Angular displacement is usually exp(5eizgp 2s 8v dixw-4sress in units of

  Angular velocity is expressed in unitsfxio f*kdg )ij+33xu4 of

  Angular acceleration is expressed in u27, / paaqhqiznits of

  A boy and a girl are riding on a merry-go-ra ui++t*kt5p 6oiq0f(f ggwh0ound 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 greater angular displacementip(u65o tift+0g0hw gqf+k *a?

  A boy and a girl are riding on a merry-go-round which is turn)gfzoc9cfl)24xd +4tzbc d;king at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greatczxo dgd)z29f bflctk44+c;) er angular speed?

  A boy and a girl are riding on a merry-go-;whut1;.hpzmc i/ 1fwnf4(std p .7jpround 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 greater linear speedhz si.pf 1(;4up.jw/dc71h; f nm wtpt?

  A boy and a girl are riding a merry-go-round which is turning at a constant ratx;p)j:2 kchqte. The boy is near the outer edge, while the girl is closer to t)tpq: h kjc2x;he center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constanf6lzki u+ 0jy0t rate. The boy is near the outer edge, while ikzu 06yj+f0lthe girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Wb op hu)w40i:jhich of the following is an accurate statement?0ij: bupo4) wh

  Rolling without slipping dwn3/mm gz1d yc, 2q4zmt50roj epends on

  Two equal forces are applied to a door. The first force is appliedoyp t ,a(hxc5)9)r np ef/xy25e6lwjy at the midpoint of the door; the second force is applijp a)t9 xorch/xnyeyf2plw) 5y 56(e,ed 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 doo sy. 4t3nt/c3m(f-s oedusqanc8g/1urknob. The first force is applied perpendicular to the door; the second force is applied at 3 uf3meu.4ns-( g/ dy/q scotant81s3c0e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicularfk728w 4buwxx to the door. The first force is twice as large as the second forcexkx4f87uww b2 . The ratio of the torque of the first to the torque of the second is

  What is the quantity used to meas, w:spz mva-a1ure an object's resistance to changes in rotation mawv-,z 1:asp?

  Consider two uniform solid spheres where both have the same diamer77(k l cu w: rhp:fr8sr. :g5 oba/(rrjofs6jter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment 7rwg /58 jar uo :r.(rs: bhl:(cs6ro kf7frjpof inertia is

  Two uniform solid spheres have the sih zr h 08e9j:qy+f8v2 fxqc2game mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to tha:h 0 8z fq2xvi+eqg82 ry9jfhct of the smaller sphere is

  Consider two uniform solid spheres where one has twicebqg h,3;8kngb w oo3ofu(p3q6 the mass and twice the diameter of the o,;(g3q3kf8 wup bgb3q h oono6ther. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radiqbxxku.cq,exq2 ov(m m .iu6hy/ .;,qus R. If these are increased to 2M an.xy/,q(.m xo;qiuk2 xc qhvm,6qb .ued 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied 81bdp f4 n8js7/fjzjzto an object, that object will

  The moment of inertia of a solid cyl.1*k9fw / tj(wqkvvr fm5x1riinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energf vw9w1. txmqjk1kfr/5i * (vry is

  Consider a motorcycle of mass 150 kg, oneo4kak-g)jc7ir 6pc 5v-i xj3x wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic eno6 ki)j4i3axvgcp5-jx c-7 k rergy 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 radius R rolls without slie 1xh)r+r+z4s 3c lvxkpping down an inclined plane starting fxr1 k+4l r+se) 3czhxvrom rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radtmf7 ndl :j(1xunn5s0 ius R rolls without slipping down an inclined plane starting from rest. The angular velocity j1n:f 5nmt 70lsu(xndof the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes whe8rm:dofr i;jou5.) j 0ac8fk hn a net external force acts on the system." This statement i0m)kji8 aruchr8fof.od5 j: ;s

