Angular displacement is usually expgr.8 r2 5aopaew)gr *uress in units of

  Angular velocity is expressed in units f/)88s muy fmoof

  Angular acceleration is e3s .pux ;l)hhs* at.sti; rth6-sm 3epxpressed in units of

  A boy and a girl are riding onlsk :*lo o(+s)2paho f a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is close 2sol) ofha+l*p:sk(or to the center. Who has the greater angular displacement?

  A boy and a girl are r95,uq6)x cq8il7wjl l(h pe xsiding on a merry-go-round which is turning at a constant rate. Th(ehqqswju6cl xxl 5ip,l97) 8e boy is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are .ebh c;12 ;qr5hg;m q307wttew pwjq ariding on a merry-go-round which is turning at a constant rate. The boy is near the outw0q;7thta5ceqw2 h;b3r mp q.w;1jg eer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding s87y1yrwa ,wua merry-go-round which is turning at a constant rate. The boy is near the outer edge, 87ywrs,auw1y while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are rt;-qi*x4t1by; rq f dpiding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Whoti pf;q*q4-; txbr1d y has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following eh(xeo5 b qt9fk)mg; +is an accurate statemen5o e+mg b(hkxtef9)q;t?

  Rolling without slipping ++ 9kjr.eg,zl, qt 9ud0g tu(g1 vnhmldepends on

  Two equal forces are applied to a door. The first force is applied at thekv0,)7 zsxay+ s5kful midpoint of the door; thz0f,v7kay u s5s+xl)ke second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is ct.6jciqpw68qi-b :s applied perpendicular to the door; the second force is a :tc ib6ij8pwc.6qsq -pplied at 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 first for,wa*f7 n-lvejx x, z 6dq;bl,yce is twice as large as the second force. The ratio of the torque of the first to the torque of tv w 7a-qb*dl,xfyej ,xz;6,n lhe second is

  What is the quantity used to measure an object's resistance to changes in rotatho;;9d; mj dqn nnt ,k)45gabyioy)n daht;o9j5,4k;gbndn mq; n?

  Consider two uniform solid sphereihb,j4 p)0 edcs where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertip)idh 4,e 0cbja to that of the smaller moment of inertia is

  Two uniform solid spheres have the sjq+xuk0 yb.c 9ame mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the sb c.j9 yk0x+uqmaller sphere is

  Consider two uniform solid spher+0qz+ v f*johfq9cp i)es where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller momen0zq* )jf+f 9qhp iv+oct of inertia is

  A uniform solid sphere has mass M and radiuq cxd5 pjvv,;.s R. If these are increased to 2M and 35 cvdj; p.xqv,R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque 1seo-mw- ,ntvjk jq ;2is applied to an object, that object will

  The moment of inertia of a solid cylif o3;duh-w.bhijr +,v m/j8d;qx6dq knder 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 mass 150 kg, x enq:v (cy0z pjj(w e2xx6c03j0ov rokil5 .,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:,e x yjw 30 jvj05x zpx o6le(0nr(kiq2cco.v 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 withou,hj1*r j1jj zqt slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottomjjrh1j q,jz*1 of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withoutqx9kpav4f,56oa -ty n- s+)cz6e ohlc slipping down an inclined plane starting from rest. The angular6)9ocyfl hatp6 s--,qocx+ e4nkza5v velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles chang hu n6vu6p wrvqpo8h4 d,moyj.;q.(9xes when a net external force act64.q r, .uqv8jpydwm6 o ;p(xu9hh novs on the system." This statement is

  In what circumstances can the angular ve bi. lj2-+eiw -kd+gwflocity of system of particles change without any change in the system's anguglfki- + .eb-i+w2wjd lar momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whzn1t:uh3llc m)lb-ms3: mn9k9ifj; tich may be prese znj lclnu9 mmis9)f1m;3hl:t3- :kbtnt. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movespbgldi 0)(sj ai 6u mh.,kn1,v close to the Sun, then which of the following best describes the orbiting speedn, ) khbd0,av (i iljmsgp61.u of the Earth about the Sun?

