Angular displacement is usualkfwn r o5.ca; )ch6b+-aoquybcf z28+ly express in units of

  Angular velocity is expggxq 8 g) rxr1x2hvf06ressed in units of

  Angular acceleration is expressed in un5,2,rlwaru9cq4sq n* zf +dxtits of

  A boy and a girl are riding on a merry-go-round which is 1)8zo nyyw, (jiy+po rturning at a constant rate. The boy is near the outer edge, and,)z+(iyp wyj8o r1 oyn 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 aj-lw fn11er4p constant rate. The boy is near the o-41n pr ljefw1uter 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 con ro-dhqe ms.rb28*/xrstant rate. The boy is near the outer edge, and the g*2eqr/d-x.o8srbm r hirl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at mc2lv;yard mlsq( ni7;g0f 4,a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greaf4ny s7v 0ill;am( rc;,mqgd 2ter centripetal acceleration?

  A boy and a girl are riding a merry-go-roundy2ejqsxn2 +ah9d d9hil:-gfp 6zg ;e5 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 greatn2 i:p9eha z-2lhx d6+9js5gyegqd; f er tangential acceleration?

  Consider a rigid body that is rotating. Which of the fsbk*p rp/e7l,ollowing is an accurate s *re,/lpp ksb7tatement?

  Rolling without slipping dex4qts*n i:*s9r;4sm fx; rtpipends on

  Two equal forces are applied to a door. The first forcpdv pqybd. ::9s0+lwqe 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 lbd.:dpsvwqq9 +p0: y the greater torque?

  Two equal forces are applc r)ao6rvcpf3kq8j /.ied 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. f3roc qr)6ka 8pv j./c Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpk8xpcc(ax k;7 endicular to the door. The first force is twice as large as the s(7;p8ca xckx kecond 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 resistance to changes in ro/zuwa 5sk/e bc82)aa 3 2ujrnv pc)q(station?2vcwa/)ub c(2pkur) /an s3ze q58asj

  Consider two uniform solid spheres where both have the same +lo-uuwc4l, m 6z pr9fdiameter, but one has twice the mass of the other. The ratio of u, lorl 9mcup+w4fz-6the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the sab; lng8 *xhca5me 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 s;5b*xcg lha8 nphere is

  Consider two uniform solr:s ultju; g0;id 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 :ul;s t;r ug0jsmaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to:07ss cap8uabuyyj3 4 2M and 3R, what happe8yasasy3 u7cu0b :p4jns to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an objetnk: +xqax; :*4o2 w ohsey3dca 27qoect, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2.9) eo 7e)o9)uaq*qduv7a hrtt If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic enete)doeq a99q7ua) u) vh* to7rrgy is

  Consider a motorcycle of mass 150 kg, one wheel of w2a+roxng93+dx y ;w. i0xmm*c*sf mad hich has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotatio m xdow03rda **gc+axym9ms;ni.+xf2 nal kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid spherse a;06m) y ,g 4by*)oi2kvmcnctbn6te of mass M and radius R rolls without slipping down an inclined plane starting from rest. The line;n6kng) 6ymst, i*mc4v c )obb2 eat0yar velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without sliprt0i/wes0df 2 os*;k y,qnt2iping down an inclined plane start0n,oktfwd r*si0i22;est/q y ing from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net externx9aatxe 33g0r6arv *0 ful.dw1g; b ehal force acts on the system." T6a 3x rrh 3 90ggex1ua*dtelvb.;a0fwhis statement is

  In what circumstances can the angular velocity of system of partin tyx(in 53;ty wfu**ecles change without any change in thny3(xi;tf ye*t n* 5wue system's angular momentum?

  The Earth orbits the Sun in cpcjl0y9k80 gan elliptical orbit. Ignore any friction which may be p8y gl0ck 9cp0jresent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipticaafc wqokkdtxgy vk 12 953bah;nk *)40l orbit. As the Earth moves close to the Sun, then which of the followiokkc*3 2)a4kk9qxg v5fy; 0dawbh1ntng best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by wm /qm*h;7 bxrb uf*wnh1 -e;gpulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of7mhge*w;b*x hmbr /n1f;wq -u rotation?

