Angular displacement is usually express in un pjftdq1opb2 ch8fw- al5y76,its of

  Angular velocity is expressed in unnr/s-,gsx mm9d 3s u1qits of

  Angular acceleration is expressed in units ..gvbvmy m3-oof

  A boy and a girl are riding on a merry-go-round which is turningbi. zmke*+57h6 elcxz at a constant rate. The boy is near the outer edge, and the girl is closer to the .*ec m6+x 7lzbhek5i zcenter. Who has the greater angular displacement?

  A boy and a girl are riding on a mer .27 yxm3yfbgkry-go-round which is turning at a constant rate. The boy is near ybfgy k .3m72xthe outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-rorr sb/pu ;4ikrdg*.jk9ya )7jund which is turning at a constant rate. The boy is nea74 s./9gradk buj)*prkrjyi ;r the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-rou 7r92vusd:gfknd which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greate:29f k7d rvugsr centripetal acceleration?

  A boy and a girl are riding a merry-go-round which j1/ 53x 7dcqnj gzl9elis turning at a constant rate. The boy is near the outer edge, while the gcjj5glz /3q1lex9n 7dirl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accura 2ek(+jg 4b0we0 snphis w5tr3te sta 0tewin s k35gp2ws0(4 hjer+btement?

  Rolling without slipping depends onkr,0:rgzordnl6 :y g.ik /t*9qpofn 9

  Two equal forces are applied to a door. The first force is applied at the *,m -yksn,h l w5aufd/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 torque? f*l /ndak-w,u5y,sh m

  Two equal forces are applied to a door at the , qpc8;m 5sz)-yyo sbidoorknob. The first force is applied perpendicular to the door; the second force is applied atsipms-y5zy;8cq,) bo 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firutcuq0 ; o,y7fru2 ru1.s vb(jst force is twice as large as the second force. The ratio of the torque of the first to the torque of the second ij0btf;ouy1 ur,72cqrs vu .(us

  What is the quantity used to measure an object's resistance toqx,jg :v3, vio changes in rotati,qvv :xoi ,3gjon?

  Consider two uniform solid spheres where both have the same diameter, bus +rv11he61/zzlr*k a vg0 xnht one has twice the mass of the other. The ratio of the larger moment of inertia to tha v1zhvhr/1kl e g06+ar*snz 1xt of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but ona/ineusu-fg( hp r 6ed0d /)l n96fw0ye has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that o6gar d0sf e)/euldfu/ -hn 0i 6p(nyw9f the smaller sphere is

  Consider two uniform solid spheres where one has tw i* 8i(bbxyfna-8 p ceoi;.bh.ice the mass and twice the diameter of the other. The ratio of the larger moment of *b (ixe fonhbibyi8. p;8- .cainertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M aj. .bxo 19ldwhnd 3R, what happb. 1.j x9wholdens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that objecn pu56i sealc.w4),lbt will

  The moment of inertia of a solid cylinder about its axis is ki 4p vsa0-/5p7 gnw2.sohnn lgiven by 0.5 MR2. If this cylinder rolls without slipping, the ratio of nknahp0-ssnl/v .w 72g o4ip5its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which h8(tzpzc2qlx :nk gs3f3 leo68as 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 energy of the bike? A(nk z2t8zlsl3ep 8x: cq6o3gf ssume the wheels are uniform disks.

  Suppose a solid sphere of mass M d) wbvb3rom* x)/9xdjru9-f g and radius R rolls without slipping down an inclined plane starting fr wrv*d)u b9x-)gmdbfx3o/ j 9rom 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 rolgre,8 so9v8bb. bu v*ils without slipping down an inclined plane starting from rest. Ti 8br9vbsgvuo8 .e, b*he angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles chang5s 3t5fd)b+hzei ee b+es when a net external force acts on the system." This statehb5eb )+ieed5t3f+s zment is

  In what circumstances can the angular velocity of systtx (/ry7+td2 qdszd6p em of particles change without any change in therp/ 6 dzt +72(ddystxq system's angular momentum?

