Angular displacement isdmo,14 mtg:f v usually express in units of

  Angular velocity is expressevf rz7dci;3, vkilw9;d in units of

  Angular acceleration ia-w.2 myx gt0as expressed in units of

  A boy and a girl are riding on a merry-go-round which is turn;eqett;q fo3 xc2uez q.y*n;*ing at a constant rate. The 2tnu f e.3;;qyqte *czeq;*xoboy is near the 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 turning at a consta hb6* mrv8x5bci 7d-nant rate. 8-m7vhi d*6 cbnab xr5The 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 ridiks;irfh 0v0 d:pp if+yb )fkmw. ,fs:fa8m8 7cng on 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 center. Wh bwf :im:k8vkdh78,frfpp i s)0f0sf.+;am yco has the greater linear speed?

  A boy and a girl are riding a mme 79lai-t7amtz7f txe o j5h6,c) qu;erry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the centj; act)6,tqx7mtil77u-m9a hz fe oe5 er. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a cme fxpgqa)d+ +xj2t/0.,egy constant rate. The boy is near the outer edge, jxf 0ted+ mayec,g 2)+qpg.x/while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating ml91-epu zwi2rczpeb-o l**(. Which of the following is an accurate statemeppb - luw*o9*ezie 2rz1( clm-nt?

  Rolling without slipping depubi: c +kknom(3ke49lends on

  Two equal forces are applied to a door. The firopj0ax35m, eto-3bcsod ;cz4 (rru:hst force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are appl5b(:j xootc3zu0ram4;-re c o, h3ds pied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a do5p 69euszkdq8i5 fiohk3n67aju1 0yzor at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to tu 5ukdh i j 7509aqzzens3168iop6fkyhe plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The fir c1j64kz gk3d7+agpkd st force is twice as large as the second force. The ratio of the torque of the firsz7 c+6dg4kajkgd31 pkt to the torque of the second is

  What is the quantity used to measure an object's resis(1zur3qc0vqqp bqk - +pma bt1h: hq8-tance to changes in rotation?0mpq q-8pcq+1 :kh3q(tbzv1b- ur a qh

  Consider two uniform solid spheres where 6*pdf-r*dyqr -17m+xzz g,o 2e3gb o zkqxfo:both have the same diameter, but one has twice the mass of the ot+orxzfz6* :,yg oeb -oxkg f3m qd7z1rd -*pq2her. 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 radibt9jm:mvq-0s2 d, n ykus of the other. The r 9y20sqjm:vn -m,bd tkatio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one5gj,1mq ibidy x0 q3r-7lru gfaoj*+( has twice the mass and twice the diameter of the other. The ratio of the larger moment of inerti ij0x5m au-or,(g3yfq+ 7lj*r igdb1qa to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and rad1v2 yroi u8)dy*ej8h rius R. If these are increased to 2M and 8)ir8 yh yu1ve2r jdo*3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that obw 7itv01bbeb:ject will

  The moment of inertia of a solid cylinder about itj52 ;jn9,a-zam yscku;. k*0heu ijmts axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational ;z90iy,s.kej akjnu-m; 5ht*acuj 2 mkinetic energy is

  Consider a motorcycle of mass 150 kgu:;uzq2o8x zxl*l zf6 , 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 of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniufz 8z*u;xxzl 62l:qoform disks.

  Suppose a solid sphere of mass M and radius R rolls without slip 8ru+147j1 nvqgq nnia p6n+pcping down an inclined plane starting from rest. The linear velocity of the sphere at the bon cgn7 + rpq+841q vpa6nuijn1ttom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippin m5+/cu jwcf/sg down an inclined plane starting fromc//+sum5 cjf w rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net e)eppp(tce q*6xternal force acts on the system." This(qctppe*pe )6 statement is

  In what circumstances can the angulaewpj,1t:y: on3,yb t ar velocity of system of particles change without any change in the system's angular momentumnpwyt3:1y,eb o, j:at?

