Angular displacement is usually.iqmlp0 k b-a- gdg-o :o2k7dl express in units of

  Angular velocity is expressed in units0p 9q8b6fp c.,): dwzpaj hqft of

  Angular acceleration is expr+2oea 8 rgxgm5essed in units of

  A boy and a girl are riding on a merry-gx uu0g2rtmzj ca99t4m3 )(:8hz*( dbcnrs mquo-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 greate u)rgd* qhctm(nzx9sm cj 3u: 8m2zau(49btr0r angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant r; ve sym1/how.ate. The boy is near the out.;1 hovywm/es er edge, 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 which is turning at a const7fdd:k5 cc1 rgant rate. The boy is near the outer ed: r1k7cfgdc5 dge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-roun3q qy0rk( q4p9 h4ruqtd which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the4 q rqhr tyqpqk039u4( greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round llya3g+1c + shzz);u owhich is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Whysczgl1 h+ u;al+z) o3o has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurateramls9zmv / 6(pfb +)w stas zav/)m69lwf+m bp(r tement?

  Rolling without slippi4xx p1o8i0 uhzsyhr8 5vw0wc1ng depends on

  Two equal forces are applied to a d7 vax12hol (gud.ck)j r:p6 rpoor. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces7pvj.p )xo rhrgdl12u (c k:6a are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is appvysuqypj*el1l9jg;69 6mpnbi. 9 b6 ulied perpendicular ql;vmp961iuun96j pj*g s l6.be yby9to 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 tm4jel gaf:47-oo6n ogo the door. The first force is twice as lamnla 6oo4gg 7f:-e4jorge 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 an object's rg)m rxc3 0wn,q,s uel6esistance to changes in rotation?6 un0,mw),rsq 3elgxc

  Consider two uniform solid spheres fn. 4t m1q5dvad.kumf 27w+nj where both have the same diameter, but one has twice the mass of the other. The ratio of the larger d24tm.qf5jnnv d 7wm.+fka 1u moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have b: h4h /14tjzt 0djef0q*ysfg the same mass, but one has twice the radius of the other. The ratio of the larger sphere's ht/ q4 z0jf:d b1tyjhef4gs0* moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the ju y)2kvp6gwu4zn)d 4*te u1w mass and twice the diameter of the other. The ratio of the larger moment juu*nyetz4 6wugdv wpk24 )1)of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are iw5v: 2i f-2ydo;gimvy-b) jzi ncreased to 2M and 3R, what happens to the ibdwoz2:m -vyi-j 5f; gv)iy2 sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an objel(/svt4 fwx m,ya w-4kct, that object will

  The moment of inertia of a solid cylinru3nmu : kk-2u /en:vk 1q1 s2pf0qecoder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotationa neuvpo0k qu 1mnfk-es3kr /qc: :2u21l kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg ctf*v+i566gct hc xr 3/vgpn/and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic en6*gt/6+ivch/ rpv3gc xf5 tcnergy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without rt .02 oxdc3zyslipping down an inclined plane starting from rest. The linear velocity of theo 2r.0d3x tcyz sphere at the bottom of the incline depends on

  Suppose a solid spher8 g/ihp+6z jzue of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline d +/8i ug6pjzhzepends on

  "The total angular momenp9q z.n+v)y3gkba5w:jf 6ks( aay;jftum of a system of particles changes when a net external +kaw( vakp3 yjy: a b95fg6nj);.qfzsforce acts on the system." This statement is

  In what circumstances can the angular velocity o o: 5rm2i, f40fgsgxab fz/0zkf system of particles change withm,igxfrof 00:s2 /zga 5bkfz4 out any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit.n njt74m5e+v-arc/ gkoe td:7 Ignore any friction which may be present. What happens over time to the Earth's angular momentum abta 7 n rjek-tgo:4 dvne/m57+cout the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth mo0jx r 56hajp7vz ft*nkiw x6635 4qikdves close to the Sun, then which of the following kq6 x4*di5 vnrz7j j53apxitwf6h06k best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstavyxg7-c ikzy5i8z rdp2w)8 eaev-6, p05 t uiretched arms close to his body. What happens to his angular momentum about the axis of0eydvi- za)p8ker 57zawvtg52iu i ,x6c y-8p rotation?