  The Earth orbits the Sun in an n8kjjx-tfmy,*p+bivi v*8/:aro(zz elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum abo*y(fz: ,zvo i*pm8r btjnx+i-/jka8v ut the Sun?

  The Earth moves about the Sun in a69) zjuk vs ovm bh;k0hk:21yrn elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth abou:kv)ubvh1oz0 sj6k 2hk 9mry;t the Sun?

  An ice skater performs6txa g-/c40cmkk i7fh)q*dzj 1v8aio a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What hap6zh 1co4q dai kk78 *m)-fi0x/g ajvctpens to his angular momentum about the axis of rotation?

  An ice skater performs a pirou*ftoj/ .4 zjf62oriafpr30 glette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy abr0tff3ajlz*ojg o 4/.62 i pfrout the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling )frl yi4n*u.+lw:tqa * 9mb jvin his outstretched arms close to his body. What happens to his*: mrllju+i4.9v*wa byt)f qn moment of inertia about the axis of rotation?

State the law of conservation of anga 7hbm8 bd -0q d/v9d0odo1pmf/93 nzpp:uaq wular momentum.

  What arc length does the Earth travel in a three 8bz-bxaq+ i yfnbs;.() .dmzq month period in its nearly circular orbit about the Su -.q)+bziz b dn.b8; (mfsyqxan with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a leng , +zmp cn5maw+h0dg1k4azvc0th of 0.30 m. What distance does the tip of the second hand sweep through in 3 aa00p c4v,mz ndc5h +1wgm+ zkminutes and 45 seconds?

  How many rad/s is 25 revolutions per mi/ (t5 dylzz-tvm3b*cld+, y 23fd zpzynute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutionj0dch )am2ob 42wkt9q s in 4.0 s. What is the frahtwm jc2 o2dqk94) b0equency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency oft)6g s+euv2u)p 9oz cbpo1mr* 0.40 kHz. The period of its tcpm bup2*r u) o1 )z6+9seogvrotation is

  A phonograph record rotates at 45 rpm. Through wnl 3)o-lajh 7dhat angle does it turn in 0.20 s)ljh lnad7-3 o?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the azj(z08h7 (pum2j c5g3 jkjguouter rzha j(j2 gj u(50c 3mgpu87jkzim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.5* *5zxezvjbs 0 revolutions in 4.0 s. What is the average angularxe zsvjz*55* b speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wh p6;ly+i;iw:0z(pew dt9fqzl6/ ayt cat is the linear speed of a point 0.10 m fromp6;if i w+y:/z(0atlty 9ldq6 wpecz; the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Thx e*dxq m1+cb:e cable which moves the car is driven bym* x xdeqc+:b1 a pulley with diameter 3.0 m. Assuming 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 sitq1b m74f iz*ln8 u*rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point o *b*74tu isi 81mnlzqfn the wheel's rim?

