Angular displacement is usually express in units of-qh/t0aax*k pq;58x fwebs5p *7+ dwtem ,gns

  Angular velocity is expres :;ncpiu,zb+w p wqz.,sed in units of

  Angular acceleration 32bh 3v e)(fxy0yzcxc is expressed in units of

  A boy and a girl are riding oq 3(6r tqmcu)mn a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to ttq(cr )mmq3 u6he center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-gpa:2 o4hv2a uuq-e;4q3y,tafv 4u qhwo-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the 2qh uyuw-qe3uvf2h vta;4o aq4p,:a4center. Who has the greater angular speed?

  A boy and a girl are riehgz -r9umj/ 0ding on a merry-go-round which is turning at a constant rate. The boy is near the out ehurgz-9jm 0/er edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-gokydl: 4i :pel7g 9n:.v:dn hcy-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to thy:l9 lnp:4e7yc. g:nkdvi: dhe center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at;yag x+hi5fjalc st2l2/ dv38 a constant rate. The boy is near the outer edge, while the girl2djy +v8tcl3;ax52f ag/ s ilh is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the l fu ;uas0e5:bfollowing is an accurate statement?0au fsu e:bl5;

  Rolling without slippi1v* prbf2btet 6n4hu5gajyp./ 59k jyng depends on

  Two equal forces are applie0ebk/gr;akk,*pz9 jid to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are appik/ekrzp b0 k,9;g* ajlied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applieo k25n +bj0knp o27kscd to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the planek+22jokpcn0kobn 5s 7 of the door. Which force exerts the greater torque?

  Two forces are applied to a doork:yur39.qjuh q nob, perpendicular to the door. The first force is twice as large as the second force. T.u:ryjq93 uqh he ratio of the torque of the first to the torque of the second is

  What is the quantity used to p) p3 bxad, )y4b6lxfameasure an object's resistance to changes in rotation?al p3bxba)f y p)x,4d6

  Consider two uniform solid spheretmk3 j45 (zw;sa9sjy;z0z tt ys where both have the same diameter, but one has twice the mw;jz 4(ykam t 03styjsz9;5ztass 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 the radius of wr t*)yh/up3x*v( qxtthe other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere iwq v h(tu3*xy)p txr*/s

  Consider two uniform solid spheres where one has twice the mas o*;ht6b)qpcg s and twice the diameter of the otoh c gq);tp6b*her. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M y 13hkz)ow7 h di+e9rhand radius R. If these are increased to 2M and 3R, what happens t39o)y+dk wih7erh 1h zo the sphere's moment of inertia about a central axis?

  If a constant net torque is --0ylsa/.1(v evv -zef e gblcapplied to an object, that object will

  The moment of inertia of a solid cylinder about its axi(jb6,*xdbbpc/ r ( sidv qmu:3s is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational d,3bbq/6 i xm vjcb (s*dpr:u(kinetic energy to its translational kinetic energy is

  Consider a motorcycle n7cuk(ueq2 z9.xxxmi9hm b 78 of mass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of 9z.2xb7mhexkxm8ic9 7uuq(nthe rotational kinetic energy 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 slipgnua0 ( ree*/zm96fucping down an inclined plane startin mg( ur6ua f0*c9/ezeng from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M z- xxrid d;ll50 i*3eaand radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incrd;lz 5x-0d ae*x li3iline depends on

  "The total angular momentum of a sy yo8wwojr5*608 oaer rstem of particles changes when a net external force80 oro6y*wre5woa rj8 acts on the system." This statement is

  In what circumstances can the angular velocity oki 7b juzldsk 2*lhsg37d75iu.+1 hvsf system of particles change withoutl75 d7ls.b1hh zusvuikki*s2g+ 7d3j any change in the system's angular momentum?

