Angular displacement is usually express in units oma(d ssqfw 0;urq68t o3x3qi0 f

  Angular velocity is exsu izwgu.+t 6skl4 1elk+mib)730h wlpressed in units of

  Angular acceleration is expressed in uni*f duylx0 oz)6ts of

  A boy and a girl are ridlk d:d u*-kn6j:8qrqaq zq,5. wls9 ujing on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl w.9 qurjqldqj k,zk5 :adu8sn6q* l:- is closer to the center. Who has the greater angular displacement?

  A boy and a girl are ri:0-*)zu. mszabz acevding 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 ha*:b . s)cu a0-zvazzmes the greater angular speed?

  A boy and a girl are riding on a merry01 f dlqjclw07-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 haj l7cw01dl0f qs the greater linear speed?

  A boy and a girl are riding a merry-go-roxd3hxl. fj r pfq2 +p(savi623und which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has2 l+d ir(xvx p f23qh.pasf36j the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which isbcctcy * i7glc:, ,wm( turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential ac mcg,t,w7 ccc(yi* :blceleration?

  Consider a rigid body that is rotating. Which of the following it: 6vjt q9kpn7 a i/m:-h:tqnes an accurate statemen :t7-q qe/apkt:nnhi:m6jt9 vt?

  Rolling without slipping depeneys- 1 dv ,tm9-ohx6ukds on

  Two equal forces are applied to a door. Thextpfx 0ek.w).lbkw vkvt6 8 8+ first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts thk f6+x) 0w8tk lxw vvte.pk.b8e greater torque?

  Two equal forces are applied to a door at the door .lt9qowzrs 2 *rgj8w7knob. The first force is applied perpendicular to the door; ther2lwr9zjw*t qg.8so 7 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 i7+5ji spu 9bidoor. The first force is twice as large as the second force. Th+ iuj7bi9 s5pie ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistancemn+co,l l o,f: to changes in rotation?, lol ,cn+mfo:

  Consider two uniform solid nqg2 mnk4iz0/ spheres where both have the same diameter, but one has twice the mass of the other. The ratio ofn mg zn4/kq02i the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one hau m3 iq3,ygbc3s twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere biy3,c3qm 3u gis

  Consider two uniform t a qz+do/4ec/)v,qiysolid spheres where one has 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 inertiad / oy/iv +a4,qe)zqct is

  A uniform solid sphere hy9z r 0b3d*frveq5k:w as mass M and radius R. If these are increased to 2M and 3R, what f e0 yr w5kr3bzd9q:*vhappens to the sphere's moment of inertia about a central axis?

  If a constant net torque is 7,+w e mg,sanyapplied to an object, that object will

  The moment of inertia of a soli ko ;3iakh(bb1d cylinder about its axis is given by 0.5 MR2. If this cylinder rolls withoua k(3bokb ih;1t slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of maa28 ffh+nr*+juka1s iss 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 e f1nrf a+*i+h2kjusa8 nergy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid spheredx 4-oa* ;ag;uo (mbajmz,gy 6 of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the inclidgb;ya*u,( aom - gx4zj6;oam ne depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an i t+dk zbj/9lxikfd55 2nclined plane starting from rest. The angular velocity of the sphere at the bott/ b kdk5dtxfil5z +2j9om of the incline depends on

  "The total angular momentum of a system of pcr8 nu1ygxo+8xv2 j5zarticles changes when a net external force acts on the system." This statement isjx5u xy 8vc+o rn82z1g

  In what circumstances can the angular velocity of systemjs(c;4zs tr ,juj 4l4 :.w is.s9qjohz of particles change without any change in the system's angular momentqz(itsojh:j9l4u; zw .j,c44j ss r.sum?

  The Earth orbits the Sun afxef2h *+f;yn nev1x* 87 choin an elliptical orbit. Ignore any friction which may be present. What hcn8n e+x eoy*f2ah;ffh*1vx7 appens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Suht 2avu .v5vvz kfvw9 xz02*/un in an elliptical orbit. As the Earth moves close to the Sun, then whiuzta 9x2.u5kvf2v*0zvh v wv/ ch 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 hisa4wr;xq u--f: o k03aqr upeo-ah)cp+0gm1ta outstretched arms close to his hop-oq-: t qre g 4kprx;aw3ma1a +c-au0 u)0fbody. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouet 5o;5hp7) +oxk ga kc6hlzus-ste (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rogcsp6 h; -7s okazu)5 o+lxk5htational kinetic energy about the axis of rotation?

  An ice skater performs a pig gawg6d.8ue) rouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment u8wed. g) gga6of inertia about the axis of rotation?

State the law of conservation of anv4,bic vy 1+4yuyum:mgular momentum.

  What arc length does the Earth travel in a three month period in iyi9 2p0yuhgv7 ts nearly circular orbit abouyuyhp 7iv g209t 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. f(t, r9fyus79hgb .u/e9xayhWhat distance does the tip of the second hand x9ga ./hrfyeut7 ys9,h f(u9bsweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutipy2z z1r8 (nrqons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thypuc1d7 s 3.pzgh)p(a e frequency of the wheel's rota17y p3d(c a)p.uzhpg stion?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.xo t9lu3)ow1l40 kHz. The periodw3tou1l 9) oxl of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in nif.l,bp0cwn4 z;f-vzu-r 4x 0.20 4bp4- 0fuirnvzc nzw-,lx.f; s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poin qtre obd.iv.p *k+83wt on the outer rim move in 2.1 sidq. * 3wte .r8+kopbv?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wtmpo,/ k9r +/ 3 fazvvszx-/fehat is the average mz f/ oav-z/f9+/prtk 3x sve,angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0/v + uyxawt,qo-,i9) csv2zb w revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the whee )v2sc- o,,bwzvaq /i+ 9txyuwl?