  The cutting cord on a gas-powered wee hy z,6q+oc*ued cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of thy*6z+euo,h cqe end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speeon )ubmpl .ztsvhaeb2 ) vfbz-kme7d/;), t: ,d of 2.0 rad/s. What is the centripetal accelerattoz/e))k2 vmbp e hab svb,)zum.7,fl n;d t-:ion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of vat6:vsk8r.ou)- ma;whf ,wd a bicycle wheel of diameteof8w-h)6;wd . vartkam su:v,r 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) mushp 9coril 1yx.4 )q;:s9 9muaxtxve; nfes6m .t a circular, rotating space station (r = 1000 m9xv6:) umlrc o s qm9.x1xn se;;if4htpaey. 9) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/s;,r8budjgj/ )a d ,8 xxzm+ ogda;*ecs. The maximum centripetal force (provided by static frictionc +gd),8gb8zjdm;eaas,ju r;d*ox/ x) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat cit x)t) kw:ot1 uw:9uppa q6nj((3hf rmrcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (prowu9 ::jp aqx 3)wh)(n1up ( k6otftrtmvided 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 whipkl vy+ zdoq5;qj4u3 (jjsb*:rled around in a smooth level table. If the maximum tension that the string can withstand is 2ys u4lpkqo(j5; z*jdq :3bjv+ 50 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 witsn-cqc3ne+j( hout slipping 10 m down a 3( ncqcj ens-+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 conswne+j5x eu8a0 tant 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 constahdrzpg6x*6i3j xh n 39nt angular 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 radxj eclkg 22yy6dkx5,; ius automobile tire rotate after starting from rest and accelerating at a constant angular accelerationjy5 ,d2klxekxyg 2;6c of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratiul k1*kse )subw en4)( .bh 8giizsn-2on 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 g.jk8) guwzj,6egc 3mmd mo48 a constant angular acceleration of,m6zm.g ugj8wm83o 4ekgc)dj $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches a c7xvxfqxn9k 8u v)nk*+3+t kln angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the afkxuv)7+k93xkn *c ln qxt+ 8vverage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows dow fjvo8mfv;qj,5*qqj 5 n uniformly from 8.40 m/s to rest over a distancmj5, v*vofq f5jqjq8; e 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 mgzw:x*bbxq i6ozt9 (1/s to rest over a distance of 115 m. What is the angular 6ogbz1q*tx( bxw9zi: acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovez5 g4 zn*0jbjbr a distance of 115 m. How long does it take for the wheel to come to the stozjbn05j4b zg* p?

  A centrifuge in a medical l6n2abfu5( 6irr vuxg3h/ey*k aboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accelerau(u h6a3 ebkr2/6*fvrn5gi xytion 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 a torque of 90h+ kv8fr5*h5/xojbo h Nm. If a 30 cm long wrench is used, what is the magnitude of the force required w5hrxj h8fo+v/o bkh*5 hen the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cz-x,q t -evng)tk2.jz m long wrench is used, what is the magnitude of thz zt -e g2tqj.vkx,n)-e force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia;.q1b *k gum n2/uoxsj $3.00 \; kgm^{2}$ 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 originvlt5;dok r 8r5l.irv 8, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the l o k .8;ir8rl5vvr5tdmoment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivotedbhjk(xqgh /f-vy .j51 about a frictionless axis thought the center O. A rope wrapped around the outer radius R1jjhf1vyb k. (qgh x/5- = 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 acceleration of the cylinder?

  A solid cylinder of mass 10 kg i6evdubrjm *h.iwc h /2ewos4z6 , i:5ss 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. How many radians does the cylinder rotate through in the first 5.0 seconds, if it rw62d j*c iozisw.hsb64e/ e:,5m vuhstarts from rest?

  A 4.00-m long rod is hinged at one ewizm6w n /hod:bp4c50 nd. The rod is initially held in the horizontal position, and then released 6mbnw5p4oz: whi 0 /dcas 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 end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mq3owz7w kb3mxrr;/ j9 ass 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 rk3z9qb jm/; 3o7xrwwthe wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of 0 s qfy5c.e0zfho;* nw dwt7a9mass 7.07 kg and n oh59zfe*d 7c s;.0w qaf0wytradius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley ofusmw * 6szxv,9 mass 7.07 kg and xm,wvu 69 s*zsradius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is req 9loqsr8nzo6; uired 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 in at )n8wnh. sr7d7;ewlertia 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 star de6.mg.j(y gqts from 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 th.(e .qdymj6gg e inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m r fsc,h guodv2 -:35vv.s mpom)olls with a speed of 10 m/s. How high up an inclined plane can g.s)u 53dpvco,v-hofv :mms2 it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released frl0o87q24i+s4vmcu)ek fyi f l om rest and allowed to roll doolkfl470c2+ 8i ymvu)i4sfq e wn 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 without sli1sqz+4y tm9knpping down a 35e incline tham 14qys k9z+tnt is 7.0 m long. Assume 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 changes by v s.28)5mjs he h*qcacv5nm4e$20 \; kgm^{2}/s$ 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 inert mtwz;cuc4ih8b3w5h , ia 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( b mj8ip/k atf0vr+c. of inertia ofmkfc 0./8tap+jrib(v
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?