Angular displacement is usualqo4-r) 4c) jsdae hk3yly express in units of

  Angular velocity is expre9ve1;h zb/ cumssed in units of

  Angular acceleration9z1s+chq q/,9qui -w7lc ng6: eihlvt is expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at734 nq+7 n-bewpn)fleai-7(iu fnhwf a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular dl) ne7(iw n+ - iefq-fbnhw7a7p43un fisplacement?

  A boy and a girl are riding on a merry-go-round which is tu*c6butv:122:kr.cstdhf-v mlg9y xu rning at a constant rate. The boy is near the outer edge, and tg2 .dhbc:u6 rk*cttx21vl-fmu: y v9she girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-y5zzgvp p6; jl*(+qjf 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 + zj;vlq*pzgp5j f(6y greater linear speed?

  A boy and a girl are riding a merry3p9j0q*ormv4 x j,nfr -go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is clos4x rvp 9j qf*rn03,ojmer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round lutyw/ h1)aka5 psn(doplm l 19 (w7r2which is turning at a constant rate. The boy is pp uhlrt 1l)5a l7((sk2ww9o /1my dannear 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 accur k:,nv4lmp ,6tii ktko2;h/nx ate statemnv;,ikk/l6 2tk tx,pho4: niment?

  Rolling without slippifod*7b .3ls m9lj jk)png depends on

  Two equal forces are applied to a door. The first force biv 8t5dlj.;; e:j*sbrsuj7fxb 7dph.7ce- k is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpen.;b i 7l.j*5c7setx -8djp vbrk:b;s 7fdjuehdicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorkry 9wf/ a.ub)fnob. 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 great.f/9) rfaw yuber torque?

  Two forces are applied to a do+4k7a;6g8dr.5 pverq bcbq b zorknob, perpendicular to the door. The first force is b6q. z5vq 87dk4c rbe+rpba;gtwice as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity usedvc: xga9ukxqz(s7 v+w; :iru/.9dccz to measure an object's resistance to changes in rotation?+a9 zwcd(:.ccius 7 uvrgzx; kvq/x9 :

  Consider two uniform solid spheres where both have the same diameter, but on2 gxx :3+lcvf;bka *mhe has twice the mass of the other. The ratio of the larger moment of inertia to thak vfmx2a cbx+*l;:3hgt of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice o ,67gge3n0b3 fo6ib ybtzjx3the radius of the other. The ratio of the larger sphere's moment of inertiabg f 76363o bb0tnzix,j ge3oy to that of the smaller sphere is

  Consider two uniform solid sphere89*8to7grxx ij3yiwp vj.ks -s where one has twice the mass and twice the diameter of the other. The ratio of the lar.y-jjr *g37xitxwo kvp9i s88ger 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 to0 o h4e y6f4uu me-q.o5mn1eew 2M and 3R, what happens twmeh54ou01e -4yq eoenf.m6uo the sphere's moment of inertia about a central axis?

  If a constant net torqu k:, -hzy.,exho3/xiwuzs sy:e is applied to an object, that object will

  The moment of inertia of a solid cylbfgo(d:b8+eathh )z (b 8f6ay inder about its axis is given by 0.5 MR2. If this cylinder rollb+ h6bzfaa8g hy (f)td8o eb:(s without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of masee lol-nbleb/ j(tj h5,5+u)r s 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What uh, lltebb-5oejr(en j)l +5/ 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 disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down an inckvw**:q kdxv3.gwd r3 qv*g*xk3rw . v3ddw:klined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippi) 6cturibk 6ou 8/+sblng down an inclined plane starting from rest. The angular velocity of the sphe8 kiloc s+)/r6ub6utbre at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net externaz n;52 ko7xw 9jhw+ceyl force acts on tho2hc;+ezwn9 xj 7k5wye system." This statement is

  In what circumstances can the angular velocity of syst x3r5d ,ghtkn)rpkkk .i8/m,5.zmlwt em of particles change without any change in the systrmwk,kp/.k )5km ,l dtz5it.8nx hg3 rem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which maa hq ((e1;78fksutvu yf 92ikey be present.s 2u e9;ff1ekvhtua(q(y78 k i What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in anbp blnk6 +-d(rh *f/qu elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about t *dfpn6+rkh(-b ql b/uhe Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hi/ ( ;znmmlx)pl.dmrm2 s outstretched arms close to his body. What happens to hi;d )p2.n (lmx/zlrmmms angular momentum about the axis of rotation?