  An ice skater performs a piroutnmz9 6 -rh ce30dmm0nette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular morzc6hm e mn3-0n d90tmmentum about the axis of rotation?

  An ice skater perfork7cxlp 1v( of2ms a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotationafk7 o2xc1lp (vl kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched oz8 i(- kdbng mprzrs0 s50n46arms close to his body. What happens to his mo06pz nm4irsg(-5rnbkd8s zo0ment of inertia about the axis of rotation?

State the law of conservation of angu(fai j cy7o8h;lar momentum.

  What arc length does the Earth travel in a three month peril vnhg 6i *o:1e d-ci(bw5kj1kod in its nearly circular orbit about theck 6loih vg(e*n1djw1k:i5b- 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 distanc4kf3u 8r*e kgal :k)zce does the tip of the second34zukkk :*ec ) afrgl8 hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent t4lpqdc 11+0+dlo oxlb o?

  A bicycle wheel rota*k ;+hmee2j /jo:gz jztes uniformly through 2.0 revolutions in 4.0 s. What is the frequency of thz+ o /jz2j;e *khegmj:e wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency opey4j2kkac 5z / 60zasf 0.40 kHz. The period of its rotation /zk6kap0y 4czjae s52 is

  A phonograph record r3qu2fkoh+ n- hotates at 45 rpm. Through what angle does it turn in 0.20 3hofq2 k +h-uns?

  A wheel of diameter 26 cm turns at 1y itbbf j0qx84u9q t0+500 rpm. How far will a point on the outer rim 9b4ifxut+q0bqjt 0 8ymove in 2.1 s?

  A bicycle wheel rotates unifoe x cqj4* knbc9lc0/7jrmly through 2.0 revolutions in 4.0 s. What is the average angular q4*ke79jbjc /xn0c l cspeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revoluf1rb tw6-;zea1 y z;sv63g u/jylwg,htions in 4.0 s. What is the lineu;y6gywe1w,lts /g -af;zvhjb16 z3 rar speed 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 whict+/yd;ysm, u rsz -2rmh 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 make the trip /;sdr-zu+ytyr ,m 2smin 12 minutes?

  A wheel of radius 1.0 m is rotating with a constj0 p k(y j-gralf5(b9bant angular speed of 2.0 rad/s. What is the lib9 gla(5yj b k-(jr0fpnear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the motorz-8fvji r2hssp- gd-- rotates at the rate of 20 rev/8j- -id -g rzfssphv-2s, 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 speed of 2.0 radgscm w7xw,gm3*( zw .v/s. What is the cm3.mgw7,(*vg wzxws centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycleku f: xjefrsoje7q 0/d42qdw3p e5;p/ wheel of diameter 70.0 cm when the bi3uer/q 5 s4d 0jwfxd7fk2oe q: ;/pepjke is moving 8.00 m/s?

  How many revolutions per mio yt -k8c/sir3nute (rpm) must a circular, rotating space station (r = 1000 m) rotate to proirokst/8-y c 3duce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of rad,k7 l*z. 1hxsberb1naius 50 m with a speed of 20 m/s. 1a.ex z,bhk7b r*n1l sThe maximum centripetal 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 ci51,qi*cq gh circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fric5gh,c1q i* iqction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to dz 9 b38of(1n) wpyyrnthe end of a 0.750-m string, is whirled around in a smooth level tabp1f r3(y 8zw)9obdynnle. 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 break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls ag.udky6qb 7 .without slipping 10 m down a lane at 4bq6d. ua .7gky.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 s lom2-7sej 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 wink;fd; r-2w v1*ryew u:n6k.ebxhu (nth a constant 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.zsbho5 k8x juh:3n8a)mv 9r ,x300-m radius automobile tire rotate after starting from rest and acceler8hv sj r: xm3a8kzhb9)nx5o,uating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and h.tz93 de8: ; xezhkqceas 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 decelerates with a cox*vtj n656bac u70ufen ;1utjnstant angular acceleratiojvjb *fca0uxut ne;7 n1t5u66n 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 r -2ddbmdv8tf 9ad/s while turning through 2.0 revolutions. What is the average angular acceleration of the whetf2-dm bd8v9 del?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s t* 5iq(,zqjf yvi7fn1oo:1xolrx4 qx 1 o rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in comingorl (xif 1x4vqoqi:5*1njy,o7fx1 q z to rest?

