Angular displacement is usually ycueja/ );m7ao6e5m ,5hawbiexpress in units of

  Angular velocity is expressed in ,u5az2cy s: bys** fgo oh0dh(units of

  Angular acceleration is y-b3zku:dp.gbtd) 4vexpressed in units of

  A boy and a girl are riding on a merry-go-roun -fmox(s) ue8md which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Whm (8)m fexou-so has the greater angular displacement?

  A boy and a girl are riding on a m-x+ci0l my5xlerry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center.5 cxlyxil0 m+- Who has the greater angular speed?

  A boy and a girl are riding ofh1iy*3ewoapq3 h5/o n a merry-go-round which is turning at a constant rate. The boy is nea 3ho h qopiwf3*/aey51r the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-zimuw+ sv/+0w round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who z+w0suv/ mw+ihas the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning atq l+x9uc wxq26 a constant rate. The boy is near the outer qculxwx+q296 edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following iw ab..utrb3 -kqifm3: )s +kges an accurate statement gs.3 emk3f rktqa-.) b+wu:ib?

  Rolling without slipp.;kt 9ffjr nh8j -q: 4gd fh6gxe89yhxing depends on

  Two equal forces are applied to a door. The first foa (qoqu6t+jb 5rce is applied at the midpoint of the door; the second force is aqutojb +6 (aq5pplied at the doorknob. Both forces 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 hwv2p op3,a 3-5xyjr8ji. lyp force is applied perpendicular to the door; the second force is axw., a 3jp8jppvr3ih - ol52yypplied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob,8ze.bmxb ldx545k i (o perpendicular to the door. The first force is twicdk 5b oemb54z (xxi.l8e as large 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 resistance to chaepy1) dgxs;016es:kj o.oa l1gz6syk nges in rotatiokkz011s1lj6x egaos d;:.osyp6 ) geyn?

  Consider two uniform solid spheres where both have the same diameter, bu4ku,ripem m, 0e03 s6saq mm.pt one has tmm,0 s,i4e 0m6s pe.kpu qam3rwice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice r)t +5 2ryvovdthe radius of the other. T+tvrovr2 5 dy)he ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twic 2fxli1ph2ns1+ runefb* gm8,e the diameter of the other. The ratio of the larger moment of f* hu1 fg2r sm81xebin,l2pn+inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If th5a4ictkgsgm ,- j zs:,ese are increased to 2M and 3R, what happens s5s,g ck-,:zijat4gm to the sphere's moment of inertia about a central axis?

  If a constant net torque ip7z8l8 zlm6c vs applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. vi((-pf gftv) If this cylinder rolls without slipping, the ratio of its rotational kineif(- t gpf()vvtic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one cna5-1ddqx t34xzk:i 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 wheels to the total translational kinetic energy of the bike? Assume the d cti-kxdx5: 1q4n az3wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls withl md 65g1x)4zy jvzwp a)jbg8,out slipping down an inclined plane db6j j5 vz,y))gp8gw41lx am zstarting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid spherep t7.vyjf9dw; . l3dsu of mass M and radius R rolls without slipping down an inclined plane starting f79uvptf3.swdlj d.y; rom rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a sfs:c2.yuuv-t ystem of particles changes when a net external force acts on the system." This stcfy:u svut2.- atement is

  In what circumstances can the angular vejo ablr:;cwli .(d , wdtfhp8z 7ep93+locity of system of particles change without+ijfr z.b3a:, ;el(hdw wp87d9 lp oct any change in the system's angular momentum?

  The Earth orbits the Sun in an eclefv:ko i19/rt 5:aylliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular mol: :v5y ek1r cio/9ftamentum about the Sun?

  The Earth moves about the6 98ggb,tv: bi r za+ bobnji3+0cn/vr Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting sp g+rr /g:ibjvvzi6ocb nbabn9t0+,3 8eed of the Earth about the Sun?

