh4 *wi6s;h w9 jtn7itangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an ac di0m.w6y-g,e h .ngobcurate statemwmi bgd6n .,0ey-goh.ent?

  Rolling without slipping depends o7gc+a weal *1wpzl3v g,u be39nv6rk*n

  Two equal forces are applied to a door. The first force is applied at the midptarm:+s q97p6t fxb7t( myu*hoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which ftafsm+m(7q6 7 9 hrbp :ty*xutorce exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first fo/cat n((a8n9zewe rq7rce is applied perpendicular to the door; the second force is applied at 30e to the plane ofq(n anz/ewec 987ta( r the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first for3non3euo)qn59k2a g *d:p wij ce is twice as large as the second force. The ratio of the torque of the first to the ton9n )e23i3j nw*u po5d qg:koarque of the second is

  What is the quantity used to measure an object's resistance t5se)6ji rn2nv i d:p6mkf8yo.by m36ho changes in rotatis3. 2bvmp5n6yj n ) 6imihe:8 6rfkydoon?

  Consider two uniform solid spheres where both have the same ou:.x+i q mwm()zw rd,diameter, but one has twice thezu+rq (.w,d:)xmoiw m mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spher2tp1 *+l xzunzes have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller szp1 z*xltun +2phere is

  Consider two uniform solid spheres where one has twice the mass and am-g;7urgr /mr :py4otwice the diameter of the other. The ratio of the larger moment of inrm4 yrgu/;r-:moa7 g pertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If t kamr922+ve + dvix-djhese are increased to 2M and 3R, what happens to the sphere's moment of inertia adj- +i+vamx 29ek2rdvbout a central axis?

  If a constant net torque is applied 7e0cc wqmh +8e(muzs/to an object, that object will

  The moment of inertia of a so wr6djs7r6:mfh rav 63d 7z4odlid cylinder 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 wheel of which has agetl p. ;ki:z9on*f5a 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 translationaklefaig9p t5. :n*; zol kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping ;;gj xw2saoqx.z(8-/ vxzjz wdown an inclined plane starting from res82.xw ojv-a qsz z(xgx;/;wj zt. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M an38( f j2b q-,hiddxfkrd radius R rolls without slipping down an inclined plane starting from r,-i8 kf2(3bh jdxfrq dest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a sys3ywg-.8c n*tf/ +jk fd5ni xwwtem of particles changes when a net external force acts on the system." This statemenc8 .w35wgxnfwd+yn-kfjt*/i t is

  In what circumstances can the angular velocity of system of particles change wiw*ccu di3z:)l4lkjj w 9 zph3gmw+() wthout any change in the system's angular m4gpm3l:iz jckw9(*dz)c wj+lw )u h3w omentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictio7 t63.qcd f acn+sjnpkje25o5n which may be present. What happens over time to the Earth's ango7jf nctjq3c2pk+s nd e5 6a5.ular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orob6th3 xqr u*6 uhea/ya5ji1; bit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the61hijx yh63tr*ube a5/ o;qua Sun?

  An ice skater performs a pirouettt,qz8i9 8qow k(z bi9e6 dck/oe (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of ro86/,ci d8qi qwoz9t b ekz(9oktation?

  An ice skater performs a p 03qdcq*- fd*;ssr(anpz 7xmcirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinem *zdqcn7p-q(d f*xa3s crs;0tic energy about the axis of rotation?

  An ice skater performs a pirouette (a fr9c.j 7 ./gi pukui4jqast spin) by pulling in his outstretched arms close to his body. What happens to his 4/ g..r7cii9 jukqupjmoment of inertia about the axis of rotation?

State the law of conservation e/ rri-vbn w3+of angular momentum.

  What arc length does the Earth travel in a three month period in 1yvs5r-jd :eg its nearly circular or j51sdv-y :egrbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance qd vk.:a3k9 rwdoes the tip of the second hand sweep through in 3 minutes and 45 secondsv:.kdk 9 wqar3?

  How many rad/s is 25 revolutions i:k)-bf9jn5vz:sex*a k5 tl t per minute equivalent to?

  A bicycle wheel rotates uniformly throug8u l0dpd:9l /ekzt)mhh 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotatiod)hm/: l0zp 9lkd u8ten?

  A pulsar (a rotating neutron star))fw(4j tbk5w m emits pulses at a frequency of 0.40 kHz. The period of its ro)(w w5bmft4 jktation is

  A phonograph record rotates at 45 rpm. Through what angle ,sr,j+oda1 zoroi*w .does it turn in 0.20 zs,dr,o.*+w 1 rojoia s?

  A wheel of diameter 26 cm turny0 gl 2pjuc)x zd77k.s8g(dno.s/qj ps at 1500 rpm. How far will a point on the outer rim move in 2.1 s7guq csyjd. . lp20josdnz7/( )g8xpk?

  A bicycle wheel rotates uniformly through 2.0 revolutiojez kceu6mvbtas 6w 82-h ;;6ins in 4.0 s. What is the averagetjkw 8-esm;za6iu26e; hb cv6 angular speed of the wheel?

  A bicycle wheel rotates unifor *5grho:qp ;okdh7+n umly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of prhog*q7;:d5+n hkuothe wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cablx 3sux+) t47bfefdv j9e which t39j) +x4xvbs df uef7moves 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 in 12 minutes?

