CIRCULAR MOTION1. Consider an arc of a circle whose length (along the curve) is s, the circle is at radius r.The angle measured, , measured in radians, is define by the following equation : rs= The equation shows that the radian is a dimensionless quantity since it is the ratio of two lengths.efinitions: One radian is that angle su!!orted by an arc length in a circle equal to the radius of the circle."ewriting the equation,s = r#. ifferentiating with res!ect to time,r vtrtsr s===$nother way of loo%ing into the above equation, when a body ma%esa com!lete circle:i) it has travel a distance of#&rii) the time ta%en is T, !eriodTherefore:Trv #=orrf v # =v = r where ' ( 2f.angular s!eed2(angular dis!lacementv ) tangential s!eed' ) angular s!eedefine ' :"ate of change of angular dis!lacement.*+,-$.T/C0C.C$, 1+1:1.Calculate the tangential s!eed and angular s!eed for a body on earth.("+ ( 2344 %m, T( #3 hr)#. $ train is travelling on a trac%, which is !art of a circle of radius 244 m,at aconstant s!eed of 54 ms61. 7hat is its angular velocity89. $ washing machine s!ins its tub at a rate of 1#44 revolutions !erminute (r!m). :fthe diameter of the tub is 95 cm, find a) the angular velocity of the tub.b) the linear s!eed of the rim of the tub.;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;9. 7hen a body is moving at constant s!eed, yet is said to accelerating. +1!lain this statement:66 $n ob?,, the body e1!eriences a constantly changing velocity. Therefore the bodymust be accelerating. This acceleration is directed towards a fi1 !oint 6 the center of the circle. *ince v = r,then acceleration, ac = r2 = v.+ven if moving around the !erimeter of the circle with a constant s!eed, there is still a change in velocity and subsequently an acceleration. This acceleration is directed towardsthe center of the circle. *+,-$.T/C0C.C$, #And in accord with >ewton@s second law of motion, an ob>>##0inimum s!eed at the to! v = rg7hat will be the minimum s!eed of the water at bottom, if the water should not s!ill at the to!8Gint : conservation of energy.1. $ 1.56%g buc%et of water is tied by a ro!e and whirled in a circle with a radius of 1.4 m. $t the to! of the circular loo!, the s!eed of the buc%et is 3.4 ms61. etermine the *+,-$.T/C0C.C$, CmgTacceleration, the net force and the individual force values when the buc%et is at the to! of the circular loo!.m ( 1.5 %ga = ________ ms-!net = _________ N#. $ 1.56%g buc%et of water is tied by a ro!e and whirled in a circle with a radius of 1.4 m. $t the bottom of the circular loo!, the s!eed of the buc%et is 2.4 m.s. etermine the acceleration, the net force and the individual force values when the buc%et is at the bottom of the circular loo!.m = 1.5 kga = ________ ms-2Fnet = _________ NLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL1. $ buc%et, containing 1.5 %g water, is tied by a ro!e and whirled in a circle ofradius 1.4 m as shown in !ig" " i. $t the bottom of the circular loo!, the s!eed of the buc%et is 3.4 ms61. etermine the centri!etal force acting on the water. ii. Jn !ig" , mar%, with labelled arrows, the direction of the weight of water W andthe reaction force R acted by the bottom of buc%et on the water.iii. Calculate the reaction force R.#. $conical!endulumconsistsofasmallbobofmass4.#4 %gattachedto an ine1tensible string of length 4.F4 m. The bob rotates in a horiEontal circle of radius *+,-$.T/C0C.C$, F!ig" 4.34 m, of which the centre is vertically below the !oint of sus!ension. ($ssume g ( 14 ms6#) 7rite down an e1!ression that relates the string tension, T with the linear s!eed, v of thebob. ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; M#Na) 7rite down an e1!ression that shows equilibriumof forces in the verticaldirection.;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;M1Nb) Calculate the linear s!eed of the bob in ms61. linear s!eed ( ;;;;;;;;;;..M9Nc) Calculate the !eriod of rotation of the bob.!eriod ( ;;;;;;;;;;;.M#Nd) ?ind the tension in the string. tension ( ;;;;;;..;;;..M#N9 (a) +1!lain what meant by angular velocity. ..;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;..*+,-$.T/C0C.C$, I4.34 m ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;....M1N(b) $nob