Angular displacement is usually express in units ofux)ogq7ny am 53d ;6mt.y p)xf

  Angular velocity is expressed in units oti8u.w;6hm hjf i(so3 f

  Angular acceleration is expressed in unitx;tixm* l-* i*0wr ains of

  A boy and a girl are riding on a merry-go-round whichina+0q pq8hh59 +0 xe4kaocvtpp6e p+ is turning at a constant rate. The boy is near the outer edge,a0xth4e5 9h+ai+q cpp+q kppov68 ne0 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 which k7y1*ilw 2hus is turning at a constant rate. The boy iy l7s*2 k1wuihs near the outer 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 tur;m xkc4y4* 6jlxpx m w/r)owth8 p1s1wning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater l h4kmswmxtlw)pw1xc /1p4x6 y *jo;8rinear speed?

  A boy and a girl are riding a merry-go-round whicwv8iup*44pi0e,rdzxs r + i9yh is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Whi*u yp 49+ ixpez,w0vr4d8isro has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a c+q 19nx9eil aoonstant rate.o9liq nex 1+9a The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. kyfunj27.ca 5 Which of the following is an accurate statement?7akuc2jf n y.5

  Rolling without slipping depe0i-diht ) ta/znds on

  Two equal forces are applied to a door. The first force is applied at thwg :/nhnp7 9npe midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the grean 7:g9npnpwh/ter torque?

  Two equal forces are applied to a d 3bc2xw07rr55rgmdrsoor at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to th03rxr 5 d5srbg7w2 mcre plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicu0 9.6x)cy7t h sbnnidfg/k .galar to the door. The first force is twice as large as the second force. The ratio of the to)sydngc6 7kgai9h0ftnx ..b/ rque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to cha 892)j o2chj dkow6bpinges in rotatio2w6ijpk odj9 o hb8)c2n?

  Consider two uniform s)/ycny7 (kpg j; atu i-l sn)*w7g.lfmolid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of th lyyjclf /mutg;ag w*7i.n n-))s(p k7e smaller moment of inertia is

  Two uniform solid spheres h0gx, -naoy 5hiave the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia ix 0a-h5o ,gynto that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass ui;a9 q+yx) khand twice the diameter of thekuxyq +i);h9 a other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere hao a5vgr(q k(ci;xd39 rs mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of iaxg3(kido 9( q5c;rrvnertia about a central axis?

  If a constant net torque is applied to an objecwd3xc,7svp yi6 :gh sxq,u 80kt, that object will

  The moment of inertia of a s0 loc.6lwo )o4*cdkyt.xba 5holid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kintl. 0ob h4klxywdc)a5o*c . 6oetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one woelh3 xde+ba6z/,8sby t w0* yheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic 8+6ytox dblby/ s,*wea 3ze0henergy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and r 6e*3v yrbxnn c:3;byeadius R rolls without slipping down an inclined plane starting from rest. The linearn nc :*36 ebvye3rxby; velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radi2glw d;ox/i dk nz/5*.lgtv-u us R rolls without slipping down an inclined plane starting from rest. The angular velocity of the spheg- l*d n/vi.ow5utdx2klg;z/ re at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net externav2k b5lhrll/x-;g .w al force acts on the system." This lalgvb;/ r -x.25lwhkstatement is

  In what circumstances can the angular velocity of syste8jj9ceadpp*h q )8*bpw5vl2k m of particles change without any change in the system's angulk 89 ech*2wd5q8j)lp*avb jpp ar momentum?

  The Earth orbits the Sun in an ellipticzc8igm 1ors9b6m -m 10otp p f*y7zw5pal orbit. Ignore any friction which may be present. What happens over time -gitmpp11wy sorz 0o96*8z pb5mm 7f cto the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an el fzl+tk;yy ey65 v4)tyliptical orbit. As the Earth moves close to the Sun, then which of the follo )yy54fy lkv6ez+tt; ywing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outst78: m ,uddgnbvretched arms close to his body. What happens to his angular momentum agvm7:n ubd 8d,bout the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulla//hcw7unrw )ing in his outstretched arms close to his body. What happens to his rotational cr 7)/w/w haunkinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast vvyo/sbb oz7u0 1wguv.i 3 7.qspin) by pulling in his outstretched arms cl i30sv y7v.uz7uvoq bw bog./1ose to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conserqrf8o+ nc6 :6d8 utxa byrm*g5vation of angular momentum.

  What arc length does the Earth tra tk 2igf0 )1;5g4myjqstp dzk0vel in a three month period in its nearly circular ork 4s0)tgmdq0k ti2 yj1fgp;5zbit 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 i42cj2e lfe 668 ybz8fntej -kn/3fwathe tip of the second hand sweep through in 3 minutes and i 264bjj lfe8 cwa-tn2e38 6fkfnyez/45 seconds?

  How many rad/s is 25 revpp8 n84p/sswlx.zyie)a 1f e*olutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the) dur3v( 6-y9q xodwvc frequency of thecu wr-dq(voxvd9)y6 3 wheel's rotation?

  A pulsar (a rotating njv) :z,g kwi;deutron star) emits pulses at a frequency of 0.40 kHz. The period of its rotation w; dk vi)zj,:gis

  A phonograph record rotates at 45 rpm. Throughwr/d.3gdpi9h uj1qq8 what angle does it turn in 0.20 u.j3q9/p1ird d wq8 hgs?