  An ice skater performs a pirouette (a fast s tvwah6n ze 23x4p0,up+imz - s6iyrx3pin) by pulling in his outstretched arms close to his nt0z hx6 42 aii,s3+ep um- v6zwpry3xbody. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pull45tibmo upv87+ cul:g ing in his outstretched arms close to his body. What happens to h+ ovpmc74b8tg luu5:i is moment of inertia about the axis of rotation?

State the law of conservation kfktob k:. luna 19x dbe:h,,*of angular momentum.

  What arc length does the Earth travel in a three month period in i4q:gnl nsvxifae d) 1nj3:1-zts nearly circular orbit about the Sun witf1nz:i)g dj:alnvqesx-341n h a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m.3 ;-)5i4jm ctcsgooc9ybgfedui. 2o+ What distance does the tip of the second hand sweep through in 3 minutesou5edot ) gc.csmjc -y9i 3f24b;+gio and 45 seconds?

  How many rad/s is 25 revolutions per minu m+ 0tslrn 5a5u0msq+ qghftsfen2+.sm:o.0 ute equivalent to?

  A bicycle wheel rotaj * 6arr3fj8to3 *8j7uphekkfth -,a htes uniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotationh r-3*t,kejjr3 u h ka7afo6tf8hj8*p?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 k mpii+z-5lhi,hsv+u:le 3e vr7/vbl2Hz. The period sruve h7+ib5/pi-mi eh ,v 3:z l2llv+of its rotation is

  A phonograph record rotates at 45 rpm. Thpxyt k2lyg9 .x*w7y3+h(vp rdrough what angle does it turn in 0.20 yr.(d2w+y3p kl 9gp v*h xxt7ys?

  A wheel of diameter 26 cm turns at 1500 rpm. How farrudn*oqd bin/n z08z u+*v00f will a point on the outer rim move i n8n+zv0**0rqz0ouud nfi/ dbn 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whas0zpc(8pzu g.l qf :4rt is the average angular sprp:z0ulp8z .( 4qcgfs eed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.vzvsa9ex 97rvxen */i(sb6t 1 What is the linear speed of a pointbv6e 1vzs 7a99nsr(ix* xt /ev 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Taf uo s+y+,,xyhe 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 the cable car to make the trip in 12 minu ,xayysuof+,+ tes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 422u-pc 8sv hqvmjkq0 ct :er1k1 *r v)fhm4dnrad/s. What is the linear spej2r: fhp1cv m28qkrc4udt*v ) eqvk4smn0-1 h ed of a point on the wheel's rim?

  The cutting cord on a gas-powecij8ws .:j+0qidlta. 6hbhu5red weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, wha.:jhlhb . s 6a+ ciujqwi0dt85t is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating withq(o v,vu7c6k v/ h7zhq a constant angular speed of 2.0 rad/s. What is the centripetal vuh v 7kq(7,ozh cq/6vacceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the ba2 q x,x,+ugzperimeter of a bicycle wheel of diamz+qg,xx2u a ,beter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a bm+vh6zoc tt8 j+gu ;r27eszs5+ua 9tcircular, rotating space station (r = 1000 m) rotat+hmj+r2z;t5s98v cu6etu o7zt+asbge to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating czst uxs q9hr92e;+(qa flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided b+xc e9 9(urt;zq2sqsh y 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 raosy- w7*nx:kkx gmr6m o8o)f*dius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frmoxx6knokfsmr*w8*7 ogy)- : iction) 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 whirlpde)kqk 60 n6ted around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what mkd )peq6 k6tn0aximum 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 )4 rmzox vrz1bf7 3,dxrolls without slipping 10 m down a labord4 )zfmxx z3vr17,ne 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 consyr(ph+( q dihdeijf.l qi j:/v*((jf .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 ac nft00xzm j,1qceleration 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 st w 7eq/fxjcd7i2 .lk,earting from rest anwk/dxeq,fli c27.e 7j d accelerating 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 accelxs+ ihlo i,z78nb,az1eration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at1vmsfi,ik +.ygr4 y:t 20 rad/s decelerates with a constant angular acceleration 1sfy,t:im gi4ykvr. +of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from resp9;+zf doozl/bmu 6r4 efy26wt and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of theo+o9y z4/ r2ufwlm b6fdp 6ez; wheel?