  An ice skater performs a pirouetux.p cqe0 +3qlx+tc2t te (a fast spin) by pulling in his outstretched armsq2t lp0+3t . u+cqexxc close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a x)(e7xcc; os mfast spin) by pulling in his outstretched arms close to hic (7;)emsx cxos body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation,5fawy5* wjn ,rq)d(w /hf+*j pqryhy of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly c. o ehs;bzyrs6j;)7s 1akc4fv ircular orbit aboutj r7sshf;k.yza c6;o1 ev4s)b the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. 4y hbn 2 dng-f:jm-.(opa3cwf What distance does the tip of the second handd b-hn(y w2 mjcfp3g.-4no f:a sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 rev, l.y8 -xani1w8q pi,xfqp25 t2fq wiholutions per minute equivalent to?

  A bicycle wheel rotates uniformlj;m(7xaa;mke, fa rvk 8dvk:b*k,dp2 y through 2.0 revolutions in 4.0 s. What is the frequencadr;a km*;m8k bxvk ek:v da( 2,p7jf,y of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses b4 wxd2l y(7daat a frequency of 0.40 kHz. The period of its 4bd7 2x awl(ydrotation is

  A phonograph record rotates at 45 rpm. Through what angle does it tui ai+fxc4+b-t(w kuq (2z3a loi4vo0rrn in 0.20 arl4uiv02w iabxc4q3f(k-oz o t (+i+s?

  A wheel of diameter 26 cm t7* h,uo :iyirpurns at 1500 rpm. How far will a point on the outer rim move i* yrip: uh7oi,n 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is4 hb :s57a6yxk 7hmj-blcw )bs the average angular jywa7hs xb)ks7cb -: 5mbl4h6 speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What *qw4k*jlu+ zi-wkk djo. .2jkis the linear speed2wk k4 *koizw .u*qjk.j -l+dj 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 cable wt;u vt6kzumv3 19j,*p.tp qz yhich moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make3ut,z qz pu p9tmk*v6;j.v1 ty the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad),uwx ,/vk5hfhnw i: o/s. What is the linear speed o,iv:w uknoh/5 ,hwx f)f a point on the wheel's rim?

  The cutting cord on a gas-p6xb.m)1 yunnt owered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate line.xmt) b6y nn1uar speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s. se0/q4vf4mnau:q 6 e.m xg2on What is the centripetal acceleration of a point on the whee fux.vn26mgq /s:4oa4nqme0 el's rim?

  What is the centripetal acceleration of a point on the perimet n76i5fp(wivfer of a bicycle wheel of diameter 70.0 cm when the fw6 f7 vipni5(bike is moving 8.00 m/s?

