Angular displacement is usually ex eu+z)ks,ztc9n46gacg.7jjo fd udz)-p:ls 6press in units of

  Angular velocity is exprex,t 3c8a8ba x kz;i4gussed in units of

  Angular acceleration is expressed lm2:1kdj kn k*8d 2uh/ fys 4jmbh;8h.htt-zein units of

  A boy and a girl are riding on a merry-go-round which is turn ou1 5l1y -add*gitxeosq, 6+ying at a constant rate. The boy is near the outer edge, and the girl is closer to the cento dsiu6 +-5 tgyy *xdeqa1l1,oer. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turqd 5y+3 dnl ;itpn)j r6x7p*ojning at a constant rate. The boy is near the outer edge, and the g3xdoln;)ny q+pdr i56tpj*j 7 irl 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 turning at a ck6 +gvjp o)drth4w6s:onstant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linea) grhw4pv6 kjt+sd: o6r speed?

  A boy and a girl are riding a merry-go-roundr ,rlis-a ,gsv4bv)zy; ;s: fn 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 greater centripetal accelef ns-via:;,r4y svlrg s,zb );ration?

  A boy and a girl are riding a merry-go-round which is turning pvyp6 dqv 6m.f:c:3q vat a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential a:p m.v6 :p6dvqyfq3vccceleration?

  Consider a rigid body that is ( r0v9f 0:p*kb2d upgjif;8s;bdtu girotating. Which of the following is an accurate st9kb(0d vp i0 ; sr2*ufd;gfpitb:8ugjatement?

  Rolling without slipping6w7j:q gtdjq 1 depends on

  Two equal forces are applied to a door. The first force is applied at t-hmnd 6pz49+ w,hxdwkhe midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to mhdpz 9 -w+nh64dwx k,the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The ce :z,(ory*)el ) pghlfirst force is applied perpendicular to the door; the second force is applied al(e,p) ezy:l*)o hc rgt 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, peyj6day (om ah41(tihgg nv;w25x).tcrpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the secondda ;ihtxwcjh4(va6)t n.g (12gomy 5y is

  What is the quantity used to measure an object's resistance to w+nm)v hc1q zm kqs/ s,o -,yl*g8-ufkchanges in rotati -mf ykvlhqn/ ,g+ mu,z)wq18o kc*ss-on?

  Consider two uniform solid h oczd. e/0r0lspheres 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 the smaller moment of inertia ishd 0 ozrel0.c/

  Two uniform solid spher( d ywy9u3nk6nlt3xx)yz8 7v ves have the same mass, but one has twice the radius of the other. The ratvz8n7wx 9 336k)lnt vy( uydxyio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres0gos*1b lihwue87 a)9w37hxv q 7xkoz where one has twice the mass and twice the diameter of the other. The ratio of the larger moment v0uwlg1)73 8xq* eh hkoa xb7szo97iw of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and rvcqo-nq7j icd( v4u0 6adius R. If these are increased to 2M and oc0-7 nvviqdjq4c( u6 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque )grh*w/hojwk * s l(9vis applied to an object, that object will

  The moment of inertia of a spgx up7v :kh:p.hvbbgb ;2h4(olid cylinder about its axis 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 wheel of which gmh +k7;d77c,udamff 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 translational kinetic energy of the bike? Assume the wdd7mfu, a7gk7cfh+ m;heels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down an34 9iseaj3rvr inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline d s9iar33v4erj epends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an inc-/5a36w 6uwyu g2xmcqre:3bt pi dp s/lined plane starting from rest. The angular velocity caib/: /3 e-m3wud xgqp2syp6r w6u5tof the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particl 9lj e8h: hxqse*j7x2des changes when a net external force acts on the system." This stat7x jslh9x*2 eh: j8qdeement is