  An ice skater perform e fv7nqof.t73s a pirouette (a fast spin) by pulling in his outstretched arms close to his bovf.7tnf 3 qe7ody. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (6 hgu7uvq:rx9a fast spin) by pulling in his outstretched arms close to his body. Whagur76qxu : 9hvt happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pul 4a1xvny tnzziy*wl gh xt.,sar./,9 )ling in his outstretched arms close to his body. What ninx9 axt14z)sg.har *y, w.,yzv/t lhappens to his moment of inertia about the axis of rotation?

State the law of conservation of ang)(vzij68vmgd i4 kg5z ular momentum.

  What arc length does the -e e 05ske. *hxbgme q:q5qpv/Earth travel in a three month period in its nearly circular orqg:5e*svq. k hq-5e0e pmexb /bit 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 does s:o8(qsd u6 bothe tip of the second hand sweep th o (qsd:8o6bsurough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equimwdm*l-dsu:i3md* ; svalent to?

  A bicycle wheel rotates uniformly throg7 g j3 f( in8b2fbw/l0vm 7;uk;zzmklugh 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotatmgf zb0/fnv;b ;g lj ilmk83wu z772k(ion?

  A pulsar (a rotating neutron star) emits pulses at a frequencv*lo5 c,s 3fhhy of 0.40 kHz. The period of ,h* 3clh5vf soits rotation is

  A phonograph record rotates at 45 rpm. Through what angleg ieti.q,.- w7gfs,2beyvux 2 does it turn in 0.20 s?w y7i,ixgs.2,q uge ebf.v -t2

  A wheel of diameter 26 cm turns at 1500 rpm. 0i i5a s1xl*zs How far will a point on the outer rim move zl ii5*0sasx1 in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revo-ps.nsf9 r z80ac ve*qlutions in 4.0 s. What is the average angcq f9zp* -s0v8 a.nrseular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is cgla3 e-5/i 85qdngi 8prk ) toc5.uyythe linear speed of a point 0.10 m from the center of ty8 5 gi ydnelckuo53c/qg-p)r85.tiahe wheel?

  A cable car at a ski resort carrie lu4o4x *; y)hic5bnfps skiers a distance of 6.8 km. The cable which moves the car)4b il4yochfxpun5 ;* 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 constant angulapxwsw yi-t -d: ctj++:r speed of 2.0 rad/s. ypw : +td-x :sic+t-jwWhat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the mounon vkn, 738ator rotates at the rate of 20 rev/s, what is va,3onkn87 nuthe approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angu ck+, (xrov fv/dqcq hc419ku2lar speed of 2.0 rad/s. What is the centripetal acceleration of a po2 hqq9c,(/ckrc voxf+v1u4d k int on the wheel's rim?

  What is the centripetal accelera0sq4,tad+pm0s5 k ork tion of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00d,oq40mkak ss p+5tr0 m/s?

  How many revolutions per minute (rpm) must nl ;w3s3b7ea)j q5 i+nicwz i3 iqf8(qa circular, rotating space station (r = 1000 m) rotate to;s ni3 (q3nqwzq38 c)f+ie7 bliwi5 aj produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m wih/9wf26lkwk (z x+ldkth a speed of 20 m/s. The maximum ce(xld2fwk/+wlz 6k9kh ntripetal 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 curvnyu8)wn(o y4 5i*b: *gd2wej-ywdad de of radius 50 m with a speed of 20 m/s. The dyw enwdgu5j):2oi b(dy**ay -8w dn4maximum 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-m string, is whirled ard-z .o y;hafjq*l3jjsc-8m+u ound in a smooth level table. If the maximum z d8 .ou+s jc;yjaq-lmh*fj3 -tension 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 7.5 kg hw3a nb4jjhkn- u(g:, and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 mnbjhgn,- 43uw(a h:kj/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 w tk,h6zhixq l+ m*3fz2 18+hueemdg 8aith 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 an7 pog (5 ems.rq/s3 kq(erhwgqb4+x5k ut)w 2rgular 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 rotat aggci+99d sk 1al6t fe4-tor4e after starting from rest and accelerating at a consta41gi 9afse o4tt 6 d+-k9grcalnt angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and h d/ 1+ izo ssba,ykp g2a/b2flap.brtd)k*1p+as an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating/ s1 6-l :whmlmwf+eqj at 20 rad/s decelerates with a constant angular accelerati+wf-ql1m6hmlj/w :eson of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an an 3 2ss- jlp-cqr6otxa2gular speed of 6.0 rad/s while turning through 2.0 revolution -j-r2c aq32lp6 xtosss. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows d /)b:nxqac-nlown uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheelb-xna)l qcn :/ rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unit*7el 8sgk ix /m6 v:*tne8;otner6, zsh(uotformly from 8.40 m/s to rest over a distance of 115 m. m; u ts866 (rg7kznxton e *ie*,t:s8tlh /ove What is the angular acceleration?