  A wheel of radius 1.0 m is rotating with a/barxcxt 0q 21 constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheex0atb 1/xq2crl's rim?

  The cutting cord on a gas-powered we,0rn(nkypa.b0z/ +cs a h h) tomzk 9(4x-cwgzed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear spee(+h cmyoh c a-0/)nzn,ktr wx a k90g4bz.(szpd of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constal 0//7btji)*b xklmd int angular speed of 2.0 rad/s. What is the cenmx jb/iktb) i *07/dlltripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point oax32l6 k6bp+5:zhn c(zftf uvn the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving k2tzbpxn3:culf 6v+z6 a5(f h8.00 m/s?

  How many revolutions p.pc4iq )c0e1jm 1:9xm bnrfu per minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial grav 0x uep1fbcn)p mj :1c9im4q.rity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radib:,uy)1clfq s9/ uhv sus 50 m with a speed of 20 m/s. The maximum centripetal focl: vbu)sus1fh y9,/q rce (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 3hs35pr9yuiz with a speed of 20 m/s. The maximum centripetal force p3urh y9s5i 3z(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 tynzjsh p1: mv3g76p:dhe end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that theh:m :1 pz7jd3 6gvsnyp 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 rol6bq strp);ru -ls without slipping 10 m down a lane at 4.3)t; u6rbs-pr q 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 witk glu6g4wc,93 j k*dwah 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 a constant angular accv ynb a+ tx0,rm00doh0eleration 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 0.3qdjr ymsr;*o):2+ l kpfok )6e00-m radius automobile tire rotate after starting from rest and accelerating at a constant angular acceksjr;lypko)fm :q6*)re2d o +leration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an6sl ,jxaomb :+ 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 av-r3f6t( ogmf ngular acceleraf fgvo r(6-3tmtion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches a6w+jo fa0,we2hy6 t odn angular speed of 6.0 rad/s while turning through 2.0 revolutions. w,j +tw2o eo6ah0y6df What 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 rlf16270vqd1ue- v .g pna:yvgca,r gqest over a distance of 115 m. Wvd7ea p g :gv. -,ug6f1nrcq y2q01valhat 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 dnae lurjd1,pf-m(9 , m/s to rest over a distance of 115 m. What is the angular acca 9nredp,lm1,u (-jdfeleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.402jfb b0 i*ys8+twg c2r m/s to rest over a distance of 115 m. How long does jtf+ywbbg0 2i2 rs8*c it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotc07n ry pfqv26ational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before2qrcf y0np67v 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 tightenir tu1:i ,1h3e7kieuw ing 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 perpend wiku1 iu7,1re het:i3icular to the wrench?

  The bolts on a car wheel require tightenin wxv f-rfql*3ds4:zk( g to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when t4r*lvswf ( :zx k3dqf-he force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofst1pso5g wrl.hw g: ;a29jqg2 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 p4 4ijfbf(rjzt / y/)xm is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the momen j/jtzpf(4 f)4byri/ xt of inertia about the origin?

  A solid cylinder of mass 10 kg is pivotedvw 4lx3/cm 8oc about a frictionless axis thought the center O. v lc8 w4o3cx/mA rope 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg imikwzy5q-dw34 y ry 18s pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radyki5 y13zq 8wrym4-wdius $R_1$ = 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 hinghg65t-t e1i4jz rfn1ged at one end. The rod is initially held in the horizontal position, and then released as the free ezgf1ent rj g1 56-4ihtnd 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 maky:9bza(p3f/kx a(en ss 1.5 kg. Neglect the mass of the axle and sprocket. If a force 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 skx3fn(:akpy9(b az/ elipping?

  A 1.53-kg mass hangs on a rope wrapped aat;a 763al,s:uwr0 fefz-x ootg bl (8round a frictionless disk pulley of mass 7.07 kg and rad,l3:olxa6wz(7abug o 0f;-eartfs8 tius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mass1)dg16f 4sv/wphh;atkz2 d jk 7.07 kg and radius 66.0 cm. What is the accelerva gkthh/)jk4dwdp1s;6z12 f ation of the mass?

  A rotating flywheel can be used to store efa8 xeb gw2h 3.hscj3:nergy. 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 in hcy36dza*:w lu: cjw3ertia 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 kt.(v(zs 4brtufby.k3 g 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 s3b( k.fy(vbr tsu4t z.phere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 1)arbd rx;k/w * qscw0nai*5 8r0 m/s. How high up an inclined pla50c;xra/wa isbw k dr)*n*r8q ne can it climb before coming to rest?

  A hoop of radius 0.50 m and a 5ryf9 7u/ sv-qe tno (ta3rl*x 9p3lmdmass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it 3lf*9a ps7 eo(ytdvm/l5r3- uq rn9xtmoving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipa6cwzjpvm 8ei o.xza.u5 zn v764q:f 4ping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of vuq z8x.j46zzevf 4apno 57imwa c:6.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 momenafrx4l9hg):0n 29bj7d* g ua8 zq r olnov68dltum 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 inertimmjh8 o ou;a/cb -jvd vh09a)rcc 2:/wa 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 extejh gb ap51dbjs ww .:qwck)5y*jt;b-f,)4urbnded has a moment of inertij 5: gr;bdf5w, a4jbb)ujwyt-.b)pksqh cw 1*a 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?