  In what circumstances can the angular velocity ;n .n:xuh8kstyd/mjh)k , 2pbof system of particles change without any change in thes8jnm);kx:, tuy h. h2np dkb/ system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction wsl -sx /tt;/mhhich may be present. What happens over ti mtss/ lth/-x;me to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in anrzmk4,tz: a 0ck-ywo 5 elliptical orbit. As the Earth moves closekw0c 4,ky zr5mta-z: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 pirouette (a fast spin) by pulling in his outstrq ,e9 8ignyb(tetched arms close to his body. What happens to his ang(q,bi89 ygnteular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullb;4o(zpta x o8ing in his outstretched arms close to his body. What happens to his ro8zpao( ;tbxo 4tational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his of0j kqv4e8x b7utstretched arms close to his body. What happens to his momenv4 bj70ek8x fqt of inertia about the axis of rotation?

State the law of conservation of angular m6xr t getqxezrm1jamz+ x)d(68 c:1p8omentum.

  What arc length does the Eartpe/lc9iy snzef-0 /4 yh travel in a three month period in its nearly circular orbit about the Sun with yfe//is - e904cnlyp za radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. iwkn i +285lhrWhat distance does the tip of the second hand sk5ihnr +8i2wlweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent to?8y /azo02x/.)hc u b(9d u)gtmxb7oksp p; isc

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.y8b a,ec: qu9c7q wbu/ What is the frequency of the wheel's rou87c9 we/:byu qab,qc tation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kH d xmp4uvopl 6+eh:xj4kg))1w z. The period of its rotatiole j6+):vogk h)w 41xx p4pdumn is

  A phonograph record rotates at 45 rpm. Throuenpsy a9pep ;hvo(2:0gh what angle does it turn in 0.20 s?0(vh9 pe: 2psnya;peo

  A wheel of diameter 26 cm turns at 1500 rpm. How far willj ib/1i. tpzq.-od 7om ij;;fm a point on the outer rim move in 2.1 1.;-q.iooj zbijdp mm7tfi/; s?

  A bicycle wheel rotates unif kff 2dz8l po*u1-srs:ormly through 2.0 revolutions in 4.0 s. What is the average angular speed lfpzr 1s8-:o* s 2kfudof the wheel?

  A bicycle wheel rotates uniformly through 2.0jr65vfc ad+8 f revolutions in 4.0 s. What is the lineaca5f jvr6+df 8r 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 chx,j ,fkpvcq* gm )(c:able which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for )*f,v(jhx:kcg pcmq ,the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating4ukkm , j -2a655mv (tyckdvhs with a constant angular speed of 2.0 rad/s. What is the linear hs2-u4vk t( mymcjvk,d 5ak56speed of a point on the wheel's rim?

  The cutting cord on a gas-powered wee0a:dd8ow* b u1 rhccl9)l8su id cutter is 0.16 m in length. If the motor rotates at the rate o8l ldhb80usr*9oi)aud :w 1ccf 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 rac)3kmc jc+dhgv +6j m.d/s. What is the centri+c6 k.mcvdjj 3mg+)hc petal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter dvx2h6 49ql oc9fpc0mof a bicycle wheel of diameter 70.0 cm when the bike is movingl02v 9h 6pxfm qdcoc49 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station (y1 cz(akajhe v621s06nkhu,jnp;b 9xr = 1000 m) a c en6,(upjk 6b29vn a1hx h1s0kyjz;rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radi pr(kh yu n 0c4vl8;4emoop7byc2 o-c2us 50 m with a speed of 20 m/s. The maximum centripetal foyek4ocnv-uhmo;2rbol( 42pp cy0c78rce (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 50 m with a sp dx c1aa qucn9oe9 gjc.*;/)oveed of 20 m/s. The maximum centripetal force (provided by staticcgax9c9*o v;e)/d o1qcn .jua 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 whv3zl,k ny1,0:hhlii 7v0ug/xh rm; ng.oji. xirled around in a smooth level table. If the maximum tension that the string1l/.nh vzoh3,hr ii0u;n.gmx0gk, lvixy7 j: 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 radi28f(n o kmnul st :;ssxtp5:d5us 9.0 cm rolls without slipping 10 m down a lane at 4.3n5sd(p8ut::5 s2;m kx lfsnto 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,oog 1s c) q4ycf2,wnyo1d a9fcra-3d 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 cons d+bn2w,i m1ostant 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 r* .)hzs u5gbfeadius automobile tire rotate after starting from restz.b )u5 fgs*eh and accelerating 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 angulahtnt,t; (v0,sz1bipu+,a znz r acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceler s+jtg5u qpfv9lzh/-5ates with a constant angular accelerat9q pjzh-gt/5lvf+ u5s ion 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 tud:t+n*xz+l x. pkiww4rning through 2.0 revolutions. What is the average axd*t w4+:lpi z.+ nkwxngular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rz*9tbi pk73nm est over a distance of 115 m. What is 7mkt n*p9iz3bthe total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ove2gw 7 pu 0pvi/ruy8b7pr a distance of 11w gpupp2i0 8rbvy7u7/5 m. What is the angular acceleration?