  The Earth orbits the Sun in an elliptical orbit. Ignore + :kuddzg0g0tkks4 ( xm;fty,any friction which may be presentf+, 0(kg :t 4kxyzud;tmgkd s0. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the7g:;wf1w - t7- gnrygh emer9x Sun in an elliptical orbit. As the Earth moves close to the Sun, then whic79gfeh ng twew-7;-y xrm gr:1h of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) byq,y2m 7 sy-sqv pulling in his outstretched arms close to his body. What happens yqv 7,m2qy-ss to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pul1u6f2zqja 5 ueling in his outstretched arms close to his body. What happens to his rotational kinetic energy abo2 56z qauf1ejuut the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstr *dv50plk( mblr+)tc qetched arms close to his body. What happens to his moment of inertia m0*trq llbp5cvk(+d) about the axis of rotation?

State the law of conservation of angular moment(nq h ssqno )/b56u(+f+bzelcum.

  What arc length does the Earth travel in a three month period in its nearly circf -hd1dn.e9e o-h6 k:8gjeytqular orbit about81q ee9- yhd-hn:de. 6kotjfg the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a htm*2 zxxolo8wjc5+;q c9/b nu:r0el clock has a length of 0.30 m. What distance does the tip of the second hand swee ot j u5z2xmb*xc;ehl+9lwc/0nr o:q8 p through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent t,vr h0sbs/jha e:a0q5 0-ocllo?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is tl1*0bzu: e)4oihz oo0va7jxbjde k0 8he frequency of the wheel's rotabalj1ojk*xh:ie 0 b z7z)4o0d8v0eu otion?

  A pulsar (a rotating neutrons 2cli+ lc7mna 3..jeu star) emits pulses at a frequency of 0.40 kHz. The period of its roa sl.+ni lmu3jce 2.7ctation is

  A phonograph record rotates at 45 rpm. Through what angle does it t8k 7udejf sf(teu-glhj;74 l*urn in 0.20 flsk 7(tl *de8ujeuf7h4-;g js?

  A wheel of diameter 26 cm turns at 1500 rpm. How fas7fa /p/ qmzt7r will a point on the outer rim move in 2.1 sszmp/ f7/ta7q?

  A bicycle wheel rotates uniformly through 2 -cvm(lh 4vudwvnh6+1.0 revolutions in 4.0 s. What is the avvh 4dlm n-(w vchv16u+erage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.0hfl8(y )m 1ykv hlok0 What is the linear speed of a point 0.10 m from the center of the w0l(khy0lv 8kh m)y 1foheel?

  A cable car at a ski resort carries skiers a distance of 6.8 kmj+b y j.: 2n- cs-tasv/kzhz) krb8u*n. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippbj2 /h:cnts+arv z8-n y*zuk-kjb. s)age, 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 rotating with a constant angular speed of 2.0 rad/ dpl.m 9,ge9uts. What is the linear speed of a point on the wheelm. ted ,9ulp9g's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 buzif1v0cfcg *3 (zro 4 qt8*. fn8aoam in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear v8fofc0*ca *u of(1t brzai84.qzg3n speed of the end of the cord?

  A wheel of radius 1.0 m is rotating wi ozpvl45nm)5 uth a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of al 5mop 4)uvnz5 point on the wheel's rim?

  What is the centripetal accelerat9lx5zozy5 w5-t z5b 0fc /rrkgion of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 5 grtzz5w/05lfb5 9o-rkz xycm/s?

  How many revolutions per minute (rpm) must a cirwcc7awo3a v3ml gmnt30) 7egiah 0b8)cular, rotating space station (r = c78gv3oag0 nm 3b a0wi3lecw7a )h) tm1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 5 g2m(*w03lxxy8uxasd 0 m with a speed of 20 m/s. The maximum centru8 algxs (3ymw0d*x2xipetal 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 mk70s;uia78o:upqeueau c)gdnq-1/u with a speed of 20 m/s. The maximum centripetal force (provided by statgcu k:ad8q 7-;s7ieo) a/ue uqnp 1u0uic 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 whz1 fglamq/ exb+49ucea : araf)2z4/ xri(;ffirled around in a smooth level table. 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 a4zf)9g/bx rx1lfz uqcr4aa (i f+:e a;/f2em to break?

