Angular displacement is usually r,c7)uut5r, / c/dxbdh he:bjexpress in units of

  Angular velocity is expressed i7ube-. k)mnzdla3dy1 n units of

  Angular acceleration is expresslwrejbtc8a/8/sep: bid vce 6,+ n7/ zed in units of

  A boy and a girl are riding on a merry-go-round loto9i2t3z* l)khbo5which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who hlbo2 ztl3 o*9ki5)oth as the greater angular displacement?

  A boy and a girl are riding on a merry-go-round whicho+s,; /3 j*dq3 jb9eunhv2ipmmz4 obl is turning at a constant rate. The boy is near the outer edge, and the girl onqm*+i29vsz jbe4/,pmj3 bh3;ou l d 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 *55zl37d zl hai)syvzturning at a constant rate. The boy is near the outer edge, and theiya)7zv *hz zs5ldl35 girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a mymb;az exr)p )+5lai6 erry-go-round which is turning at a constant rate. The boy is near the outer edge, while the p;)yxm5a la)ze6r+bi girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-rounxu c i 1;xmx99ml+:iwod which is turning at a constant rate. The boy is near the outer edge, while th 1:cxlxwi9 xmu9om;i+e girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is ro/ v4mno0ra )grhg+s* stating. Which of the following is an accurate statem/gmaso r+vnh *0 4r)sgent?

  Rolling without slipping depends; 20.*gto b9hipn ofns on

  Two equal forces are applied ttzap17 n+8nzr :aps8 yo a door. The first force is applied at the midpoint of the door; the second force is applied at the doyna81:z sp+rap8z7t norknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a (r+ynqe,w v/x door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater trvqew+x,/y n( orque?

  Two forces are applied to a doorknob, perpendicul;c2dtocr )( agar 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 t;()rgdt ac c2ohe second is

  What is the quantity used to measure ag:hq uc.r- m m;ut.b5zyz mh/7n object's resistance to changes in rotationych.r7;t .guu mh b-/mz5qm:z?

  Consider two uniform solid spheres where both have the same diq j/kcq1ys i+/az*;n*cm jl2f, cayh5ameter, but one hasa*s 1+2jz*/ia fc ;hmqqkny5l/ cjcy, twice the mass 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 t pv+zz1lx wi(0he other. The ratio of the larger sphere's moment of inerlw+xz0i( pz1v tia to that of the smaller sphere is

  Consider two uniform solid spheres wha. xf * pz* 6(tv.l,q4agvjxljere one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the l qjl p4f.aj xt6zvx(*v,a g*.smaller moment of inertia is

  A uniform solid sphere has mas2m -cy1m0yijky pt-od1 6zh k9s M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a centot9h- yyp -zj06 ck 1mdim12kyral axis?

  If a constant net tov.djc 30d oen,3,+ 5gdxk apxmz8u/8f lbz/k krque is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. Ijudj / ifnt -d(/00lzxf tn(-0 uzj fjld0dx// tihis cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, ony3vf 5v+g /zzn .s6b2:kqnny:zrts: ke wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kineti y/vqr zg 2:6n.k: s:5syvt+n k3nbzzfc 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 slr frl6y q)n(2eipping down an inclinylr( 62rqf)ened plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphe z4xs 84gb6.wa/r dcrure of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the /4arczw8ub. r6xsd 4g incline depends on

  "The total angular momentum of a system of particles changes when a net externxqcm9 + w0y at e;fto+24clhc)al force acts on the sys+ f0 9qtlw)ot;ecmx4ch2ay+ ctem." This statement is

  In what circumstances can thlbji(u qfrb dt) 3h650 .7vvsju40nxre angular velocity of system of particles change without any change in the system's angular m b.vvs3r50(njq hul7di4uxb j ) 0rt6fomentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction(y,oo y 1h)hyocg 2b/m which may be present. What happens over time to the E o2hy g(/) b1y,ycmhooarth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptjqx bpcf-5 4z asg;r 60ih+5fxical orbit. As the Earth moves close to the Sun, then which of the following best descr6fzbxh5fj-r;0xi +4g 5sqcp aibes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche0t.4f.uekym9s c yl 7*l2yyhjd arms close 7.h09sk.y c*m yftyl2ul j4ey to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in (3k.v3t ikn38ie:qepq2yp (1:tk2zusvb voj his outstretched arms close to his body. What happens to his rotational kinetic energy kk2:n zii 3j3pe:83. vt(keq qs2(t1v uoy pvbabout the axis of rotation?