  The Earth orbits the Sun in an euw5e0(ow1a5 bfa+s -5oqu+qjx: g vitlliptical orbit. Ignore any friction which may be present. What happens over time to tbxgios1u 5oa -5t5weq a wjv+q +(fu0:he Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. Asov 5*gf 3o1odn):m l(v, xoooa the Earth moves closenovx,o)*3al: dgo1oom f(5v o to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette7k3) -lkk7j6xqumhzz (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum aboum z7-6uj kql3k)hzkx7t the axis of rotation?

  An ice skater performs a piiws + t jv73o:bq+2dxs9z 7gch 2cjnp(rouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational j bp3 h+nqc2d c st97xz7g 2jis+vw:o(kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pu41o 2k( ocex)ffv3msbe yzq 9nk p30n.lling in his outstretched arms close to hisx4c1n .) e ek o0pvmy9nqzfsb(3k2f 3o body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angularz:iy.* 1v*8dp ivbap fx8.jdi momentum.

  What arc length does the 0d7 .b*fxin voglmuho3yb. )9 Earth travel in a three month period in its nearly circular orbit about the Sun with a radius ofn ob0xi*fyd .3m.bovlugh 79) $1.5 \times 10^{11} \; m$?

  The second hand of a clocb cn2ld01gr b d2og;(292 a- qxiznqipk has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 secon1g0plz2od(brxaniq i q 2 gd;n92b-2cds?

  How many rad/s is 25 revolutk sb3hf*w ,fx:q4a8m3xvy)stions per minute equivalent to?

  A bicycle wheel rotates uniformly through 29sr5c;i uk9 twnig9-i .0 revolutions in 4.0 s. What is the frn;-9w9trsuic g9i ik 5equency of the wheel's rotation?

  A pulsar (a rotating g424t gdbza;0fzyvph-34f hicp 1l+s neutron star) emits pulses at a frequency of 0.40 kHz. The period of its rotation is h44l+c4f-fgd z3p 1tyzvgai;sb 0hp2

  A phonograph record rotates at 45 rpm. Throughaae180o 8 cidu: hb/i uvq h4/+ynn0my what angle does it turn in 0.20 s yviaq4n+8:m0u 0 / ai1e/dny hu8cohb?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on rz+rqj *3hmo*au+du - the outer rim move in hod+ru qzr3a *mj+ u-*2.1 s?

  A bicycle wheel rotates uniformly through 2.0 nsuy .ms(nx0( revolutions in 4.0 s. What is the average angular speed of the why.nu( ms0(nsx eel?

  A bicycle wheel rotates uniformly through 2.0 r57f.p+:2zj z oxkx sxuevolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the wh+sxz27 jfz5xkup : xo.eel?

  A cable car at a ski resort carries skiers a distancnrqg.ka w4-7z e of 6.8 km. The 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 t-. zg47aqnrkw o make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatz10r2q w +e;z8cb*afc+g awkying with a constant angular speed of 2.0 rad/s. What is the linear speed of a point1*8w2f ; cz yercza+kbwq+ga0 on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length.6i.lwp-h 0 qsv8q +jjl If the motor rotates at the raqv6ll i 8+.j-h0spjq wte of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s.exucx+- m-fh+ s2;bii What is the centripetal acceleration of a point on thf+-ebi xhx+-;umc2sie wheel's rim?