  How many revolutions per0 )czpkm(2embb,li,(n /qfc y minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity oypmiknb), (,me/ 2cz0 (cqfblf $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius.*b he-jr-itqq a;up7 50 m with a speed of 20 m/s. The maximum centripetal a bp-uqij7qe - .r;ht*force (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 sqgho(pprnvk f4( 68f s/m/,zzpeed of 20 m/s. The maximum centripetal force (provided by static friction) is gps(n4 h/ p/zm8ko6f,r (vzfq$1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to therhkhbc 74.:up-/rwo x end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can bok.r:7hx/ pwchru- 4withstand 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 radius 9.0 cm rolls without sli - g 9isa: efh0u+yovhr3hfo7qe:j.2npping 10 m down a lane at 4.3 m/s.qif-e:ogo3.0 hv: +yu 9fa hnh2s7rje
(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 a 9x ,um3y,eieongular 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 angular2:kukx;eilkr l x3 do*u n6y3, 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 automobile tire roxe6hm0rmne 6; kaa 29wtate after starting from ea6r h 0296me k;nmxawrest 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 ncy)i psau/7k06aay3celeration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerate xywhj-k) n2bk) 9zbe(s with a constant angular accelera2nxwh j -y( )bke)b9kztion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angula)isd g, z:lj1bho1wf*r speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular awb* z s)ljh,1 od1fi:gcceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformlv 0 iem*y45wr9n1hca zy from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotate 1ha59mz0vr4i *wnyces in coming to rest?

  A wheel of diameter of 68.0 cm slowgk9/ 0i4vl nods down uniformly from 8.40 m/s to rest over a distance of 115 m. What ilo /9d 0gk4ivns the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unifi7rz*c2w+g pb ormly from 8.40 m/s to rest over a distance of 115 m. How long does it wcz+ 27ig*rpb take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3 8r/hbt1h5zcpqz a 2*8.sla+iggqmw4600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration befora8s 8/hgpi1gzaq 4+ hr2 *.ltcmbqzw5e 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 * nb+ pwie4*wpNm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is pe b*4*epwipn w+rpendicular to the wrench?

  The bolts on a car wheel require tighteng24hy/ q+v79qfxwi fn ing to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the f fqv4ygiq n/w7 +h9f2xorce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia7 ttxsr1sm3a1 $3.00 \; kgm^{2}$ 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 acruvj*)f s f4+t the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the+r4 vfsu*f)cj moment of inertia about the origin?

  A solid cylinder of masd3o:jy: dwzq/zp2c4b s 10 kg is pivoted about a frictionless 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 angu zpw q4/:dj:cyd32ob zlar acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a freg b520x ihcw/c0ng)-gorj h)y )3bh(pqj-xnictionless 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. How many radians does the cylinder rotate through in the firsr0n 0 )b -j-g))bhwgo3x5g/ n c q(xphyejhi2ct 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initiallyqdwq3d/e ) uv0 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 mom edvdqqwu )30/ent of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel tojlhgl40s pk4pcc ( 0b2 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 radius 4.0 cm for 4.1 s, whatp l 4 bg20s4c0jpcl(hk linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a ro(9l 6q ym0+ojmqzw6bg pe wrapped around a frictionless disk pulley of mass 7.07 kg and rad ojz(qym96g +q0wbl6 mius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aro u9d-+zuao i:ewn (2tcund a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whata+twu di cu:zeon(- 92 is the acceleration of the mass?

  A rotating flywheel can be used to store energ5(5bvi2kj.o0rlwe i j: r-oc)+csrpdm: ,uzty. 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 inertia og t a0 )xo h5xgc7o/qt j+by.qj:d4dy(f $5.00 \; kgm^{2}$ 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 radiay,i2fy. g54h (mx;me;n )um/wrg xs qus 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclinexy; hrwfqg;x)n,(sgeu/aym.m24 5m i d 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 l514sh0ybw a hl,uc 5r0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb5wch4y51 srl, al0hub before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rqpll8 n,fnhd8 .tv-r1qb0 9 ex1oqu(d est and allowed to roll down anf8eqq, br duhlqo n8.1xt0 nvlp (d-91 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 without slipping down* rc4q j5;lbjy a 35e incline that is 7.0 m long. Assume it started from rest.qyjj l5r* ;4bc 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 c 8xu++ *4wp :o4.fxbblnbkpvahanges 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 momentx d5q;81y2rec 8 ospts 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 exte kq)n5xek9.zhnded has a moment of inerti)x.nhezk 95kq a 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?