  An ice skater performs a pirouette (a f5a. di(qg 7 k37s rlpen4/lmw45wa xyo7sju9rast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotationas4qxn g4pm7ld. kaljr 7( / sy53w9urew5 7oi?

  An ice skater performs a pirouette (a fast spin) by pulling inx jufrfm;0mrt 0s.5yg3w 1/ey his outstretched arms close to his body. What happens to his moment of inertia about the axis of rw/r y5tfmfmrjsg030u1y. ;x eotation?

State the law of conservatis7nv(z6h b8z1. +p zly-d ydsdon of angular momentum.

  What arc length does thss3w x+-j *qpr z2(pf k+ilug-e Earth travel in a three month period in its nearly circular orbit about the Sun with a radiusxlpz2sgjq s3-kp-fu*+i + rw( of $1.5 \times 10^{11} \; m$?

  The second hand of a clock16 5r,zck .b3mk; +ooapyfcnl has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minn1;k.ozobl +pyacm5cf r36 k, utes and 45 seconds?

  How many rad/s is 25 revopypj4bvp0;k py1yr 6)lutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. 1awv x8c0f- o9lqjd.9ae)y ixWhat is the frequency of 1ydvwxx).al - a89 jco0e9i qfthe wheel's rotation?

  A pulsar (a rotating neutron star) emits p*gi0g8g2 ql n:gro(zpz4ff 1 tulses at a frequency of 0.40 kHz. The period(8 f2rqpzz1fnt 0go :gl*4ggi of its rotation is

  A phonograph record rotates ao aoc+1ri9 an3t 45 rpm. Through what angle does it turn in 0.20 a3r aciono+91s?

  A wheel of diameter 26 cm turns at 1e6sa 8m,.6bclz qhd)u500 rpm. How far will a point on the outer rim move in aqm86c. )sdl, 6ehbz u2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is th f/uca k,f75efe average aa/ kcf7fu5fe,ngular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is tdnnzf438ryx - he linear speed 8 yd nrx43znf-of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers t ,y,42dl2bxnbce/i r l y)hl*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 th,nrhil e/yx,y clbb4)d2lt 2*e cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rd b)91bjgee)h 0iu muyx.85ab ad/s. What is the linear speed of a point on j a ux1) ihyeb)9g.d58be0 bmuthe wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If q;379 rey w g,ctrfh(bthe motor rotates at the rate of 20 rev/s, what is the approximate linear etf;bw c 73g,9 yrqr(hspeed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular:rl*16.zlyers g6rh d speed of 2.0 rad/s. What is the centripetal acceleration of a point on th1rz*g .ld6rs6ehy:rle wheel's rim?

  What is the centripetal acceleration of a point on the per;tich0sm eo1 -imeter of a bicycle wheel of diameter 70.0 cm when the bike is moo-c10e;m tsihving 8.00 m/s?

  How many revolutions pe nven0kxk:- 5pr minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artifici-0k5vkn:ep xn al gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m wi ov+2w9n0ynzl +pt p5uth a speed of 20 m/s. The maximum centripetal force (provided by static friction)o5lzptw n +uv 2yp90n+ is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circu qu6faj2f -ap4e0dr-jlar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictidaqp 4ej- af2f6ru0j -on) 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 0.750jqam +9q-ovoge,v/jn,3.5xs wllb 5 a-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 s 5qsax, aq9eoj /w.v5nlb-m,v o3l+gjtring is not to break?