  In what circumstances c9us y- 8mcik4ui idq*/an the angular velocity of system of particles change without any cha9usimd k/8y*c -4 iiuqnge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictionx8cbd5 u 3nip7 which may be present. What happens over time to 58x bp73ni cduthe Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth mp;6 s03avur ymnll:*b oves close to the Sun, then which of the follo ;v rsp*a:6nyllu 03bmwing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a piroung0rruf 6h(v 1ette (a fast spin) by pulling in his outstretched arms close to his body. What hav6f r0(ng1 urhppens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouetttk y23ssfv w cc24u5i*e (a fast spin) by pulling in his outstretched arms close to his body. What c fc24 s isvy2k5*t3wuhappens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched miwc+v 3pyc f9p/ f3i5arms close to his body. What happens to his moment of inertia about th p mf9/ cvwp33+yicfi5e axis of rotation?

State the law of conservauz /c8yya2g7hs: ,8 jy dvnp8rtion of angular momentum.

  What arc length does the Earth travel in ,bfw; 37bzrtig ) r+wf/wlea0y5:nh wa three month period in its nearly circular orbit about the Sun wiewffb 7a+3 g ,wwwri:z)/5 r0nhytl;b th 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 the tipnr:h- yy;k jm/ of the second hand sweep through yk /y; jhnm-:rin 3 minutes and 45 seconds?

  How many rad/s is 25 revolut0h 6;rxv; w,jx bvqk5mions per minute equivalent to?

  A bicycle wheel rotates uniformly throughy 7dxjowravp01 ib*58b9 qi,o 2.0 revolutions in 4.0 s. What is the frequency of thd75 8iiwooj9 0qy,bx*avb rp1e wheel's rotation?

  A pulsar (a rotating neutron sta2b4 tnh-ei:xqr) emits pulses at a frequency of 0.40 kHz. The p:24e ibh-nt xqeriod of its rotation is

  A phonograph record rotates at 45 rpm. en: f up-q4:qjThrough what angle does it turn in 0.20 seuj4q -qpf:n: ?

  A wheel of diameter 26 cm turns at 1500 rpm. How far wif*npj 7 44 o(,4pqc95sgo a,iou,i2chp xzyxfll a point on the outer rim mayonp5 4cus(fxp4 *,io,9q c7gzhp fojix,24ove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revol;p he f)gr8,k7jwmog* m6s y5 3qd1hfjutions in 4.0 s. What is the average sh;8)5h , jm 7mrpdofg3q wg1f6*jy keangular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolumud4 yk72o p-bo/ah u6jy* a;jtions in 4.0 s. What is the linear speed of a point 0.10 m from the ce yod*y6-hb 2oaauujjkp m4 7;/nter of the wheel?

  A cable car at a ski resort carries skiers /0y cq0aqv9v-g j+l ol;-qrjf a distance of 6.8 km. The cable which qo-9 lgq0f;/j crjqay0lv +-vmoves 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?

  A wheel of radius 1.0 m 0f+ckl, 23 rut4j-le ow5or rgis rotating with a constant angular speed of 2.0 rad/s. What is the linea4feg+c l2-ulrtr 3 j,5krowo0 r speed of a point on the wheel's rim?

  The cutting cord on (kq1z*z,eini a gas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linea z1kni q(,*iezr speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant nihhixn7zm-):9tp*uj5(x h cangular speed of 2.0 rad/s. What is the centripetal acceleration of a point o mn*x:xji5inh hh7t9-pu) cz (n the wheel's rim?

  What is the centripetal accelerkavd*rg(k5bn k *;5 zjation of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8g5ad;(kn*rk v *zjb5 k.00 m/s?

