Angular displacement is usually express in u+bdcx, 1j isxdqjzj9p7 :zz;:nits of

  Angular velocity is expressedgj9zn)2n pu; o in units of

  Angular acceleration is exprexn,ev-*t gogjdn;00 essed in units of

  A boy and a girl are riding on a merry-go-rounri* bsr7l4e8q3 0zjcfd which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has*l0b cqr84ifj er3z s7 the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which ij.cq*cd3drzm/i(l2d f,u l u2 s turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who du , d.cfdq c(z*lru2ij/2ml3has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is tu8ob kk)on5 ciqnq 78(c2kl;swrning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linqkow ql7 o)(si8 n5 k8ck;2cnbear speed?

  A boy and a girl are.)rcw , d:tvws riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is clw),r dw vs:t.coser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a fi 0wi9 pr+9:a:forrkmerry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer toaw0i +o::r9kfp 9r fir the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whi ut:uej rt;(vk5ar0*tch of the following is an accurate statement*trr(5tvtk ;euu j0:a?

  Rolling without slipping depends odz4e -wqz 8p5en

  Two equal forces are applied to a door. The tu ciquw0*8b- al6; 5bzjaye-first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpend tu--0 cae;qibjlu8zya b65w*icular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The firstw ejm68q*tay 5 force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exereqt 8a*6w5myjts the greater torque?

  Two forces are applied tm8izokt 9k5q9a6 g) jeo a doorknob, perpendicular to the door. The first force is twice as largi 5mtqg8a 96zok9)kjee as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to cha,n ww jqycx)59nges in rotaticn5qy )wjwx9 ,on?

  Consider two uniform solid spheres where both have the same diameter,b1noa1j;v.s e but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment1sv;1ojnb . ea of inertia is

  Two uniform solid spheres have the 9us 4iuzs7k; 9fken5-5 f buxlsame mass, but one has twice the radius of the other. The ratio of the largf- nz 95eubss5l9kx4uk fui7; er sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spibo bt )e7bkv (p5b4jp5crr::heres where one has twice the mass and twice the diameter of the other. The ratio of the larger(bpob5c 4)57re: pkv ti:bjbr moment of inertia to that of the smaller moment of inertia is

  A uniform solid spheuvm/r h, j23ci1fts1yre has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a 2iym3j fu, t1s/vh1cr central axis?

  If a constant net torque is applied to annunfa456u d 5k object, that object will

  The moment of inertia of a solid cylinder about its axis is given byh1 az)fu2nw )o $\frac{1}{2} MR^2$. 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 has a mass of 10 kg azb. vuzef5u4c5-suc5 nd 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 wheels are uniform disks4 bzccf5 euz5v.5s-uu.

  Suppose a solid sphere of mass M and radirclxhc/ k17uip03) nc1iq8d w us R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphe k1i0i8p/d3x7cwr ccun h1)ql re at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slijy mp*e 4wxu3*xq1h* x3e b,qxpping down an inclined pla,xx*wy4x uq*e mpebhq31x3* j ne starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum 2b1(2o*u9unwvfmp vy34imilau7 a p3of a system of particles changes when a net external force acts on the system." This statemenily w7o3 au219uv3p*fp2 va (imbu4mnt is

  In what circumstances can the angular6pttpmuj4k ez,9 v hmui--4,a velocity of system of particles change without any change in the system's angvuk4,u -zm46mp e9h j piatt,-ular momentum?

  The Earth orbits the Sun i; ijgn;mmcz3t2 g 3ys*n an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum abou cg;mzj2sg*i y;nm t33t the Sun?

  The Earth moves about tw4 thuv-g e/ur h69*ij1n4kdc he Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the or-h u 4et w46j9nr*u1cgih/dvkbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (aweea-4 1l70f0ye )jr cx7ommg fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momewac7ro l0 eex7m041) -ejgmfyntum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his ou +wu7b,lg l5u wt8;: -7lrsq2izbgz tgtstretched arms close to his bi gbsl728- +zbul5 l:gw;,grqtztu7w ody. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a piro*r(ogu0d .ghquette (a fast spin) by pulling in his outstretched arms close to his body. What happens to o *rhg.g0uq( dhis moment of inertia about the axis of rotation?

State the law of conservation of angular momentum p 5)a-dpu q y,:..jcdwnh5hgj.

  What arc length does the Earth travel in j -tz;jg ns+tz /.;3 csjqkbwi04nkm- a three month period in its nearly circular orbktqncz0k/g4 mj ;s-w ;zin -s t.jj3b+it about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 my6y; /bptuh0- lf v-rd rhsr4j*,r/ha. What distance does the tip of the second hand sweep throu-/0*-r arjtslh;y,4 y6 up hrrhf db/vgh in 3 minutes and 45 seconds?

  How many rad/s is 25 rev0i3mddo v /hn,olutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. i2f,vh e,ct7 m)3uiit What is the fuiit mfh v7c,2t )ie,3requency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at twfwit-7);vx.nu u .za frequency of 0.40 kHz. The period ownx).-;f .ztuw7tivu f its rotation is

  A phonograph record rotates at 45 rpm. Through what angle l d+xeer4yr,3h/0mh w does it turn in 0.20 s?yhl,mw 30dee/ +rh4r x

  A wheel of diameter 2x yrbvew8,*;pm xkw;6rez kr/r5.yb 66 cm turns at 1500 rpm. How far will a point on the outer rim6xrbr k/8wmv; e5yy *br ; ewrkx.6z,p move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutionsm grxmc5pzo7;, xg ,6i in 4.0 s. What is the average angular specmzx5pg o,m;x7 g,6ri ed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wno hfa9p: *q-/rw8 k ni0;z kr-ewt5gahat is the linear speed of a point 0.10 m from the center o;k i5a -n0nhor-gwprt k*/zqe98 f:wa f the wheel?