  A bowling ball of mass 7.5 kg t1gm:u,q;1pm b4g 1 siuk-w gvand radius 9.0 cm rolls without slipping 10 m down a lane at 4b g1s1mvi,t1wk4;u q: m-upgg.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 cu*qz r4t, bv0r-8juoi 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 constanq,feilcu2n;;5a*pc bt 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 i0 wv*v8fa. .:hta0vt .uynlja 0.300-m radius automobile tire rotate after starting from rest and accelerating at a constant anf a: . *n8v.u0ivha.vtlyt0w jgular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an1l.zd ;zr u hrjq;rosor51u-6 ad h05c angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rcg4l: 7bbeqr.txr0dc;f -- wkad/s decelerates with a constant angular acceleration of rcrtx 40.; -wbf7l cekg :dq-b$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest as j nfpoln/73zkby21:nd reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the whe1p ls 27bnz/fn:j y3okel?

  A wheel of diameter of 68.0 cm slows d2h :sj:p (eseij bl/8vown uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates :bjj ieh e(p/vs:2l8s in coming to rest?

  A wheel of diameter of 6lpz-eh k3fvj,p+/ ,lu8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 3pzlk vp +e-h ,fl,/ujm. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unif scuu0t+8w2twormly from 8.40 m/s to rest over a distance ouutc +st w0w82f 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speedimoc 9w4meo3 : of 3600 rev/min. When switched off, it rotates 50.0 times m3w: om e9oi4cat 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 tigyyvy 00ld,zlcj+58kl 4 kl f2ehtening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnzeyyvjfcky+l 08 l,lk d5l024 itude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torquktzsp-o7 pep ( +h/;xw+-spfke of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force applied atpet-(hsp7p kp+f-kz w+;o / sx $53^{\circ}$ to the wrench?

  A wheel with moment o;4x )j/mxxcxpuy5t3s f 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 modeledvctm-1aj(2v9k vel). )cri ov as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. Wheol) 2(vvkv1rvct9-j. cm)ia at is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted 4y6e2t1dhrni 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 around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) hi2 dey 641trn What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought * i+s sie4yr6( jhmf1fuqq r+-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 f4fu iq1+rhr-ssjy+e(6qm fi*orce 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 al 6v,i-5wudknb w .0)gxpsm9rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (Tv)lgxk5i .6mbs,dp0n- a9wwu he moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to bet/; baon3)t2nc jjdp2 a ring of radius 30 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 of radius 4.0 cm for 4.1 s, what linear speed does the wheel achievtpjo t2 )jn32cbn/;a de, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlesk2yr ps7c -nngbi8(vr1 ,j z uz7m74lis disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular avr 8i izk4bp 1j ynm7n,r2cg77zsl-( ucceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mass-78w qdkhe92np zed*r 7.07 kg and radius 66.0edqhpnw9 z8d 7k e*-r2 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store ener 2j7o*2,zn(vjzjefhegy. 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 inertia /,awai/k ;ap o-d/p xwof $5.00 \; kgm^{2}$ 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 radius 0.010 m starts from rest and rol pvvq-c;)s1zk o :zy vznu3f:lyni 47-ls without slipping down a 1 c7:o-z13v)yu l qk y znn4zv;:sf-vip.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rok*kg,ri)q6 fmm:k0 ghlls with a speed of 10 m/s. How hig rk)*mk6f,h0: g mqikgh up 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 tse8f h-* fxszz-, ;hgreleased from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of *fsgz- ,-fs8 ztex;h h3.0 m?

A solid sphere of mass 1.5 kg and radiusg9 ) f*9,7nj yewdvluv 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 is given by *l ,wyvnuj7 d9) v9egf$I = (2/5)MR^2$.
(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 changrt1 / 9t h8rlmiyjgo l*pq9 :it9yk21kes 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 ih(xj *q hx3 0 ;iqwxfqv.3wx6dnertia 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 extended has a moment b z8c9; wwse9nof inertia o zs 9n;b98wwecf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?