  A wheel of diameter 26 cmnrwx-u;/gx s t :,ae3 +-dr0haej )mdc turns at 1500 rpm. How far will a point on the outer rim move 0xg ,x-dru wa+-) rna3sj:;ct ed mh/ein 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutwyg-.psmka yz x78: s)ilai**ions in 4.0 s. What is the average angular speed of the ag*:iasz-s) yiwp7 x . ykml*8wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is fo:io che qzt- qw(+9.the lineahqt 9.+oifoew:zc - q(r speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whicg2wyoq05m,nq/ n e(bc+9jh ish 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 minutes?yqq gcmosh + 529enwb/j0n,( i

  A wheel of radius 1.0 m is rotating with a constant angularh-mki * e/g6.uoavz p3 speed of 2.0 rad/s. What is a3o u/vzkg-ph i e.*m6the 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 t.em d+ybw+ 8z wuno0zg+g5h4ahe motor rotates at the rate of 20 rev/s, what is the approximate linear speed of d4zhnm g gy+o8z05 wa+web+u. the end of the cord?

  A wheel of radius 1.0 m is rotating with a constantq*h-6oor+sku; jrvr - angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on -;kourv*hrq+- 6s rjo the wheel's rim?

  What is the centripetal acceleration of a point on ezxdtx3b bc8 k43y6.xthe perimeter of a bicycle wheel of diameter xc 8.xb3xtk6bz ed4 3y70.0 cm when the bike is moving 8.00 m/s?

  How many revolutionsm zrmt (hiulm7* ,ah;/ per minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravim; i aum,tr/mh7l(hz*ty of $9.80 \; m/s^2$?

  A car is negotiating a flat circu/dof1vg1dm7sc,ea * ro+ e ce5lar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (prv*+c/caf7eer5 1,dsmd e o1og ovided 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 20 m/. c( viw;3c rq*gicw-bs. The maximum cri-( w*wc 3 gq;b.viccentripetal 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 whirle0bsn-:7c,qjg/0 c7u/ds4b khpfs-hnvro h w 6d 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 /bjv,gb ho-h p7h67fd wkrus: c -nc4s/sq00nstring is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls withnv1xc;qz: oll l+ pn+4out slipping 10 m down a lane at 4.3 4n znv++cx:qo1;p lll 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 acceleration ol . mn+c-aygvf 64f4zxf $4.5 rad/s^2$. 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 acceleration of+ wl k6vp:lo8d $4.5 rad/s^2$. 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 rad,as+6 tisaqe 4ius automobile tire rotate after starting from rest and accelerating at a constant angular accelerat +st,si4aaq6eion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular ac7 ac7 z8pn(itvwl/6zg celeration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constant angular a4zb8y2 aiu :jscceleration of y24suaj8:ibz $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rr; tlbn/bjq2, est and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceq,rj/ nb;tb l2leration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ov1zvjtm(j4se, e : 1jtrer a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to restr 1 1zj4,metj(te jvs:?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rejez.0wyfh(x0 hx,r 2qgc yu: *:h2exhst over a distance of 115 m. What is the angular accel2y jeh.:f0e(r wg 2hh: *uxzhyqxx0,ceration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40po/u0uz6 2b yo m/s to rest over a distance0yuoozb6 2pu/ of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates k mjf(xkkd5j16( 6 bynat a rotational speed of 3600 rev/min. When sw k 6fyj6x(j5dm1knk(bitched 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 torqudgwjln,n1 7 t5e of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicujwn,571gltn d lar to the wrench?

  The bolts on a car wheel require tightening gjzt mw o( 867q7ii00snh 9fujto a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requiui7f6(7 wj8zog09j0nh qms tired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia joh01wg g4i f1 9*hawvjogz-9$3.00 \; kgm^{2}$ 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 atvo7p jvhz,72) v fu;gp the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origiu j;hg,77 vpv)z2o fpvn?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought the wj bc :h3g3xd5 b+j4ruzk.wjyqn n(lbf 3s403center 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 s0 3.35bckr sdwx(zj +43 gfuqb4b3wln: yhnjjection 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?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoav+f-pjk l(ndq pqp +w6( :xz aq4cy22ught the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. p wq+pc 4f2pynl d6qa-xj(+2: qa(v kzA 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 seconds, if it starts from rest?

  A 4.00-m long rod is ii2vf se +5 gxyiqqegjiwr:*)d4:kp*- 6)s ephinged at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the anex dpg-:ij4i*e)pif)*5syi 6g:2esrqvk q+wgular 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 cmnmt0;d67w2-xiv j hg d 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 achd-t;2 06mh ig x7njvdwieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless djp1.pc uc)cs 9isk pulley of mass 7.07 k1sj) u pc.cp9cg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulsk.yf v b 2x89l-*lcphh m :yof/n/t;nley of mass 7.07 kg and radius 66.0 cm. W;9/ .b nhcm-sp:vkx l8yyt/of*lhfn 2hat is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required toq5cnm wfv 5.z s8wwj1 dw4yt/bt,zr53 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 oypdm2 1;vu) g0vy yox-f $5.00 \; kgm^{2}$ 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 i 4asao(xnan;10 5bodradius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What iaoi 0asoad( 41b5 nn;xs 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 rolls with a speed of 102xpcl1d*0 mwj m/s. How high up an inclined plane dxm2*pjcw l01can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest fo14gr --)jlxfw t1pd+, fzqg and allowed to roll down an inclined plane. Hoq w-rf t,-f+)ozx1jpdg 1 gf4lw 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 rqh*0 k8pbqaz3 0c(dsqolls without slipping down a 35e incline that is 7.0 m long. Assume itzq(s0qq p08 a*3c kbdh 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 chavmykfi v smbv9ll9.n 0y 2m,3)nges 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 momedf7tp 3 t*9ag8m(ds uynt of inertia 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 a69rv anlxv;oujgr odf+ c27z,;s;2xt/bybn (rms extended has a moment of inertia coby6 ln7(rg a/, xz2; ;jn 9u;vs+2ovdbtrxfof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?