Angular displacement is usually express in unisd4)gj1p; sxc ts of

  Angular velocity is expressed in uninu :v,jhy 8 6ilvs2g0y-w3nnb ts of

  Angular acceleration is expressed in24:(r 8m0r ltaxip ney units of

  A boy and a girl are riding on a merry-go-round which is turning at a cs :)x5q/ghm( lsfe(wconstant rate.fw () esx: ms/(qc5ghl The boy is near the 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 whichuisc ea6el 2rm-zytx(*w o1 2sy z0/n+ is turning at a constant rate. The boy is near the outer edge, and the girl isos0 i yne2t1eymx/ + -uz*2wzla6(rcs closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is tur nxrq2.y +d/zhning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater lidz. /2 hqny+rxnear speed?

  A boy and a girl are riding 7: :oieoqe:cpa merry-go-round which is turning at a constant rate. The boyepiqoceo: 7:: 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-round which is turning at a consta:g9vc3,c xj:up( dq ckalso xe-407gtnt rate. The boy is near the outer edge, while the girl is closer to tc ,uc3vqp0g:tge4:( d xak 9s-c oj7xlhe center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of)sofra7e(:u smtg8 g6j bp:-r the following is an accurate stossf:r-: agpr 86bu(m7 egj)tatement?

  Rolling without slipping dem3he1m;vqmg,/rotnjq37d) jgmv 8 m3 pends on

  Two equal forces are applied to a door. The first force is applied y zgf8m*.kk u 2vi/k2wat the midpoint of the door; the second force is applied at *2gmkvwf/zu.yi 2kk 8the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are app4 p,/gy9ne3 f9xe ytlmlied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greatyn3fe/m g9y 4xt9,l eper torque?

  Two forces are applied to a doorknob,qcl28)jv9s kq perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of tj2cqk)vq9 8sl he second is

  What is the quantity used to measure an 6 ;ey()qxhrqb/h7c:* hy(kubibikiv69 r4dpobject's resistance to changes in rotation?69k(c7hi ibrivbbqpkqrdy 6u()h y4*xh e: ;/

  Consider two uniform solid spheres where both ha wqlwr1ku2siz-7-2egxo q yah i.7a 2 :ezc..qve the same diameter, but one has twice the mass of the other. The ratio of the larger momeriaqqs o.2egwci xu2wh -. 77e1k :-aql2z .zynt of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice thewd6uekwq.v;x +(7 fe a radius of the othw7v; q6wae+uf dke.( xer. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one hae +4fpl-8konjhk 0r+b 0vj(nys twice the mass and twice the diameter of the other. The ratio of the larger moment of 8 n4pjr(oj b k00nklvyh+ef+-inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius Rh1alw)i- 2xrdl6t)) m/zmhuacf:;bg . If these are increased to 2M and 3R, what hap f -xrdwa u;ac6i)1 :)/tz2blmg) hhmlpens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied:q/ ra8q8tha e to an object, that object will

  The moment of inertialsr::s6 mpbkndjg5 81 of a solid 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 dtdi rcxr: 243150 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 the wherrc:di 2t4 3xdels 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 . p:js0tx.mk zdown an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the ixm.p.t j0s: kzncline depends on

  Suppose a solid sphere 4r 0u7,p d2pogrnd ex;of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere 0ded ru pgn4x2,7ro;pat the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when atrpeoe4 .cr( 2vzzd34 net external force acts on the system." Tdvzco2.pe( 4 4etr3rzhis statement is

  In what circumstances can the angular velocity of system of part1zom mh/r :h1licles change without any change in the shhmm 1o /:r1zlystem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction nwco/k+. a;kbh mvu*s8p5 n5ewhich may be present. What o;k+a5m bh*wkv5u p/e.nc8sn happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipticalmoe96ih ev u52 orbit. As the Earth moves close to the Sun, then which of the following best describes the orbitino5i9mue v6 eh2g speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pullin3hd6; xfe )cczg in his outstretched arms close to his body. What happens to his ad e zch6;3xc)fngular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in h1ywa 8p0txwe*unlxkm9/ ; -w tis outstretched arms close to his body. What happens to his rotational kinetic e u/0lw nt9ay;-x 8*texmwp1 wknergy about the axis of rotation?

  An ice skater performs a pirouette (a fast2 ;8d;)tjfjk4onl/ ;nt*,t h mbwvyxv spin) by pulling in his outstretched arms close to his body. What happens to his moment of ineywovl;jt)txvkdn*2/ ; 84nm fb ;h,t jrtia about the axis of rotation?

State the law of conservation of angular mome.or v z-kv4h ;km.y,(*slp3jtuve6i lntum.

  What arc length does the Earth travel in1.ql8fgdw(4rf8 e tw5 c* f-jjhmm 8kr a three month period in its nearly circular orbit about the Sun with a ramrkcmfg(4f*8 j 8wwht-de 1q fr.j85ldius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the ti.cxf 9muxbfc4l1k800uk qm 2 yp of the second hand sweep through in 3kum02b lufmk0x.498 y cxfqc1 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute 2 x;dqv2uy r)dequivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in5vg0yd6+fd60q n w7y1 d1t9y ljevce h 4.0 s. What is the frequency of +ygwyded15q tly19 0 v j0df7vn6 che6the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a freq:bkjl(n5 yy8w i dvj09uency of 0.40 kHz. The period of i0nj wj:dk5vl8y(by 9 its rotation is

  A phonograph record ro4vhqr; .:anaj tates at 45 rpm. Through what angle does it turn in 0.20 s?:.rv ;qah4nj a