  A cable car at a ski resort carri1+g .ef+.vhis+zgtj,j:rd oe es skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter ej.gh:zj + e,+v.+fitr1so gd3.0 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 constant angul*1x6cx:mtqny - kf3jnu)c d 6 nk9px+var speed of 2.0 rad/s. What is the linear speed of a point on t:ctkxcxm6-f+ nndp3 y9vk n xqj6)*u 1he wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. fa n0m lcjvkci ;e(gr/154+lu If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed oa4;c 1iknr5cm0feu/llj+g v( f the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad5tgf(yei+ ke,/mgdr3 /s. What is the centripetal acceleration of akf ety,m gig+/r5(d3e point on the wheel's rim?

  What is the centripetal acceleration of 2vi9.tbhw7jr 7 6,uhkv,ed wha point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is movinivh,h7r2ewu hwb9djv k ,.76tg 8.00 m/s?

  How many revolutions per minute (rpje.68b hxo2hcpk hr8/f2 o.sbm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity of kfo8 sb.p 6b.h2orhe j8/xhc2 $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed ofvlgm n3,; +r6hnjel( e 20 m/s. The maxim,r;n+e (njh6mllve3 g um 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 of 20gnt2vxlte+b d *p(j y+ yq19:i m/s. T*idtt+ y91j(qlvy n+:bgepx 2he 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-mp-z:aha9lr(2 2 pd)wrych 5 hg, *acku 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 string is cyc5 d hpp2a-hkg* 2a(,lz:9rwhr)a unot to break?

  A bowling ball of mass 7.5 kg and radixqe5a + s3ir1ous 9.0 cm rolls without slipping 10 m down a lane 1 x5+qsr3iaoe 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 acceleratio)z9 ;kae6/ot;as jqwob tbl.:n 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 accelerat.w8ryvfy7hw*:uhod ) ion 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 starting e *6 j.vxob6s kswa9yu :t-gn6from rest and accelerating a6ew j. u6ob6s:kyx 9tag- sv*nt 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 accl0wt4 gbulpam,u,d:ny d(;c,i:1qa 1o. xjlgeleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotat b v87pubf3j1+e;etep ing at 20 rad/s decelerates with a constant angular acceleration +;7ebjt81ee pbv 3u pfof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s w a fryf7y75f.mhile turning through 2.0 revolutions. What is the av7f.r y7fam 5fyerage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8m/x-bcnbj2)8l oi-it p7 6*szu w 8ngl,9ilpc.40 m/s to rest over a distance of 115 m. What is t)n n8i/zl89i 76clxlpsi-b2*ujgtmob c,-w phe total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unifhoql- )b1ljyf;t: fdn)6bi k0 ormly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleraj -bbk06tl)hqif f1; ):ldnoytion?

  A wheel of diameter of 68.0 cm slows dow*9tuj7 3 l5e:ucj bag6wbh ft3,;i8m ykgpzn -n uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the6u 39jf-pmc:h;,jnk eubigya8w t5g 37l*t bz stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/g(nck sk+ 5n cf845hwimin. When switched off, it rotates 50.0 times at a constant angular acceleratiocf5s hn4( k5gnc8+ iwkn 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 torqje .n)rd3vv i3ue of 90 Nm. If a 30 cm long wrench is used, what is the m.dr3 3vnejvi) agnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90fy1 tztf(-t+o tg:nef. 1-all Nm. If a 30 cm long wrench is used, what is the magnitude of the force req 1g:l t z+f(-tl-n yftof.e1atuired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti9+alo3u1 3pa fj )c1h-buanl ia $3.00 \; kgm^{2}$ 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 may. 2)vx/jyho /zgfx7 is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. W)ag hvoxzy.2f /yjx/ 7hat is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fri )u(yir/ jfc )f1gfyg.ctionless 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 acceleration of the cylinder(. ffjgy) cy)/if u1gr?

  A solid cylinder of mass 10 kg is3y -b o f7d3t0jxlnqn. pivoted 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 arod.jtqn-f 3y30olx7b nund 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 helde d;m,ibsi0y . in the horizontal pos;m,.ii d0 sbeyition, 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 about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. nnag-uo m:u zn7x0+f1 7bmw /y 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 :/x7 + guz1oyma -n0n wnu7bfmachieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wjrj,-:dk)iwspc::v irapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is td:vi:r,js w:c -)ikjphe angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley s (.aq.gc gt* t/q*emtof mass 7.07 kg and radius 66.0 cm. What is the acct/* c(*te amq.s t.qggeleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to st ja-q3knf 4*je;td(etore $1.00 \times 10^{6} \; J$ 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 inertiar*n81tei w.hy8 u* vh2s.geri 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 an /y/v0r4 g5u a4pgzrixd 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 incryi/zx 4ru5p ga/gv4 0lined plane?

  A solid sphere of mass 1.0 kg i,h:- 2m8 f+gqc6ixws: *w .jtzookseand radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb beforeg-+isx,ofz 6 m*8k2ow j:cwthqis.:e coming to rest?

  A hoop of radius 0.50 m a 9m1m2v(lurba nd a mass 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 distance of 3.0 m?urml bva(2 91m

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping downjc:cal; .xq)j a 35e incline that is 7. la j;cc.x)qj:0 m 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 e27e, h+bt n*;b*h1m faqyr nschanges 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 o(t rf2cnrv5: lf $5.0 \; kgm^{2}$ 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 d 59+ psaov0y7:2zfpat *yy tvhas a moment of inertia2z*0oyt :ppy yas 9fatd+v v75 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?