  A wheel of diameter of 68.0 cm slows dy4saqe r i-q-:own uniformly from 8.40 m/s to rest over a distance of 115 m. -4:s iqrya-qeWhat is the angular acceleration?

  A wheel of diameter of 68.wm vu9r/8; hcy noe;kqb zr*4.0 cm slows down uniformly from 8.40 m/s to rest over a distance ofrk ;4 9y*m.co8h/;qzwue rvnb 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3 vhv ddf8o7)6r600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration df)vovd86hr7before 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 c+w, a,c fqh5+ytq )b;ngjsu7umyj;6 90 Nm. If a 30 cm long wrench is used, what is thq6fjj+5,,u y+ gwnqha)cs ym;c7ub ;t e magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel requxf986myg69zzl;h vbnn mko, t.bz8c(ire tightening to a torque of 90 Nm. If a 30 cm long w9.66(v,nb 8hfy; glk cmzxz9zmn8o bt rench 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 bjq-m x rw(8of+tw1a6inertia $3.00 \; kgm^{2}$ 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 iiu xear8ltw6n+ky wl946 .f/v s at the origin, mass 2m is at x = a,vkl946wny xr+uti6 8 /elf.a w 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 g ;e8gxu;w3jrfrictionless axis thought the ;8uxe3jg;rwg center O. A rope 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 pivoted about a frictionless axis thought tmno- k wxqmkf5: 303hxhe k3o:3xxwkqhmn 50fm-center O. A rope 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 initially held in the hor8zp*d jkh0 qg y6sup 3:*pz6qgizontal position, an*86gz gyd:j *h 3pu6pqqszpk 0d 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 end is ML2/3.)

  Consider a bicycle wheel to befiwe(d skl+s m.956fvfd r*r8 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 form*fkvef9 i6.wslr(5rs+df d8 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on qm z b-:e3)fosa rope wrapped around a frictionless disk pulley of mass 7.07 kg and ras3 zefmq:o b)-dius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionw 8 tf,lk4fyv j8oh:my+v-m+tyj3.teless disk pulley of mass 7.07 kg and radius 66.0 cm. Whvf:o+4tmm. +y vht3 yykjf-lt8j8 ,e wat is the acceleration of the mass?

  A rotating flywheel can be used to store4nfyrlqdnok+uj q12 hh6m0 5/ 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 ine,rst7pyu 6sg0o:ncd +rtia 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 ys.r;y cw n-( g/5x:a(cyhrm nstarts from rest and rolls without slipping down a 1.0-m high inclined planey;yc5/xa-s: r.gcr yn(w h( nm. 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 rolnffcpyzc+5uc 48j-ui17 /zyals with a speed of 10 m/s. How high up an inclined/yc51nc z78auypuc+f-iz 4f j plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released .w )u1+zn qrjdo6 c+kun41lui from rest and allowed to roll down an inclined pland)+ q ilc. run1k u+j641znuwoe. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 1,1urq0q 4-+o8yltgo.(aibadaz gu f: i 8wu0h5 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it8r u bliaf1: zu oa-gdh0i,q w4yq08u.a+got( 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 mo i / x:,lq(rnu.nckqy7mentum 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 inertia of szu h,gs1u1),mo ihej,+ we5h$5.0 \; kgm^{2}$ 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-ibjw .7obt4wc(d , .ona(zbm of inertia-(m b(,bzdwn4abj7.o.witc o 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?