Angular displacement is usually qoaj159: e8/h sekxfl express in units of

  Angular velocity is expressed in;s*3 q5emub0cg:tc in units of

  Angular acceleration is exprei *93zhazr.ef sumx9-ssed in units of

  A boy and a girl are riding/cpv97lp uc 1f on a merry-go-round 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 g/pcuv7lfcp 1 9reater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turnnmxp*0zfh-- 6g8 onxb ing at a constant rate. The boy is near the outer edge, and the girl is closer to th-hn6bx-xzpm* nfg0 o 8e center. Who has the greater angular speed?

  A boy and a girl are riding afusycm39p 02on a merry-go-round 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 speedumcs 0f392py a?

  A boy and a girl are rii749ylnsgy- vr9 2fpj ding 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 p99rg v nsi fl7yy-j42has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant ra7j (2 4x:vttkbrlt:b lte. The boyj4 7 l2:(btvtt:lrxkb 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. Which of the f7or0 bf-ool r+ollowing is an accurate sta7rl-o0b fo+or tement?

  Rolling without slip3pm udw i+sjwagtx /o,q6/81 yping depends on

  Two equal forces are applied to a door.k 1.lgko.zfs7px ,-qhi-js7j The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicula 7q7pjxjhf1 sk-o.z.s -g,likr to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at(zp4. c ca -c6 q4fvqjapa62ap the doorknob. The first force is applied perpendicular to the door;-6.cc4 v2zpf qa aqjc6pa4a(p the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the dova*r jadg507q 4lv cd uo*5z-ior. The first force is twice as large as the second force. The ratio of the torque of the f7rzcol dqaua5vgi d*j*0v4-5 irst to the torque of the second is

  What is the quantity used to me6c e4rgxpnr* /asure an object's resistance to changes in rotatiorg*c 6p/ x4ernn?

  Consider two uniform solid spheres lmdq h +a(g-4jyb;b1jwhere both have the same diameter, but one has twice the mass of the other. The ratio of the larger momeh1jj-gb ;+y4qb(l ad mnt of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the pbncs4 jgflj7 g0f9:s6 wdh/,radius of the other. The ratio of the largefchb,dp0/s 6wgg j:79js4nfl r sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice thef)0hu u9 ff3awlc- 0rwn xtoq,8soo-. diameter98aotrhfow nf-s )0,.wx uof- 3cu0lq of the other. 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 radius R. If these are increased tooo/ 6zd1 * q0doazak+m 2M and 3R, what happens to the sphere's moment of inertia z*o1zdoao0a d6k/m+ qabout a central axis?

  If a constant net torque is applied to an object, 7f bb)57bndzxthat object will

  The moment of inertia of a solid cylinder about its axis is g0ih.dk v1nq.1 ameug.iven by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotaa0 e1d.i.v1 umgq k.hntional kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 18+pod yguz5** duti9x 50 kg, one 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 translation5i+ u8d*pgx9zuoyt *dal kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and rht9kiao5xc , v fe8y)t-0eq, gdc..q uadius R rolls without slipping down an inclined plane starting from rest. The linef5d-ue avxtqh c.k0.gy9,tq i8e,o) car velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radoqko v aa n( 6*l4d8s:6ubp/)n hivdq6ius R rolls without slipping down an inclined plane starting frqhliv b:q/n6 ds6a 8ponu o*v(k6) 4daom rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes whenz1g-tlh 0yk9o a net external force acts on the system." This lz 9y-g 01htkostatement is

  In what circumstances can the angjzk t5 ;rjuo /3+upvfb(p6;ya ular velocity of system of particles change without any change p kobza5+jy pv/;ur 6;tujf(3 in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Igno/ 72dzbd8 krzlwe0fl2re any friction which may be present. What happens over time to the Earth's angular momentum about the0z blfd2kzw2/8 7rde l Sun?

  The Earth moves about the Sun in an4majn9j 3rf y8 elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about8 4mn farj3yj9 the Sun?

