Angular displacement is usually exprcfe1n c6gpmfi7)55ca8h mp,less in units of

  Angular velocity is expressed in uniafapbg akfc829 qw 1 f3o*s :qub3/x7vts of

  Angular acceleration is exprd0, ( 5;ndidhaire:eh,7o ptyessed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constant rwrsi8. 5/a nrrate. The boy is near the outer edge, and the girl is closer to the cent sr/ian.wr5r 8er. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turni:en; 6pv t.dthq9psqk w zv;93ng at a constant rate. The boy is near the outer edge, and the girl kh3qt6v; sv ezqtw:; 99pd n.pis closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round whichi03 4q.tmy-60ioxbyiqbiba ah)o sfu655yf , is turning at a constant rate. The boy is near the outer edge, and the giri56oiqshai-, t0 y6 ffb5 myb0.b 4xoyu a3)qil is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constan(cy/.uuwyxxe ev) e0b 7dlr0:t rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal :rxued0e)7bxv /u y cy.we(0l acceleration?

  A boy and a girl are f43m/) jf:r .qfornuyriding a merry-go-round which is turning at a constant rate.: um4f/j3y)qfrrf. no The boy 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 following is an accuratea 0i.icg i -5+iyetw8whb,c7t stgcthw+ wit75i.8i iay0b- c ,eatement?

  Rolling without slipping depends owu;m8s wje l14n

  Two equal forces are applied to a door.f3)j,v*hg 8 t jaaxxi4 The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torqujx aa)v8j*tifh,34 xg e?

  Two equal forces are applied to a door at the doorkkgw) w glle4ba4m/1v 0nob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. g a/w41gbllvk0w) 4m eWhich force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first f0 sgt.o8-k.s-1 n+immwz dmvl r8p 1myorce is twice as large as the second force. The ratio n vdks1 opz-mi+8m0-gwm y..m t1ls8rof the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance tob;e, xxi(o t3f changes in rotation3;xbtie, x(fo ?

  Consider two uniform solid sphex+kln t ry1sutn;0)35 8w fwclres where both have the same diameter, but one has twice the mass of the other. The ratio of the largeswu)1t x3t8 n5wy;lc+r nk0flr moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres 4g+,hwq*4utzqw+b dm ug+qgh(m3by ,have the same mass, but one has twice the radius of the other. The rwtm+4 ,*z+bdmqqb(y wg+g, hgu4quh3 atio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass andpb105 j)zpwgaje4 1nv twice the diameter of the other. The ratio of the larger momeepg)0p nva41w j1z5 jbnt 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) assk0e19:njjf td xx5j2a( c to 2M and 3R, what ha0ad5 xx9s2j(s a)1kfn ce:tj jppens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied tocj kktv05+n5k 2qu81 qts 1tcw an object, that object will

  The moment of inertia - s77wm:j yiloof a solid 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 mai oa fu;.uv y/m-g2hx*ss 150 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 translational kinetic ener2*a/y ;-.gvfhmxu iu ogy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass.ie)oqk d+ .)xr kdy)h M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline deie.yk q)d.) ok+xr d)hpends on

  Suppose a solid sphere of mass Mv)xh2b m e gbe,f4-;xj and radius R rolls without slipping down an inclined plane startin42jbmg, ex ;efhb- )xvg from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changesy8 eebk1tbg/ucl6 p 2zd(o8w v5 p71of when a net external forclczwbe6k8 u 7y2/b( pde1ogf p1t v8o5e acts on the system." This statement is

  In what circumstances can the angular velocity of system of particdtho7/v6hc /rik 1:emles change without any change /dv:/kecr1o 7t 6ihhmin the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any ;dn s57.yny-.m jx yiifriction which may be present. What happens over tim xnd;njyms.7y ii- y5.e to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical gafk. re6:cf67e 4z dzorbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting rdckg:6. e67zef z4faspeed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulliuplztb6::dn8t w 1ag* ng in his outstretched arms close to his body. What happens to his angular momentl *t a8d6zunw1pbg :t:um about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstre7zo*ed(hvp vca. t28btched arms close to his body. What happens to his rotati8tdov(bzph7 c*e2 . avonal kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched vv1bp(b v oe +l7c43j.kd7azhxwin8 7arms close to his body. What happens to his moment of inertia about t.4k3 nvv+ h al1 7z8cijw(bebvod7px7 he axis of rotation?

State the law of conservation of angular mome*7jy6l hw(a,q vwr8ev ntum.

  What arc length does the Earth travel in a three month period in its nearlc/q,dmyl p7y 3y circular orbit about the Sun with a radi 3y,ym/cd7p qlus of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the.d3qd 2zpvr j vlo*)uu u( (0ygv(c6hd tip of the second hand sweepcly* u 3d(uqgrvdd)j.(2z vu p(ohv60 through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent to,g8vm nt8 -icsw8 .ejd?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thew99yjn: ,id vo frequency of the wheel's rovn yid9o9: wj,tation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of bhyb1p9mt x 840.40 kHz. The periodthy1 pbm 8bx49 of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.20brdd(99izwc0or -5 -w;igr is s?- 9iczg;dr r0obrwdi5wis-9(

  A wheel of diameter 26 cm tdek;p 8xby f;1y+ bu;turns at 1500 rpm. How far will a point on the outer rim move in 2b1u d+ep;yf8yx b ;;tk.1 s?

  A bicycle wheel rotatek7 zx5 aj7h:dcc* f8ggs uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed :j*gccgx8ahdz 7fk57 of the wheel?