  A wheel of diameter of 68.0 p/b9;tr 9z wcyi--cje cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m.-bwy9;ci pr zc e9tj/- How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rota1wb 6xvc0(d z.51vw lw0k/5z pwivyzztes at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleradz16c0kx. 55 zw(l0zpywvz1b wv ivw /tion 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 torque of 1wvy m uqp4;/u90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when tu /1 ;pqwymu4vhe force is perpendicular to the wrench?

  The bolts on a car wheel require tightes;qqeo0g:qiiq r 6m6)c *q6r/mwcl p6ning to a torque of 90 Nm. If a 30 cm long wrench is used, what is the mq6e)0 rm;rp cq6q6i/*: q 6oc wmigsqlagnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of5 y2iq b6ztt86/rvon x/w5p ej 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 follu1yz9+dli2ar 3v ypl )v4wa o3ows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the dzwpv 2yu4aroyl3 3) 1i lv+9aorigin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thougrn)pt y 0.r2jvnix2b,ht the c2itjv ,xry0p.rb n)n2enter O. A rope wrapped around 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 frictionlz1 yjzj kf,/l1ess axis thought the center O. A ropz,/ yl1k1fjz je wrapped around 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 held in t56z oh;z olpt.he horizontal position, and then released as the free end is allowed to fallz.hl5o ;zp 6ot. 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 rx+o b u:fpq ,iiq7z4d3ing 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, what linear speed doesb:pqod+i4,3f uixz7 q the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a ri6u+ fm 6 gaec32 qo7wqkvsn*)ope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the 37 2qmnfukasi6 gc+*ew6v o )qpulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk / jwno+xuo(borr / 0bxx609blpulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration o0oub(xb6nxb lo0r/j +/9wxor f the mass?

  A rotating flywheel can be used to9x*:ylig) s9 z t:iyvp 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 of inen v/tlnr;)t- h(i(q ndrtia 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.a;/ ggkivd1e;*r n/ xt010 m starts from rest and rolls without slipping down k ;irv/ge*/;nd x1tg aa 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 radd*y *jnh je)8 +:yulq:azp)b yius 0.010 m rolls with a speed of 10 m/s. How high up an incb*j lnj):qya)+e*dy hzu:yp8 lined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and 0ld;h+y)ejl 1rmozh* a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it;hlr* jyom 01l +ehdz) moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and rxeo/r)- 3eb l,q*5 ve7 dqcegxadius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a spe cqx/e7 *3v5egb,oe - xrlq)dhere 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 moml/m0wmci9i8s,vnlt zb4 x:0x entum 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 inertia of , 1(on3bblk/swr8uol $5.0 \; kgm^{2}$ 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 5.00k(pko-(jd3k8f8p ma7 fw 0fki rad/s with arms extended has a moment of inertia 7f((kkpf w3omp8faji 8-0kdk 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?