  An ice skater performs a pirouette (a fast spin) by pul/b1roibrw g/5l *3 safling in his outstretched arms close to his body. What happens to his angular momentum1fbl bo3igwas/r/ 5 *r about the axis of rotation?

  An ice skater performs a piroueyo2f23 t 3fk4rcnbj:utte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic ener f3cojnf4ru 2 :byt23kgy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulliy(jkaonns2et 2a,lao9w7x + upv,1 (png in his outstretched armn ,n2p 9y sva, 2j1oo(t(expku+aw7a ls close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of3o ehlq:p ooqm1ugxtd.) ;i5 8 angular momentum.

  What arc length does the Earth travel in a three month period i)j6x. bn//8ga z(suj)n( aknbcq z2zin its nearly circulaju z ( z.k)(ai/ ngn 8z/b)sbqcx62njar orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of h5dlcgd q37 mt9dm3x:0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 dhgd xtq 7 5l393cdmm:seconds?

  How many rad/s is 25 revolutions 6e92sf fzs:l l*edku;per minute equivalent to?

  A bicycle wheel rotatet5d/) gsr h.;ci oz5nes uniformly through 2.0 revolutions in 4.0 s. What is the frequenc es/5ti5;norzg ).hcd y of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. T6xln*oy+wniaiy 7c3 jwa5p9 8;qxb /ghe pion8 n6xyq /* 9i lxaj;bac 5gywpw7+3eriod of its rotation is

  A phonograph record rotates at 45 rpm. Through whafua171 0pko1 5vdfcyrt angle does it turn in 0.20 s? 51prcffu0oya vdk711

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outer /a v/p/sr1nb d78jjbg rim mr b7 bs/jgdpn8j1v/a/ ove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ,jc)xtgmra 9- is the average angular speed of the wga xcjm) -r9,theel?

  A bicycle wheel rotates uniformm/ vv+ hnodu.)ly through 2.0 revolutions in 4.0 s. What is the li nvm/+ .huod)vnear 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 bx+qkf-n 0j(s km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assumi0+jn fbkx(-q sng 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. 8,cz 9h-mzpgq* .v0nzmxj7uj 0 rad/s. What is the linear speed of a point on t gh z*m07m-9nzpc.xz jj,uvq8he wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.(xzm c+ 60mv8ih(h5rm * ggbbf16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linez058b(*bvir 6 fm mgh+hg xm(car speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a rdr b,jl 816lzconstant angular speed of 2.0 rad/s. What is the centripetad6r1rl ,zlb8 jl acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle wzz *ck4eug. os9*q(c sz2mrsq hv4: ,mheel of diameter 70.0 cm when the bike iskm4ssug 9hzv :(* r4q.s*,mc2eoqczz moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotat9sf5dmm/pijb)h 4,ux u9qm7ning space station (r = 1000 m) fh7xi j) mqnmud/b9p 9us,5 m4rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m withmha)l947q qpv; / al-be cn:u31p erye a speed of 20 m/s. The maximum centripetal force (provided by static frictionc phq4a;1e)uvby3elm :lp7 qe a9n/r-) 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 s+0ovr mvj(jonz-+g1fa 4 fa0iy sh;,with a speed of 20 m/s. The maximum centripetal force (provided r+z01v4jjo m; s,aa+fn sgi0-fv( yohby 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 kg3xn92 2m aiptb8b1o6wqi i7 string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum l26x2o wn7t qiai1i9bm8k g3pb inear 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 t);s9k+zk.8 oy6cbnd rn-tmjk t5e, ldown a lane at 4.3 m/sc-m+borknk)t t.etk ,lys6d8n 95 zj;.
(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 wic- mug7g: eq/hp 3bef9th 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 angular accelera ;xv;x;vq . ;oykrmv5rn-c0dstion 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 automobil)h h8iyr*ksf(n cl0g3e tire rotate after starting from rest and acceleratis(g)flhch0i3 *8nyrkng at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has u9;qy rh9u-, d zqg0gdan 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 k+khi.j 9z+3wy ikga ow26nj: constant angular acceleration o:o3+k6w + k9nyjikzi2g.ajwhf $-5.0 \; rad/s^2$. 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 tur-. jwl ;/b gyuxc)zpxkl4e0(3xbz+v dning through 2.v4 k/z+ezbxl0x dwy3xcp g lb)-(u;.j0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows dowoq95e+px- ulvl*/c l.m nnn:yn uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions txvn*cpn:mnu y.l+9 e-oll/ q5he wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to re):xkf)0kpq rnle a w902nq-al st over a distance of 115 m. r9x2 lfaawq- : e)pnnk) k00lqWhat is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unifo/3, prt pvp 9rja-xkw8 2yf,jzrmly from 8.40 m/s to rest over a distance of 115 m. How long does it take wr kjj2p8z-fr3yx v/,p ,9tapfor the wheel to come to the stop?