  A wheel of diameter of 68.0 cm slows down uniformly * * x2tk opetp( *dvphl;qh e(:2p9yprfrom 8.40 m/s to rest over a distance of 115 m. What is the t *pt odpl*vpxk2(ph;he y9:e(*qp2rtotal number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm si pe 6z9,6zy(v, tnrorlows down uniformly from 8.40 m/s to rest over a distainztz(o,r6yerp 6, 9vnce of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniforml8*gag .bkketmb/9iq ,j ede0(. mdw2qy from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to thei28ge0/jt.m 9gdba w(q,.k deeqkmb* stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/m mb6rr0 5 inrgcka0u-mm t7b-5in. When switche kinr0brb-6ua 50mtg 7mc5 rm-d 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 tighteningtb 13y /6yvytg2 (aaym*gg;yo to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requirem12ya*a3otybt;y y/g6v (gygd when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torqu,.rq e;p3u2 zsi.r xgue of 90 Nm. If a 30 cm long wrer s2.pz 3, ;gerxu.quinch is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner3ott:)nqc4 egwb9 9* 9ncxzkl tia $3.00 \; kgm^{2}$ 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, m2wv e6 h8xy fm,x c3,hby+n 9uybqzy11ass 2m is at x = a, and, mass 3m is at x = 2a. What is t98 eh6hy,+yyz uwqvbyfnc1bm,x3x 21 he moment of inertia about the origin?

  A solid cylinder of mass 10c /mdk/9s z h:b:jtjm*p*fi;o kg is 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 around another section of radius R2 = 0.50 m exertd;t9f jp/*:zmb:h kmc* /josis a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 ;z8/* kmdr4 , lpg7ejx2o gbzwkg is 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 around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radiano r /j*zlzg8;7 e24kx p,bmgdws does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged atecez i10*n2mw one end. The rod is initially held in the horizontal position, and then rele10 n*zewc ei2mased 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. Neglect *jc1)0ily76f1antk(on o momthe 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 witml0 *c6m 7o)n (fa1y oijko1nthout slipping?

  A 1.53-kg mass hangs ha;3u.eee/qg yy y 1/ton a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius g y3ytu;a/h y1/eeqe.66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped v;6vh j zwd:3h-ktomjn-8 rs+around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accele+mn v:sjvjhdr z;k368t how-- ration of the mass?

  A rotating flywheel vf:j kg2 x3gmhge0,n* can be used to store energy. 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 ofiatpd6hqe5f 6s5 x* g31y7xe i inertia 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 radius 0.010 m startsjj 8h+ 3ku6g9ggmfqe8 2u*pna 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 inclined plane?u +ujpnfj8 3 68mkgaeg2*g qh9

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls w-0 hzn/xnev(ezrl x5vit ; 1s*ith a speed of 10 m/s. How high up an inclined plane can it climb before comi1xsv;t(r * hz5l -0 eizvexnn/ng to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest an s968 bonkskqueru 5d9xh c(ttx50h-s.c j02jd allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?n5xt c2.b9e kh rot9qu5k0sjjsc 6shu8x(0- d

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slippij;tr 4 pm5mn1nhuuu., ng down a 35e incline that is 7.0 m long. Assume it started from rest. 5pnm1 ju.nt,m4 hu ur; 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 changes byrfl(x g6i n,3kw(y;za $20 \; kgm^{2}/s$ 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 inertoeh71 v qu z0nkn+o/n:ia 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 extendt+qv dtq 5j2q5 1eb9cued has a moment of inertia b5cqvud+e9 5t21 tqqj 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?