  A wheel of diameter of 6gjo g b1dsp07;8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wg; 7dp1go0bj sheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/mj8/zjcr ehi *54nl0n qin. When switchece zjhr/0 l5 nqi8j*4nd 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 tightening to a torque of 90 Nm. If a 30kf+ psc/vcf*0 djcy6e y2u3s: cm long wrench is used, what is the magnfdsy3*: 2cuyve f/60p +kcjscitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm loqb 3x 8.gei wspo.ap0,ng wrench is used, what is the .p0 qs3e., opawxib8g magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o:yvv1ik+jr* e2:zwjef 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 follocqv+w5k7kl 7i:kdfe 9ws: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment 57kice9vwkdkl: +qf 7of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis tblzqxr3g0/+p tw3c5 ahought 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 radic/5wz al+tr3 qgx0pb3 us R2 = 0.50 m exerts 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 kg is pivoted about n td99va*ll/ca 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 radians does the cylinder rotate through in the first 5.0 se l/a9ldv9*c tnconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. bk8r hz:p,fsu i8j(/eThe rod 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? (The moment of inertia of a rod about one end is ML2/3.ipsuj( zf:8/,e8 bkhr )

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 tnqoj46rbsjd t ct01+ bc-69t kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied t tctc1qdrjb6n j9s+tt- b60o4angentially 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 frictionlkzw :itdux6* 2ess disk pulley of mass 7.07 kg and radius 66.0 cm. What is thuwtxk :z 2d*6ie angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mo (g p42uwmh(kfmp3rnwrgw4 1fo 01(oass 7.07 kg and radius 66.0 cm. What is the accelef oum2 ((orpg4m fgwp43nw r (0o11hkwration of the mass?

  A rotating flywheel can be used to store energy. If it iss(8 gfwpnr;k*v*-qo e 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 inertiapa+lb mx:0osd7pe)6rprt( (n 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 che/mcxmq.x* j) 0yb7 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of theebm c mqc7x jy*/h0.)x sphere 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 10 o+ze2kgwe-2lrmtyv+9g 44t k m/s. How high up an inclined plane can it climb before coming to re94ggl+eme-y 2v ztr kt ow2+k4st?

  A hoop of radius 0.50 m and a mass of 0.20 klx8ox fnjol , d11zr;5-lkrv0g is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance ofl5 vfz;-d1o8x, xn kr01llorj 3.0 m?

A solid sphere of mass 1.5 kg and radius 2w.+ )ly/e u;x fcsdsu15 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 sphulc 2wf/ +s sy;uexd).ere 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 momentazv l9f,zckty/ 2c(; yum 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 inertia of x 95qqyi)el 39r8v tblxowe .cf7yj(* $5.0 \; kgm^{2}$ 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/-diomz j+ 4 j4x9bse-cs with arms extended has a moment of inertiz44iobj9exmdsj -+- c 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?