  A centrifuge in a medical laborat6974(mvs6:5 lthq b ehrfy z7b)*zz unkr0we vory rotates at a rotational speed of 3600 rev/min. When switc:kh z nz*5 )z(whr s9bb6ruvmy7607teql4 fevhed 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 uty/f23d3*bg3k jenzsy4ov. to a torque of 90 Nm. If a 30 cm long wrench is used, what is2gt/4.* 3fbzjveduyoy3s 3n k the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tig 45c 98xarhj*f lw0zkv4xhjx/htening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitu x4j/5a9*lj h0kxrc8zvfhwx4de of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertwvsfnbhq r( ,qw+*t 05ia $3.00 \; kgm^{2}$ 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 at the ora-dqw35kw6cz( 85cmg hcp- ohigin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?who5 a6 (5 mgz8kpqwcdc- h-3c

  A solid cylinder of mass 10 kg is pivoted about a frictionles7(rneowb;.r; ua,ei7ca4avfe+ m3 dv s 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 acceleration o a.b ;c;77emdaoirfr,e43uevw+nv (af the cylinder?

  A solid cylinder of ice eyj 7 a:u,h0v3l/wmass 10 kg is pivoted about a frictionless axis thought the center O. A rope w7luve0,hc3wjea:i y /rapped 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end.4j-lqsf1 rv*nh ya1 r6 The rod is initially held in the horizontal position, arnh lr1-1y4sj6av *fqnd 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.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 ;g* m+*zczakn2zvdzxu,d hh41 q2 *xukg. Neglect the mass of the axle and sprocket. If a forced x;v4zduxn2 qg*u,z+ *zh chmk21*az 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, assuming it rolls without slipping?

  A 1.53-kg mass hangs o- dt:v; ;ksbafqd 6v9mn a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular6a-k: mqfbvs;;v9td d acceleration of the pulley?

  A 1.53-kg mass hangs on a rope w.e) gcvo qcs50py5p11xs nh3a rapped around a frictionless disk pulley of mass 7.07 ksae qg1p.51ovnxch50c)s p 3yg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used tola:;sea6kjysy 3 *u9fmt18s37 rtej q4,zptx store energy. If it is 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 ofi 2ntzpb b :paq6v)-,f inertia 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 rollse:a3jh *(kg ndhwi f.i+9tap, without slipping down a 1.pet i:gj (dkif* nh.3,+a9 awh0-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 m rolls with a (a,6v sxinya1x2:bzfs 9 , nj5vd8pbrspeed of 10 m/s. How high up an inclined plane can it cpd1an58 xxnrszb2,b,sva6y vif (9 :jlimb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fr6z/f(k qfgb;pom rest and allowed to roll down anqp;6kzg f/ (bf inclined 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 1ptn67uq 1tf2xt; u* kb5 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The mub7tfxp 1u6n2tq tk *;oment 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 by egv45h w/j t9ni;q(a k$20 \; kgm^{2}/s$ 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 mo t-t7 *6rdq.pz/ynpl jki4-ve u7mn 0gment 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 ;xug dz99 r;p*fhv g:larms extended has a moment of inertial: vxr;gu*p gh9;9z df 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?