Angular displacement is usually expr0klld;,b8skvrju.bph 2 b8bdr gl+ a1 -t+b (pess in units of

  Angular velocity is expresse/jn p s17cjepu/n w(ru+h6.yf d in units of

  Angular acceleration is expressed in units uge be4m/38svca3 v0irp r q:zl;;snc,ov3x1 of

  A boy and a girl are riding on a merry-go-round which is turning at a cr0ds +kmg* r,ni:qit.onstant rate. The boy is near thmtk r ,sdnr0:*g+. qiie outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turniu(y2iy rf 24kx)/m-.c eyavx. 7vf yfbng at a constant rate. The boy is near the outer ed 7ib -2yy xmxf fuekv.c(.r2fay/4) yvge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding omk*uu.l6h8 v(zw 3s .zgc k9opn a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the ks.v (u9l38 p*kzu.hg ozmcw6center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is tuf2/buutzuu ( 1rning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetalzu u1fbuut (2/ acceleration?

  A boy and a girl are riding a merry-go-round which is turn8xc1ir njm/c *l iao8+ing at a constant rate. The boy is near the o*ca o ir/m1 cjx8n+8iluter edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotat4n cqxty*t 5/mr+0.kx jfw9qoing. Which of the following is an accurate statemtywcft o59 qm x+n4q/.*j 0xrkent?

  Rolling without slipping dependa 5p3x*gb qqp+s on

  Two equal forces are applied to c1cwx9is p-0 p9t3adia door. 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 doors9i p-td1c3w 9 pxia0c. Which force exerts the greater torque?

  Two equal forces are applied t5 (d0q.p zrooso a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to tsqd0.o(5 rp ozhe plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. + xowbl:ec6n /p(us,,9 gf.m8q esayw The first force is t sylew9bo./sefqn,mxp+w,(:8c aug6 wice 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 used to measure an object's resistance to change mbi*u-svg+alfz uzvl-8 ;., ms in rotatil;8.* l,ufmzz igbua v-m +vs-on?

  Consider two uniform solid spheres where both have the same diameter, xambf)r au//9but one has twice the mass of the other. r//ab a9xu )mf The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid sphipl:a ,au:y r**:9wotuaz9ix eres have the same mass, but one has twice the radius of the other. The r:xo yi,pa rw9:t :*zauaui*l9atio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solni8 q p5*d:eheid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to tedi*:neh5qp 8hat of the smaller moment of inertia is

  A uniform solid sphere has mass M and radi7 t-. ;t7k9ij zqrkhlrus R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central tilk q.7-k;j7z 9trrhaxis?

  If a constant net to;8dr f.p -iyzcrque is applied to an object, that object will

  The moment of inertia of a solid cylinder about its a5f0cta 7xh/ ;d7sg z.r pt/gf51oijd sxis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational k .cx50s;7io1fg /t7rd t p/zd5 sjfghainetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel* ,) wrvhs)-xppr2+juzlpu*8o uam9t ybp0s7 of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of t *h wo,pz)slat upjys0 7-*)pvb9 +xu2r8pu mrhe wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and ryauyuuj -8 .muie2:bi+ f x8g6vfc68r adius R rolls without slipping down an inclined plane starting from rest. The linear velocbgivmu8fa:.+uj6i2 -y 8u f 6eucr 8yxity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radiusn+9jt2m- jss a R rolls without slipping down an inc9sn+ mas2tj- jlined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of pvw e sm-;:4xrcarticles changes when a net external forv;x-r: swmec 4ce acts on the system." This statement is

  In what circumstances can the angular veloci:5vv * )rdwkicjf ((hcty of system of particles change without any change v c(ijv() d*5 :frhwckin the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which8 n;okf nc. k9e;oysjcbh/1j * may be present. What happk yc/;oj*jo nfc1bsn.hke;98ens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. fundb*50 -fvzqtfxi5w8h j -, As the Earth moves close to the 5 bit8fz*qnu dhv5x-fj,-fw 0Sun, 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 hv03jy v id9g(rso j bw)a,hk6x6lr:2 fis outstretched arms close to his body. What happens to his angular momentum about the axis of rotati j2bv9idswjlvf rh (,0r3ay)6 k:xg o6on?