  A wheel of diameter 26 cmif;th,h n)x3,slur)7 rrp3a n turns at 1500 rpm. How far will a point on the outer rim move in 2.1 s,7fr;nrsxt)una l hh)i pr ,33?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thehu4 ezz516ky j average angular speed of the wheeuykz 14j6hz 5el?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is th,.sta:* zu mk4i zlx7he linear speed of a point 0.10 m from the center of the wheel?mlxz 4us7z k.,:*ahit

  A cable car at a ski resort carries skiers a distance of 6.8 a(oq 26t fn9fm)iuyd+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 iy6)f(d2oq +fam t9n urotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m -0:z rwr vly f,h:k9vlis rotating with a constant angular speed of 2.0 rad/s. What is the linear speed z:0rh w:9kvy vl-fl,r of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0g-yt oz05bd m(.16 m in length. If the motor rotates at the rate of 20 rev/sd5 0t(ogzy b-m, 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 s+e ilcrx0r. +;z1ix nwpeed of 2.0 rad/s. What isrl r.xiz+e;wxn+ 1ic0 the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a gv l89wx.4eowe r/; mnpoint on the perimeter of a bicycle wheel of diameter 70.0 cm when the bikem8 xge 4e.w wlov9rn/; is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circulpo g8ad c2jpq9((ddr3ar, rotating space station (r = 10pa(dj 2 d3gorqdp8(c900 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 fsr: n836 az rzq.st4 48n*uyke bu+by3sjq6em with a speed of 20 m/s. The maximum centri qty.ue4 6zynq*u4sbnb3sr+k j8fz:a 6s 3 re8petal 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 sp(+s(de3js nlv eed of 20 m/s. The maximum s sne j(lv(3+dcentripetal 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 around in 6 t3w;nksn lfd+ *v+bla smooth level table. If the maximum tensionllntd +wv3k6; s*n+b f 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,:w pirsi+citf vq7/0 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 ipi+7,wv/0:fics r qtm/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 cqneqqhj p(:4 d3nt3o -onstant 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 constanttz: k4rsg6f2l angular 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 rotall)zpp2mre(mzu/ k jh8 rmqas 579 7r6te after starting from rest and accelerpl msu q7zr(epzj 7)kmh96l8 ar5m2/rating 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 accelerat f ;fmb+ 2rb7w dp+d4x79m,iaq fofj4fion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decely4z7 0fd9jy .bf7slglerates with a constant angular accelerat j407lf.7yzdgyb9 fslion of $-5.0 \; rad/s^2$. 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 whilesvl*1w r u2/cz turning through 2.0 revolutions. What is the average angular accev rw/*uzc2l 1sleration of the wheel?

  A wheel of diameter of 68.0 cm slowy4/fz 8crwn x4s down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to /r n8yfzwxc44rest?

  A wheel of diameter ofh2- 0ul 4yjr,kx tct.gtfk7s; 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is7c4rtsk,2t-h kg .lx; y0utfj the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniforw 5ayfo styrmh:vm)p((;+ f( dmly from 8.40 m/s to rest over a distance of 115 m. How longs:rt +y(wfh((m5;modfy )pav does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a nymh20yh.jz6 rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to rest0 j 2.mhyzhyn6.
(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 90 N*m j t(grtn,7rm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to tnr(,t7jtr* gm he wrench?

  The bolts on a car whew7 rah1 tn(fc5el require tightening 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 apctw5a f1 (nh7rplied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiahy8 - f eko;xygz7s r1--,emsh $3.00 \; kgm^{2}$ 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,7cgloxr 3h6-a rq4x+t mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of iagrr o74x+q3t-6hxl cnertia about the origin?

  A solid cylinder of masjdxi :/r 2m:kss 10 kg is pivoted about a frictionless axis thought the c s2jdk/ri :x:menter O. A 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;un*xy)j ;n r z- 2f(fxqhcgpo8nf o9g-kob0+ 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer rad8p;9- knob+ (xf 2u ;hz g-x*fn)gycf r0oojnqius $R_1$ = 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 held in the hoenc z03m *bjd:rizontal position, and then released as the e:0* dc3zmjb nfree 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.i sxz7tio,cx,p m/,xx- i /lc/)x6pn b Neglect the mass of the axle and sprocx,/,cb nxpp/x-il i tox s7z,x6mi/ )cket. 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictk7x)jw7 b a8crvp)jk 2ionless disk pulley of mass 7.07 kg and radius 66.0 cm. vax)jk c br2j)k 7p78w What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapp69h t6*cfh)ckh9 zmgzed around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What itz6g zhc69 f* h9kchm)s the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it r hguw-kd0joha8( f o9 wb,n-x; ,aas.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 inertilua2 s/,h,iyea 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 d6bd dbjg m8-(xx(ga4radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sp(db 6x8x4(gjg- abmd dhere when it reaches the bottom of the inclined plane?

  A solid sphere of massn bho 5-/c fsy /4vbur)dgz6+f 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it csr hvzy +of-b6u)bdg4/5c/ fnlimb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releazec9 ws22(wvb xd mh*+sed from rest and allowed to roll down az9vcdh x+*m2( 2sewb wn 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 slippin 1m2koc/ualf)v fh3 ,k 5.rworg down a 35e incline that is 7.0 m longr chfrk2u av1f /k3woo)l,.5m. 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 changescwbb*.i) xfs+ 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 og(jmnw r3w 0lc5/y g19 jizn-rf $5.0 \; kgm^{2}$ 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 ggj + gu i8u7,b;tx3ilhas a moment of inertia gjb 3u7xigt ,l;+iug 8of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?