  A bowling ball of mass 7.5 kg g hiux sr/8c 1+4pkus8ow) q-tand radius 9.0 cm rolls without slipping 10 m down a lane +guxiswq/ h u- sp 418to)8rkcat 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 coe a3wz/xe*cp 5nstant 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 acceleratz d1l s witrb .,4kyq:3qlxe61ion 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 autom.u53 gl.b)lnsnqz7 roobile tire rotate after starting from rest and accelerating at a constant angular acceleration of5 7.3s)lzl.nonb rgqu $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an an44 hojw p g-0rn;df:lfgular 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 i y6z*(vok9aqwith a constant angular acceleration (ioqv*k z6a y9of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/; )cffzba34on t s7p3v8tbr,k s while turning through 2.0 revolutions. What is the average bv3r;sz8ac o)tnp7, ff43kt bangular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows dowu0n.*d 39xnw4dmzbdcdf v d2e 5)r,ad n uniformly from 8.40 m/s to rest over a distance of 115 m. What is thc03d,2bu).d*9dfwdv r4 nne5ddxamz e total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm sl9w dr:(b+dk4as/puvj8k t) t myi6gf*ows down uniformly from 8.40 m/s to rest over a distance of 11 tk)m 4kbvia:sr6 8pd9d(gyf*+ /wt ju5 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cmn6 .s,tlt o*hw;vyis4 slows down uniformly from 8.40 m/s to rest over a distance of 115 m. o itw,h; l.y46vnt s*sHow long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotaw31rborau2 -vyd6 ae /tes at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration -ar2b/rauw1 ve63 odybefore 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 tightenih y3 48xi.j p4qk.2k j0pyprtnng 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 is perpendiculathk2i qy4kjjn03 rpp4y x8.p.r to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. Ihl;1ww0 -l bxsf a 30 cm long wrench is used, what is the magnitude of the force required when the fow- l;wxs10h lbrce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertg q ejt +lspvws16;ep,.n1+y:gkr v6lia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mou;dgw;;:9rsbzf blq1deled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a;ufr:q d;9 zglb1 ;swb. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivotes(u;b,-rkwttis v*0 dd 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 rtwb s,iv;su0*tkd (- 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 0b 16ezr4 /znq tg3spukg 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 nts01/zg3r bp zeq46uR2 = 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. jr 5pp6jjhfk )9m;;ktThe rod is 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 p9p)rk;fj 5t;hjmk j6 rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass tdw gaz5*lrfe/ .geu:+d1 q1o1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is afga1e* d/uz:qo et+.w dgr51l pplied tangentially 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 frictiq2w+0jex.zaqmeasla : ke.p++7+eidz *8wbh onless disk pulley of mass 7.07 kg and radius 66ax 8eekpa. dwqe7aqm+ibh s0+zzw.lj2 * e +:+.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless dis5w:jsr (4wuvt k pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the masv4stj5ru (:w ws?

  A rotating flywheel can be used gi)x3w3ci 1byto store 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 inertia f2pfhu 7//g-hz e(musv t nhr, u6u*4xof $5.00 \; kgm^{2}$ 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 d4fi 4yn(bmi8:7o vs z w. pzn0i7a6zuand radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high i747zufz p6o n4bz:w.vasii0d 8i y (nmnclined 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 speed of 10 m/s. wt04rtr tfuc)bf-fl.3h l;5 d How high up atbfr 5wtc rl0tf3 d-hu)lf;4.n inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from re)xe*:rv 2nxuast and allowed tor)2ex:xv* ua n 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 r0,jrte6b .xlde x bq1t,6srl-u 4af*w adius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is rlx,w*bj ,fl6 -1 b.qdsa4e x tu0ert6given 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 7q m++q dvn+iuf;s7dulp6s 6e$20 \; kgm^{2}/s$ 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 ood90a+vz zof;uo)*a rf 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 extended h7 o/tb x-w 55kjmnc7svas a moment of inertia jk 7xc5ow sm5/-v7bntof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?