  An ice skater performs a piroggg 6 4f 1f4txd52wl5we+shcuuette (a fast spin) by pulling in his outstretched arms close to his body. What happens to15 lf46sch 5 ggxet2fw+dguw4 his rotational kinetic energy about the axis of rotation?

  An ice skater perfor9an67e 78 vlba;nh,mic5vf,b f nxsv+ms a pirouette (a fast spin) by pulling in his outstretched arms close to his bih9s57 6,nb +n7cl ;xe bv,fvafvma n8ody. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of p4d; h.*d bqthh+pvvj*zm9 +n angular momentum.

  What arc length does .j nsgmj rlvs49+ tk.r pz/1v*the Earth travel in a three month period in its nearly circular orbit about the Sunk.vjms+9/vrsg ljn tp.z1 *r4 with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distu 6( *:1gpqx( ti)r( fot5dt-tqa qcnhance does the tip of the seconu tni(q (1xa) pgt6 (q5t:*rot-hcd fqd hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalksbwy*t( ; +*6eo xn kd*eaf9hent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wip y*ioi,nf+6-5irxug9af:f hat is the frequency of the whe9:rxifyi+ ,nf fg*iou aip65-el's rotation?

  A pulsar (a rotating neutron sta g ffjii;ar.:*r) emits pulses at a frequency of 0.40 kHz. The period of its rotatioiaj*f; g:fri .n is

  A phonograph record rotates at 45 rpm. Through what v+ xm0q w9aqt,de*y 3yangle does it turn in 0.20 s? wqevy0 y,a*93mt+ xdq

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on z/ zrn20ru pr(the outer rn /(u rpzrz02rim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is t /efqxg:uwd +*,fsr 8she average angular speed of the wheel?gfds e,+ ufr*w/xqs:8

  A bicycle wheel rotates uniformly through 8t v mejb;r ,99o:bzee2.0 revolutions in 4.0 s. What is the linear speed z:j 8 btb9eroe,ev;9m of a point 0.10 m from the center of the wheel?

  A cable car at a ski hj 98 :- kwovybo*--e) fnlrrbresort carries skiers a 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 cable ca9b-*n8 ryk- vr jwelo- h:)obfr to make the trip in 12 minutes?

  A wheel of radius 1.0 m isw *xke wg 8e4kl; o+y(ml,/z: .ewr6pj4s lvzk rotating with a constant angular speed of 2.0 rad/s. What is the linear spee s+ k/4;wwlk e zk6*elpog (r8lyex.w,4mzjv:d of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. ;zxpi 83f n+il6 7xugk1pt2fibo6tn+ If the motor rotates at the rate of 20 rev/s, what is the +x6fx8tp 2k1p +;73iiu6niogztln bf approximate linear speed of the end of the cord?

  A wheel of radius 1.0 mi99 qk-ekcwx 0 is rotating with a constant angular speed of 2.0 rad/s. What is the centriqk9-0w k9xcei petal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on0+z- xkvwn4q nd yka 9)vas7l1i-fzo1 the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 7akvkxowfa14 0sy1z zv q-+n)ndl9-i m/s?

