Angular displacement is usually exprecq 1 qgh5y+kyrn. ;6fess in units of

  Angular velocity is expressed in units o :jt2lb h 4v2aehp:6ovbh t3z)f

  Angular acceleration is expressed5j n;)f3yqgpq in units of

  A boy and a girl are riding on a. 5 vm/aogt 9(f:rpmid merry-go-round which is turning at a constant rate. The boy is near the oomfta md:v.5p9(i/g ruter edge, 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.k-6e3vfio e s which is turning at a constant rate. The boy is near the outer edge, and the girl is closer tokf. 6es e3vi-o 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 constant cw)5.e q 1jm5ej1bmwh.u /nkkf m1q0nrate511njk c )u kej/wfw5 qmmeb.0mq 1.nh. The boy is near 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-round which is tur/f*wob )ehy b xih8n31lht56lning at a constant rate. The boy is near the outer edge, while the girl is closer tli/3hxb n1lfho tw8h)6 5 eb*yo the center. Who has the greater centripetal acceleration?

  A boy and a girl are 1zf dw4x4bf) criding a merry-go-round 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 gre)4fxwdf b4z1 cater tangential acceleration?

  Consider a rigid body that yv( zsbtu2(8pis rotating. Which of the following is an accurate statemesuvy(bt8z 2p( nt?

  Rolling without slipping depe 66kyfss* 0hhtnds on

  Two equal forces are applied to a door. The first fords*zc35uw4 0qh be3 xpjn k3ibhd) 0p:ce is applied at the midpoint of the door; the secq:iphbwp0*nhsz 43b 3kd e 0dc )ju35xond force is applied 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 force iz czfw;3-w1d,rm kuwq4/s4 s1gpm a+is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the grea+/z1d c qr;au k,swim431wf-mgwp4sz ter torque?

  Two forces are applied to a doorknob, perpendicular to thenp-*wh)nm h3m door. The first force is twice as large as the second force. The ratio of the torque of thmw-3 ) hhnpnm*e first to the torque of the second is

  What is the quantity used to measure an obrxdz.-o )* badject's resistance to changes in rotation?)bd .*- dxorza

  Consider two uniform solid sphereu ;1e 65pg:qe04 bjkt/; rgi o.afufhws where both have the same diameter, but one has twice the mass ;1wuf /;jgfgbe:uo h. k4t065piaeqrof 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, butkzth)o04zt v: one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere :t)z40tovhzk is

  Consider two uniform solid spheres where one has twice+ f p:ekh.x je:o(.glk the mass and twice the diameter of the other. The ratio of the ljo(k.eplk gh.: : +fexarger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are incre*q- u f;-/qs/r--hwio trwuaxased to 2M and 3R, what happens to the sphereih-wtw - */;/ sf-ruqroxuaq- 's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object will5 no t:xkil whdg5u(27l /kux.

  The moment of inertia of a solid cylinder about its axi i .y3 pw:oilo.jxm9hsn11s(d s is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one /+. 44/eaiv(dae)jzuq sc h ze;ycza: wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energ zveiqdya;ze 4a:/u.ha cze j(+)4s/cy 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 tb t+u9niz5 88rq6lhx R rolls without slipping down an incli5qt69+hi ruzl 8 btx8nned plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolur 4n f/y5 0vk.;vxrhgls without slipping down an inclined plane starting from restv; x40ghvkf /u.y 5rrn. 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 exb7- y+fycqq7rternal force acts on the system." This statemen7+cqr 7qf- ybyt is

  In what circumstances can the angular velocity of system of particles change witl+vo8*:o5i s urudmo mb3r 07mhout any change in the systeo5rdmrms*uub:o8 3m7 0v+o ilm's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fr s wxqo-,.jzp6zl .uw 1b/zq,wiction which may be present. What happens over time to the Earth's angular momentum awq wx 6l.1jzsq,oz- p,. w/uzbbout the Sun?

  The Earth moves about the Sun i y46x2tdsp9k dn an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes tht d ysx6dk2p49e orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched7csu8y9hb(xtg,ax57 n; zmwy arms closgnm;s5 779,wxbahyuyx t8cz(e to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (an+ra:j, xlcw/ fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy xl :/ n+jawr,cabout the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his 4y s xe9+uat1poutstretched arms close to his be1tua+94p s xyody. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentu. xwuys(pafh1j 4 n.,dm.

  What arc length does the Earth travel in a three skvn0z d1;fk ,pi6p0amonth period in its nearly circulps;k0v a6fp,0dni k1 zar orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clockozq 1:7vl,teh fms) rha+t 7o3 has a length of 0.30 m. What distance does the tip of t7t)o7thsler1 m a zof3 vhq:,+he second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute (a*8gv4i5pd z8p a vmnequivalent to?

  A bicycle wheel rotates u06j/;. p7c:asldemwjf3vs lfniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rp3 ;/c:jvml 7w0jls6 d ae.ffsotation?

  A pulsar (a rotating neutron star) emits puloo. ndmhn(7ams fn:1ck*h *q, ses at a frequency of 0.40 kHz. The period of its rotat(d.mqhk,*nh1 omcn ofns :a*7 ion is

  A phonograph record rotates at 45 rpm. Throug+2o cdk iu.1deh what angle does it turn in 0.20 s?+dku1.ei2oc d

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point ovksvsgbg 7g50;h) k:wn the outer )vkv:k5b7whg0s g; gsrim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is 1fx 5znzrg, m5the average angular speed ofz mf1x,5nr5z g the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wbyy*kw8- d5j j sv ukx tkgk6(2yo595d3sb o;qhat is the linear speed of a point 0.10 m from the cenj5ok-jktgb8 (q6 2yd yb5ws9suk5kv od* ;3yxter of the wheel?