  An ice skater performs a pirouette (a fast snys o r57*fauo-xa9k 4efn ./wpin) by pulling in his outstretched arms close to his body. What h9ea nf5yro ok*nw7s/4 -f. axuappens to his moment of inertia about the axis of rotation?

State the law of conservats wl8:2b dx -7zie8nzmbhx66i ion of angular momentum.

  What arc length does the Earth travo ;ry:d3s 2gdoel in a three month period in its nearly circular orbit about the; 2oyor3sgd:d Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What 3/r jj+)6ofjnm p)kvqgfn7hv8+ vy /adistance does the tip of the second hand sweep through in 3 minutes and 45 sec+gn 6j/y)7vn/prqf3okf)+ vvhj8 mjaonds?

  How many rad/s is 25 revolutions l z0l:yw4tga; per minute equivalent to?

  A bicycle wheel rotates u ouuc3jkj6 ,b/niformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel'co, kb6jj/ 3uus rotation?

  A pulsar (a rotating neutron star) emits puz bwuk7j +s3z8lses at a frequency of 0.40 kHz. The period of its rotation i8b+zsj w73kuzs

  A phonograph record rnj;y0d3)3 qzn/afvdf8 m p6 xcotates at 45 rpm. Through what angle does it turn in 0.20 s) va/yxq3cmpz8f jf0;3d nd6n?

  A wheel of diameter 26 cm tur9:dozcem +d -eb6v(mp ns at 1500 rpm. How far will a point on the outer rim move in 2.o mcd9evz(:b- dm+6ep 1 s?

  A bicycle wheel rotat:j/ nr ys+fl6zl8)9dli (x nites uniformly through 2.0 revolutions in 4.0 s. What is the average angular speed ol(nd ry)s/9ljit fi:+n86lz xf the wheel?

  A bicycle wheel rotates uniformly through 2.0 revown43,velngw 4ofk 0k+xhq+*, dv+l jqlutions in 4.0 s. What is the linear speed of a point 0.10 m frwxnjng*3vwv4q, 4lo+ 0q+hke+lk, d fom the center of the wheel?

  A cable car at a ski resort carries skiers )ides-p8y3+rdlo ) so a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Ass)s odp-r3)o eldysi8+uming 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 rotatho(k*f( )ietx0.:un+*xdz l k r2sa aig 1jwy+ing with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the w(nyd.o2)a(fj:rixs az+0e1tku l *xw*i+ khgheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. -9gab5hq,91wpoaw f h sb0g7iIf the motor rotates at the rate of 20 re09g ip7 1-g hbsahw9 ,ofq5abwv/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 0 b(dfkwq13lt c+n kn1speed of 2.0 rad/s. What is the centripetal acceleration w0n3bk1d( k1c+ltfqnof a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter*56e 5c8w ipwily.v dr of a bicycle wheel of diameter 70.0 cm when the bike is movi 5d5w6. 8cpiwrv*l yeing 8.00 m/s?