  A bicycle wheel rotates uni+;s1k ymp6 xrmformly through 2.0 revolutions in 4.0 s. What is the linear speed of kpsymmx+;61r a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of- gcg+5 v+0wf/g79 fbi ojamyd 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no ybgo+ dfjc+ w9 7gg/a5vfi-0mslippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1. xtq386,cjarm 0 m is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the whee,t m3a 6jrcqx8l's rim?

  The cutting cord on a gas-powered we+: e 5nazhm3pdb;o d*eed cutter is 0.16 m in length. If the motor +haoe5b:* d dze3; nmprotates at the rate 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 withlbg ;r:-.og1ik (f vzw a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the ww v.;f1z-bor lig g(k:heel's rim?

  What is the centripetal acceleration of a point on the perimeter of tm,:gxgj9+m p a bicycle wheel of pmg xt,+m:jg9diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space sta(j)fmu .js+,h7 r*ofvknmyw54k) yqy ;ex y4ation (r = 1000 m) rotate to produce an artificial gravity mrfk4 5ja,*jyxhf k yy).)y+ (ws uqoenvm4;7of $9.80 \; m/s^2$?

  A car is negotiating a flat circular caeko.o7y )h-ye ,5 shwurve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) is yo.aho )s,ey5k-7ew h $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m:ws7vm *wjl kpso b:kn(cd+kn5+7pt 1 /s. The maximum nl 5kc( p7op+j*k+n7 w: m1ws:tdsvbk 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 endw5y: i th0k uqw)wzs5; dp5)x y4rf9bw of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if the string is not to breryubtfkidw wqyw;s z x0h))wp 5:5459ak?

  A bowling ball of massfcqd6syd 1yn 8t 1wylgg4+g/vax7u ;- 7.5 kg and radius 9.0 cm rolls without slipping 10 m down a lane ;gy1vga yd/t +ngxf7uw 4lc-86q1 yds 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 constan f+fq wp mx94i-zce,5ft 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 a:qf gyk2 40lit:bpsv /8p/svu ngular 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.9oi (:eapj prtu(aa)1(o-b t4mvfl l automobile tire rotate after starting from rest and accelerating at a constant angular acceleration o)e:t orp ( l.i91f vb(pja4-olam uta(f $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has3k5fd8fmx +7mxw y a*uyuk2; p 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 dk8b621rx:ew v3oa vg ws9pm rv(z)o1recelerates with a constant angular acceleration of:vz 1ko2r sp3 aoxvbwr r)v1e896(wgm $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speedrm5n92f 43nx l qvqj3o of 6.0 rad/s while turning througvq5o3 4 9f32nrln jxqmh 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 h ecm;;x)o3 axxg4r /cm/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to rexx;hg) amce3 4o;/cxr st?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40i nq6 .c leah +,/q c1nsdiz85n,rt-yl m/s to rest over a distance of 115 m. What is thez-enn85qrt/yl slc, c61a inq.i ,d +h angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovssng 3fnr n3y q4v34i2vxzg)2er a distance of 1znxg) 2g3qv34r 3ni2yfs 4nsv 15 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatioj .ucg y-q2y(onal speed of 3600 rev/min. When swit.qy- (guyo2 cjched 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 tighteningzlfmyft .6 dgk*8) qf7 to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular 8 dlfmgqkz*6.yt7 f)fto the wrench?

  The bolts on a car wheelpo 6rt zxp/po .l, dc5lc)*q8y require tightening to a torque of 90 Nm. If a 30 cm long wrel*cop6 ptcqpx5 l dyo) .zr,/8nch 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 inerp- hf*.7 c( rpsb7z4(u mgsx;dgm8wbttia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled9c-b3g 0q2) dar g4 v6hkcdghv as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. Whac c 6d3 9g r0)ghdhbgvk2v4qa-t is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis tt veky z7ie+ afg35q2:vaq6v 7hought the center O. A rope7 yakfvvziag7teeq5+36q v :2 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 pivotet2l47jwo*lkpl(y c. lzvw *n/d about a frictionless axis thought the center O. A rop* koz w /l4njt*(ly c7v.lp2wle 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 inw 4ul+l0mo (:rk -aofkitially held in the horizontal position, and 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 one4r-0o+:uollk m w (akf end is ML2/3.)

  Consider a bicycle wheel to be a ring4j ve oa.vv;,e 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 spee vao4 .v,v;jeed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley om3.qhqnl6yd58wps 1h v/w5 rof mass 7.07 kg and radw5q sh /3rl5h8qmyw1 pdn.v6oius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a friction9:n p;c qol pzz(su06aless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acpz s9pa n6l0(:zoq;cu celeration of the mass?

  A rotating flywheel ca*65 6wu-ohcc9s jnv3+esrpnn n be used to 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 in4p 0h* 3vmrp+it ss8bhe0tra ok70; toertia 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+kofr 2 xgs +x*ovl2t n4l0).joxk gw: rolls without sli*o x)+ o.jlox+t2fw 4vgsknl2 gr:kx0pping 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 m rolls withc/j-*wxdicnn mn( f53 a speed of 10 m/s. How high up an inclined plane can it climb before coming to n-c* 3xncjwnd/5m fi(rest?

  A hoop of radius 0.50 m and a mass of 0.20 j(+ )ee;cik)8i5vjc bf1hr d akg is released from rest and allowed to roll down an inclined plane. How fast is it moving afterv ;ck18 j)j)cebfida5 +ir(e h dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping do* ygu(tr/z pv4wn a 35e incline that is 7.0 m long. Assume it started from rest. The mov/gzu( y*tp r4ment 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 mobfwd2 8*d :dlxmentum 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 momekt 0hwi4+rb:,ygqkl+ nt 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 of3u1gzizrw6lr4,;1e8lfs v qj inertia o4is3 vz1u wlgz,q e86;lrrj1ff
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?