  How many revolutions per minute (pi;sz4k,;xo xq p,b;kix z x gzy)3j-+rpm) must a circular, rotating space station (r = 4qbx kix,zjs -,+xk;3yp)zo;i gp ;zx1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m2 k 6tt*g2xkzg with a speed of 20 m/s. The maximum centripetal forckg 2z62g*xt tke (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 dnok(:so:-ai pti 7 l9a speed of 20 m/s. i9kn : (-o7 sal:todip The maximum 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 end of a 0.750-m string, is wd1he1-(we3*hzt op/fif u lc;hirled around in a smooth level table. If the maximum tension that the string can ic1 fpu3h*-/zldw1oh e( te;fwithstand 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 withb)x/yrlw3 7cowgv2 v -out slipping 10 m down acv 2)/wr gvb73- xowyl 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 with a constant m75/ii 3wk4s 0 lh: 4kezzgbfrangular 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 on g-f(3zm 1ojgf $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does af;s0w 5 ny)uxlh7/v ca 0.300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular acceleration au5/v csy)h ;wl7fnx 0of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acja ay;syrle8(),n(om celeration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 ro2ps***. bix qx7lxp;nqfe o+ad/s decelerates with a constant angular accelera qb2xiep *o*7x+fqpsxlo;. *n tion 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 to);nh5mql mx ee(x35*lfm bv 0urning bmeq) ml( ;350v fxm l*o5nhxethrough 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 m/s to rest overzp-mgywhj - 3: a distance of 115 m. What is the total numbe y3wjzh :mg-p-r of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down o5obrryo4fu* yk.jt(-8 ch e*k9dt ;tuniformly from 8.40 m/s to rest over a distance of 1bk-oj9y( ed*;rhkyru .toc f5tt8 *4 o15 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40.dx n-;b (jnxk. 0zfvz5s6sjzuvn j59 m/s to rest over a distance of 115 m. How long does it take for the wheel u9j(0kxbnd5nzv s6xs. z-5f;n .vjjz to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational spea3at;,dpev,p *bae y+ed of 3600 rev/min. When switched off, it rotatee;,+ ebpp* d3,ataavys 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 tightening to/m tj)ya ,grm)xf4j3y a torque of 90 Nm. If a 30 cm long wrench is used, whagr m, 4/ty)jm )3xayjft is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require3p vqszmf56c- m24e rz tightening 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 ape3f4sm- r52 mz zvqcp6plied at $53^{\circ}$ to the wrench?

  A wheel with moment yyy (qn:1a1o p7uta-h nhqi;0 of 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 1 hfg x ,c6 *mjwvnx0szjj :,c(h;hfj-as follows: 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 origin?(jwz j6hfxhm 1csxjcf*,jh0g-; n ,v :

  A solid cylinder of mass938crgxd v(v1;dmsr i 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 angular accelirr svcm1d9x ( g83;dveration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionliv7h;+j; eewj ess 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 ra;+w;jj7ihe vedius R2 = 0.50 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 initially held in the horizhrxw1ohl, 07w ontal 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 enx7wlhrh,1 o0wd is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kze33+yfw; i svyb1h6s g. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangibv3s+ zfsy6e1; y w3hentially to a sprocket of radius 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 a rope wrapped around a frictionless disk paksg ujrkwmf o.p5;(1e( n geh84c3g 5ulley of mass 7.07 kg and radius 66.0 5wgon 8e(ga m k; 3hu4c(gf.kj5p1srecm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangsm/ +d8b)w5v-aq-twtsc*yaxpa -,z br on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accel,pm vbs*-+ydtbrqz a /)w- w8tcaa x5-eration of the mass?

  A rotating flywheel can be used to store energy. If it is required to stog p 7okl.0 o qvdza2szf6: ubfc0(v3l/re $1.00 \times 10^{6} \; J$ 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 ineb4yn nd8mrpvxf18( )w*v 3ch/ /ctrsrrtia 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 fri .(qbly lik ap9do +s)3k(m(kom rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclili)k9m ai+y.(kd(l bops3k q(ned plane?

  A solid sphere of mass 1.0 kg a w;vayp7+wvys q1s c.:nd radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb befvcs.ys apv:71qwwy ; +ore coming to rest?

  A hoop of radius 0.50 m and a mass orv,ahdob1c/ gt (26rv f 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical 2cv1o arv,th(g rdb6/ distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rollo0 ergb a fl1:,vv)wu1s without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphe lea1:wo1 ,f )0uvgrbvre 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 mom w1l7bw-4h y zs*x:vnjentum 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 ghr03 xc5a- gainertia 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 e/sj6igd1yl+c*wc o7pyv. d c 7xtended has a moment of inertia pw*cvi.d jscc g67d+y o1 l/y7of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?