  A cable car at a ski resort carries skiers a i a,myx.5j:msopqa9x20zem8 distance 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 cablep aza2m,jeqms8 i5:m0 o. xyx9 car to make the trip in 12 minutes?

  A wheel of radius 1.0b( a*(u9x,/ vosxyqnz m is rotating with a constant angular speed of 2.0 rad/s. What is the linear spee uxy x,z/o (9b(*vsaqnd of a point on the wheel's rim?

  The cutting cord on a gas-powered weedur 4mly;(+ 3(krud:ndd;gtcs cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate43(us y;lu+d ddtkgr(r; cnm: linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a consta huop)h:bmnm:4 qfn; 3nt angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel'4:mh nmb3uofn:q;)p h s rim?

  What is the centripetal6t7szds8- d m, 4kuouz acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cus4o,u-8zz7 ds t6dmkm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular-ztv2 2s8 m+a4agua ij, rotating space station (r tsmu-z2gjaa+2i 4 a8v = 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50v ,-fz*va ybo1t4svbi(ycj8w y9 u5y( m with a speed of 20 m/s. The maximum centripetal force (provi s v5t1v9z-yyfy i*j (a bc,(8v4ubyowded by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating lqj7o1mo3f,w+k m 1y ja flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centri + y3o1wo kl7fjmmj,1qpetal 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 2bmf 8yz fch55z3eei 5string, is whirled around in a smooth level table. If the maximum tension that the strin f2c fybei85zem5h 5z3g 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 radihy0 /f)zo8sf mnpc5 *jus 9.0 cm rolls without slipping 10 m down a lane at 4.3) zmyf*5 os 0fhcjn/p8 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 acceleru- ,v5uxxcpphik535 h ation 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 accel+wa 6r-q+slxkeration 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 stz) xoeuz0bqk89g bz+:f fnv u,,b1i1 rarting from rest and accelerating at a constant zb8n 0zbr qv)oxeg,+f1 uib1 ,u9:zkf angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratuzu1iwoehjoi*1w :8l7. yu00s l pks:ion 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 angula lr mh*2c kmg+u-/y qp,p,z-nur acceleratipu+y- cu,/ m2,kp l*rgn-qmhzon 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 speesq akhjn+ (:)5dhvk9rtj k-b* d of 6.0 rad/s while turning through 2.0 revolutionsdt-*hjbkj5(+ ) :nvaq hksr9k . What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8(0-:tya d3a2q*hkwhw1 u y*kg pa7rgx.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in cominggkwapq 02auaw 3*xrgd t* yk1(7 hy-:h to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ohzlv k2i( 6 )p:dhf*llver a distance of 115 m. What is the angul(k )vh6lplh*lz:d2i f ar acceleration?

  A wheel of diameter of 68.0 cm slows jlut6wtr3 7z,down uniformly from 8.40 m/s to rest over a dista 6j tuzrw73,tlnce of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotate; sraujax-6xo f4d,y.s at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration beforxo;jy,u 6-4rasfd. xae 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 90 Nm. If a 30 c : sigfoo+r/.8vasciys:bz )5m long wrench is used, what is the magnitude of the force required when the force isfo.5)cz:bis:goa/ ir s 8+syv perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of f5,ivwdmtqk p5qz tm0 6n;7 h(90 Nm. If a 30 cm long wrench is used, what if0 , tk qw6 hzp;57mqdntim(v5s the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iu kty(-9kdemg s8a+a 8nertia $3.00 \; kgm^{2}$ 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 origin, mass 2:hkzz18)w fid m is at x = a, and, mass 3m is at x = 2a. What is the m18fd i) wzhk:zoment of inertia about the origin?

  A solid cylinder of mass aja 6)en1vj9w 10 kg is pivoted about a frictionless axis thought the center Owja n )j69ave1. 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 ka-r8cy4y) nk pivoted about a frictionless axis thought the center O. A rope wrapp 8n-aykr ky4c)ed 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 js1ij.lg 3h1q6 md0a02wfroi initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular accelerati oim.0sgj6wihr3f1 2 a0dqlj1 on 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 cj5b e 0d4onso9 ol)nt-m 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, assuming it rbd9 nojeo-4ntl 05os)olls without slipping?

  A 1.53-kg mass hangs g9pu(luu, w q5on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accqul u5,9wpu(geleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless d6*5s -vz5hb sdw1jy loisk pulley of mass 7.07 kg and ra1sd5*5b zy l -ovshj6wdius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is re n(cz06r)b5tjvxn liy369 k niquired 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 ofbq s. *rcjts(*hm74gf 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 masyu6l dg (ndl26s 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of thl6ng2lddyu 6( e 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 speed of3fy idm y4dyl j4g5fakf7z *5f 59v1f.5miyam 10 m/s. How high up an i1 f9yg4f5i3kd.7mfff 4y i5vz55a admjy*l mynclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass ofcc 156me v pr.s3 nwnbw5lrdhi 2w)w87 0.20 kg is released from rest and allowed to roll down an inclined plane. How )wncw71ri3n p25hewd. cl8rvm sb 6w5fast 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 slipping down a 35tqbwi x;cu:q 0-f*rw .e incline that is 7.0 m long. Assr.:wx qi f*bwuq0t-c;ume 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 chamu1 (pi 5w2zr+bq)6v1gmxju u/ ysm;anges 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 mome)q/xdqwrdo( 9nt 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 momenrk +9taa2 xtf+t of inertiaktr a+ +f9t2xa 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?