  How many revolutions per minute (*p bw4eq(* wwhrpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificia4p *hq (wweb*wl gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular cuv; fap1fr -l6 dxo+yy2rve of radius 50 m with a speed of 20 m/s. The mvyl fxr61od+;payf -2 aximum centripetal 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 radi12egdd-yi2 ; ;qf5jdzy- peqtus 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fricti z dy 5iy2;q-2pjf1eq-;tg dedon) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached vnmken19p q oo7nt,86:lq lh 5it.i(o to the end of a 0.750-m string, is whirled around in a smooth level8 ,l(optq qtimn6l9ohe nk5i o1 .vn7: table. If the maximum 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 and radius 9.0 cm rolls without sr m 4viv.tj.0plipping 10 m down a lane at 4.pr mjv4t.i.0v 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 constant angular acceleration of4p21/brxo pi-qdg 99akwj(0vqr f)0pzta gt. $4.5 rad/s^2$. 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 constj87 z;ae65- kt ur* tfgk/luyst(lny-ant 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 tira*vk9es u)*h2u q zsfjaed; *+e rotate after starting from rest and accelerating at a constant angular accuejsks)*9*fvu* d+aaz2 q;h e eleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an htpn jq(y;2tp3y- rz8rga8j , angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating atzf o(7zts1j-: g8i r:agt6 zol 20 rad/s decelerates with a constant angular acceleratil1gt t7:i:( zz-6ojzsa8 rog fon 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 while turninh1razn- f ap0:mo1) mxg through 2.0o m1a-1nx )za:rf 0hpm revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter o e6q;j +vir/ql2sx5nof 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the tlr o5;2/ j6vqxqen+siotal number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter ofx atva 8v3tn q)bb(19b 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 1v3a t8a9bvqx nb(tb)115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm 6e6fdjkv8 0nymq48di slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to thj 6yd8d viqme6n0 4kf8e stop?

  A centrifuge in a medi1ico; sjc*g t1cal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before g t ccis1*j1;ocoming 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 30 cfbx 2kb-4 n7gcm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrenc 7 4ck2-gbbnxfh?

  The bolts on a car wheel require tightening to a torque of 90 Nvk + f;(rrx+tme8o2,ttiow- :8*qxfz m ) kwnsm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force appl,mtxs-k2rqe iokvw++mfr)* tx t: 8z;f(o8wnied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia f0r);r39r4km 2jlv/qelgfvd$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule ihz8ncv () 9ipps modeled as follows: mass m is at the origin, mass 2m is at x = a,) 9p8cvz(h inp and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a - hx4 5ufgljuk2nb53mzk:.ze frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a fox2:zjnk-gum3ueb z5k.h 5fl 4 rce 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.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought thrt/o ee7q2u9 ke center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to et/qk9o2eu r7the 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initiallyy)uyg4l f799egit5c n 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/giu7n 4f)g9cy t5l9ey3.)

  Consider a bicycle whpffw -/n m1-cdeel to be 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, wh1nw-p cfmf /-dat linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley w)znq)j:4nt 8t;izbwp( irx ot0v w-) of mass 7.07 kg and radius 66):)0obwtr(wxnj z4nv;twq- itiz)p 8.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frxa3j8;ik7c cx6adp(h n9e5avictionless disk pulley of mass 7.07 kg and radiuc76 (c5 38a;xapnhk 9adivjex s 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is za6d03 uz 8p t7mvjih/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 in;k a2pxk )ulv0ertia 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 starts from rest and roll6wuqm/+bl edksu.z /).a m;et s without slipping down a 1.0-m high inclined plane. What is the speed of the spherea/le/dekt;sz )w b6+uq u. m.m when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.f uj2cug0b-j)xlwx5d:y 8jz;0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclinedwj:lj-jd8)b0gx fyu x cuz; 52 plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mas1p:e- fx,n5(okf tweuwbn9/ is of 0.20 kg is released from rest and allowed to roll downe-u(pn:e tfk 9x5b nw,o/1wfi an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg ani;/s)hp.: d5e)kxrwf eutb 0nd radius 15 cm rolls without slipping down a 35e incline that isw5r:esn xfuhik)/.e)btdp ; 0 7.0 m long. 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 changes mb1k .:*vz 9wysm4t- zwbqab 4by $20 \; kgm^{2}/s$ 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 momenty0rhdwuin7a 9hr) c, wgx016a 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 w .(b-oebds2; g t p:ek1esek8mith arms extended has a moment of inertia pes8.d kebtb : 1mk2;e-o e(gsof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?