  What is the centripetal acceleration of a point on the perimeter b5v p sn o9r *5ktf;xvmauf,72of a bicycle wheel of diameter 70.0 cm when tnv b;pk5rt m92uffs5 ,*a vx7ohe bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotai+yij-+ni 9us ting space station (r = 1000 m) rotate to produce an artifiys i9+ui ji+-ncial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of y9eh gn4esx:(u1ph8hg2od z720 m/s. The maximum centripetal foro sgzd:hg4u2ne7e(ph y1xh 98ce (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 radius 50fow9a9ugv .q)m cn o86 m with a speed of 20 m/s. The maximum cenonquf8 o96.avgcm w9)tripetal 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 whirl6 8ymf-)ap ocped around in a smooth level table. If the maximum tension that the stra8oc6-fy)m pping 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 1lmzfargee8v5p yz4rja*.4+-q b6: q zcu0i l9.0 cm rolls without slipping 10 m down a lane at 4.3g4 4e+vq6 ca*r 01zpbil:5fazz-m euj lyq8 r. 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 s*ldo4gf;ypya-mgq9f * 0y6 y with 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 cg9am)j- 2 fy5jzon5 ly 5j,uyzonstant 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 tire rotate after starting fvy6f m0.tw h 8rtb/r.1q vwv0grom rest and y.v t/wb0rv0rq8vg.mf1 w h6taccelerating 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 acceleratb q1j7bu.u ( r0ofa,wxion 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 i:r(9o dbd hs3/ej3c ,mmh ,hcacceleration of : ,9,/s33or djimbmcdhhch(e $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speejo i(7sxt6v (eg joq/6d of 6.0 rad/s while turning thro7js(o6/ et 6gjx(qiv ough 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rw+ ;q6-r* a jec,wxzswest over a distance of 115 m. What is the total number-c s, wz+* awqwr6;xej of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down ukebbiws 0--c,c b ue.d z6b)d7niformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleratibi0)se k 6 cez7 ud.dc--wbb,bon?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest o2ua lq2u* t5bp :bcrh9ver a dist a lbup*:2uh5r92bcqtance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a meej: nb,w9mxt+dical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration 9tb+,xj: we mnbefore 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 tighteni0p1rik( qb,:jt1duy kng to a torque of 90 Nm. If a 30 cm long wrench is used,(,r:bdk1 t ukpy1i jq0 what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a xj0j d1j j aqf1mvl3fvr73ej o22( ;sctorque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force re ecf1vl2fvjra ; j 1jjo033 xj72smd(qquired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofkhrs6npwh71aq /r2z1by-z 5y cld1 w- 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 follows: massrq 6jjksv55vcu)fj- g *wxv/0 m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. j-vq jr*)v xuj6 /50vfsgkw c5What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg isyx7vt ,x ex,jrkb5-u2 a9,yjk 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. (See Fig. 8-1.) What is the angular r jy u,2kx5ja-yx ,kx9 v7,bteacceleration of the cylinder?

  A solid cylinder of mass 10 kg ish : n l;+1hi1/ ze3mzghlubq6 exv5f-i 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 ebi f ez6n;3g+hh 1qhi:l1-um vlz 5x/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 ong2y d 3--m *g(hwp+ajioy0qnie end. The rod is initially held in the horizontal position, and then released as the q g(a ijpo0h*y2 gm-3iwn-+ydfree 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 radiuo.msf/ gq*m 8ss 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, wh* g8/ .ofqmsmsat linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a friq* (el;tzip a,ctionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pull* ;z(eiplq,ta ey?

  A 1.53-kg mass hangs on a rope wrapped i:cwh6,.g cja j,wgv fig75h/ around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the masf/jhhjwc .v:g5g ia7w,6icg,s?

  A rotating flywheel can be used to store energy. If it is requ6:pmu*p ,m fpxired 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 f rcmbc.:xb80inertia 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 fvu 6u((*jvl2e rz5glrest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bott(r*fvv( guul6z2j 5elom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0. qz/ 6ce3nk)thr(y v7d010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to rest/3nd zrkt v( ye7cq6)h?

  A hoop of radius 0.50 m and a mass zd z:9fld:s2p 9xwaff yh:s 1s km,4n6of 0.20 kg is released from rest and allowed to roll down an inclined61xdy ,ns:h fzs9z:9l24ms: pdkaffw plane. How 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 rolls without slil) q8vkh6m bp8y8)dk;v8bth/es.gn npping down a 35e incline thatg b8 qvltnm)h;6vk) ebhnk8s. p/8yd 8 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 m5nkao 79h xc.aomentum 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 6kv)w vm4l5djw-5kcs moment 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 arms extended has a moment o07e) svnl6j5q 9fzxdsf inerti6fv7xs95 z neldq0s )ja 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?