  A cable car at a ski mr. xmkw3r: hc6xgt-6 resort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pu t6:mr.m-h kx3c rwgx6lley 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 angular speed of 2.0 rad/ (s,ok,y(ftz bs. What(ofyst,k b(z, is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered w t2;pj.kz3e v8qvfo7l eed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, whl q ejz8t7ok2pv.fv ;3at is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angula6i pg,chm7:e1b q-jmnx.; yh vr speed of 2.0 rad/s. What is the centripetal acceleration of a point on the whee cxge76m,p.j1qhbvn ; h:-ymil's rim?

  What is the centripetal acceleration of a point on th o6buo7u+leb xhx81s3e perimeter of a bicycle wheel of diamet6 o xhseu31ubbx7lo 8+er 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circ7j p r*ps75sdfl7p gv(jbx 12cular, rotating space station (r = 1000 m) rotate to produce an artifdpcjs 5 vpfl7x1j*(2 77gpsrb icial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m wi)xfe4ty jj/ d:t6 kso+,e5gn oth a speed of 20 m/s. The maximum ck6n4o)ftj:s5,tegjxode y + /entripetal 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 of7e et. elj(53rn4j,rr uj +rzfitc7)i radius 50 m with a speed of 20 m/s. The 7f)rrtl .nr c+ tze jei3j5ji,r 74(uemaximum 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 0.7u 5* mvzmr-2h*7qyjm* g(rmso50-m string, is whirled around in a smooth level table. If the maximum tension that the strm ojm *yg-us52r( *r *hzqmvm7ing 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 slipping 10 m ix.is0 k+6wmk down a lx+0m iksk6i .wane 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 co bgo)sn bp (mwvu s8u9y,u7:d.nstant 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 z(zx)cnr :v.g dx4v a*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 rovvd ;+ehw w0aik r+sy42k; gz3+vev u1tate after starting from rest and accelerating at a constant angular acceleration of +us ea vei3r;dz4g w+wkhvk 1v0;y2v+ $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, x*4+sc c v6ui vxlv8q4and has an angular acceleration 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*, pa3zxal7pmoe9 pl ; acceleraxa3p7l* ,l9pe ;omzpation of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches a 5abof ;k dqtdv)8pr*d/3qa )an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleratiktrv bdoqda;/) 8pq*d5 a3)fa on of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tokswc :6xwz7d0,eg av.).op fi rest over a distance of 115 m. What is the total number 7g6pc).,fwia0w.skzv xe d o :of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 6j32v k3v;tz7x 4kk lpzp9 m3w,cjve6f8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accelel73 x 4p3kv9kf cp3kj 6ev,j2zwz vm;tration?

  A wheel of diameter of 68.0 cm slows ; 94pmnze8wax down uniformly from 8.40 m/s to rest over a distance pwm49na zx8e;of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medicaan(ait/nlc;7vbztd7or9 : u/ oj;m. el laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming da(ne/a l ui7bt o7cm n9;jzov.;/:trto 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 reqan a.x9t0(u2 hk lgei(uire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what 2 ntg((ali .09 xehukais the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightenin/4hqq-kc v1s ag to a torque of 90 Nm. If a 30 cm longqc-k1a4/hs qv wrench 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 inert+g id(b. bi6j6gsxaq9jo3 t h*. 7rrueia $3.00 \; kgm^{2}$ 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 aikvohb -myi95 b.a 6ek qeb09d5c- zb)t the origin, mass 2m is at x = a, and, m. i k6)chb-bq a9-5mve yd5zb9 kebio0ass 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 frictionlesj j/m)9u;y4dlb5lkb/ykd t 3gs axis thought the center O. A rope wrapped aroumd dl4ykj/l )9tb; kj/g5 b3yund the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thougk:2 ci)c.. boi 2qwnttht the center O. A rope wrapped ct q ii)2k: w.c2.btonaround the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 initially hel v-ywdr718vlhuag4v m pf5( :ad in the horizontal position, and then releasvdagl7p yfvh- v8(a:1wmu4r5 ed 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+net b(esm *(sb5bdj zy5i3q . 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 achieve, assuminsn 5b.5st mq*3( (z+e ejybidbg it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped aroun,l exdb.s/91osq wli +d a frictionless disk pulley of mass 7is,.eldol 1 9 w/sq+xb.07 kg 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 frictionlessq31wpaxift7 7 disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration o7qa37iwpt xf1f the mass?

  A rotating flywheel can be used to store energy. If it is required to s j1,kf,j08mg p2b 8ka gluzjx7tore $1.00 \times 10^{6} \; J$ 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 o 9qcwg.fd 2g yq8t.9iaf $5.00 \; kgm^{2}$ 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 rolluv ,bm,z)3xk3vy vqg/s without slippi33y mqzb kv,v/,)gv uxng down a 1.0-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 m6hnt7)it4q en rolls with a speed of 10 m/s. How high up an inclined plane caq)7 e4 6hnttnin it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest ai49kfpy bvs3)nd allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.04s9i yfk)3 pbv m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping do ud sqanmv-p+14 .8te.krvkl -wn a 35e imqrkse-- k ln.8d4+ta pv 1vu.ncline that is 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 momen/vock pu:dudl e :*;o-tum 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 iw3w x3. - 2ng4xxvbtnk nvd(o4nertia 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 of inertiej ;af,eh)zw7 a oah ezf),w je;7f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?