  How many revolutions qz1rd;*e/ht :q vel b;per minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity: de zevtqr/1l*qb;h; of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve od g (jv*hjrvivb+,v):f radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictior,jd*v + vvgv( j)b:hin) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curvesux )dl5h8p0b of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictiond )b0p 5s8uhlx) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached 7lp fhps0lekuh:)h73to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximu7ps):u0l7hh 3ke phfl m tension that the string 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 masdevqcdk bx;5z* qt)h6x +(4hls 7.5 kg and radius 9.0 cm rolls without slipping 10 m down 56;lexdk4x(ht zb+ qc)h *vq da lane 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 wite.dj3s* z 6vsih 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 acceleration ;(sh /nvgmsd,g3pi 3jkl , y *:ylusp5of $4.5 rad/s^2$. 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 rotate7edj5b ony;aq 10z;kq after starting from ae5 ;01b 7jzdok ;qynqrest 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 angular ac-3sygg; u 3qt8ryzlm :cy6 4roceleration 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 constan,jh 5o9jj 9ep 8 f5ob+3nemblot angular acceleratio5j8o b,ejn 3pome95ohjb+9lf n 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 turning klso h+7oyea8cv7 0n5 (fttud1jru5) through 2.0 revolutions. What is the av ordc t5 0ltj(u1 v7uyk)ae ns8f75+hoerage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s y67;y s2sf-3boehpozto rest over a distao3bs so;h7 6yf -ey2zpnce of 115 m. What is the 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/s8bh5agxes/ 3)qxg b9z to rest over a distance of 115 m. What is the angulaqb se)9h3g xa5/8 zgbxr acceleration?

  A wheel of diameter of 68.0 cm slows7dvtp)e mx)/ jv zg(h7 down uniformly from 8.40 m/s to rest over a distance of 115 m. How lon7) )t/x(de hmvg 7pvjzg does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a roti uq(vuo4e u2wu. ;vgqaqq(i8xc 62a(ational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant auqvw6q(uuu2( o iq (q; gce8iaax42.vngular 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 tirsy +isxid18) ghtening 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 i1 8r isds)+yxis perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque .sj4 .xcv+wjhof 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forcv4wxhs+. jj.ce applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofziiq 8d1d rchc 4/4zq jt,jap:(lrr+; 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: mass minay6 c2p 3sc j1g6dp, is at the origin, mass 2m is at,613dpcas gynjc 26 ip x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought t wqmxx1);a2lyh 7xo v9he center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the righ27;o1yvxx w )l9 xqahmt. 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 of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis 1rms) 3ytntc*y76g jethought 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 = mery *j37 1)gytcs6nt0.50 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. The rod is nk)l*)0eg :copc+jq p initially 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 one)j:p pc *gk)0lecq on+ end is ML2/3.)

  Consider a bicycle weh ;j9j;r8g6- a( 1ybosw. vgujf)bh sheel to be a ring 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 radi; wusjjfoahg1ye 6b.rb8 gs;9)v- ( hjus 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 on b 6cmo2htbl8/a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whatl 8/mcbt6b2 ho is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlessmem6lzjnz(/ 1 , i ,mo**7arrd ip3fcv disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of (3a e nm/dm*6ifmlcv7oj p,r*,r1zzi the mass?

  A rotating flywheel can be used to sto8 ovdyhpu).vf,b8dlb *a w i6:re 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 inertiu,d2l pif*s)clp7vmup y: m /6a 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 /,pb /wqnlii) 7zulrsnpd5 7iz2v a,/starts from rest and rolls without slipping dowppl l,/2i nzd7 sb 5q7nzawviur), i//n 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 with a sp)xt3./ozkgpy,n :w.q rx .bwr eed of 10 m/s. How high up an inclined plane can it climb before coming to res tr. ,.xn)pz.ow:bwg /rx3kyqt?

  A hoop of radius 0.50 m and a mass w,) scvjoi3; tof 0.20 kg is released from rest and allowed to cv t)so;iw j3,roll down an 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 15 cm rolls i)0pk6na8k o7ql*qqo grz 1c5without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphereikla 6cr5pq0 8 kno 1)gz7*oqq 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 my qjzezw5;;l2 omentum 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 ineregs p75 7(m ecbxh(,xdxkn j5/tia 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 3wepsuo ilr,m 8) j,vu-afk5,c7 t4njhas a moment of inertia e, jc j73u ,r)pias8, f45nklmwto -vuof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?