Circular Motion IBH revision

Linear Motion Linear velocity is how far something travels in one second We measure it in ms -1 Angular Velocity Angular velocity is how much something rotates in one second We measure it in radians per second V = d/t d   =  /t

There are 2  radians in a circle. If an object rotates at 10 revs per minute what is its angular velocity in radians per second? 10 x 2  / 60 = 1.05 rad/sec  =  / t

V =  r The yellow circle moves faster than the pink speed = distance / time = r  / t (  =  / t) =  r v =  r A point further from the centre will move faster

Centripetal acceleration An object moving in a circle is continually changing direction. This means its velocity is changing It is accelerating even though its speed is constant To make the object accelerate there must be a force acting This force acts towards the centre of the circle. It is at right angles to the motion so does no work F

a =  2 r  V = V 2 - V 1  is small so  = sin  = tan   =  v/v  v = v  a =  v/t = v  /t = v  a =  2 r = v 2 /r you need to know this derivation  V2V2 V1V1 -V 1 VV V2V2  a =  2 r

question A 1000 kg car rounds a bend with radius 10m at a speed of 10 ms -1. What is its acceleration? a = v 2 /r = 10ms -2 What will be the acceleration at 20 ms -1 ? 40 ms -2 (4 times bigger) What would be the acceleration at 10 ms -1 if the radius of the curve was 5m a = 20ms -2 What is the force acting on the car in this case F = ma = mv 2 /r = N

Centrifugal force The force changes the direction of the rectangle the circle keeps going in a straight line As viewed from the rectangle it will appear to fly outward There is no force acting on the circle it meerly keeps going in a straight line

Loop the Loop When the object is at the top the force acting on it is mg It accelerates downward at 10 ms -2 It is moving in a circular path so the acceleration towards the centre (downwards) is v 2 /r If mg > mv 2 /r then object will fall of If mg < mv 2 /r then the reaction force from track will make up the difference mg

Banked Corner There are only 2 the combination of these 2 forces causes the change of direction The vector sum of these two forces is mv 2 /r What are the forces acting on the object ? mg R mv 2 /r R   tan  = v 2 /rg