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Centripetal Force & Acceleration

"Centripetal" means "seeking the centre" … it comes from the Latin word peto (I seek)

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Working out centripetal acceleration

Symbols
ϴ (theta) = Angular displacement (radians)
Ѡ (omega) = Angular velocity (radians / sec)
α (alpha) = Angular acceleration (radians / sec)
v = Velocity (metres /sec)
r = Radius of motion (metres)

centripetal accelerationVector Diagram

Now (a)acceleration = Change in velocity    = acceleration formula - change in velocity over change in time
                                         Time 

From the vector diagram above change in velocity = velocity times change in angular displacement so putting them together we get

     but

So by substitution a =

 

But  

So again by substitution
Centripetal Acceleration =    or   = 

These apply if the mass of the rotating object and radius are fixed.

Using the equation worked out above we can calculate centripetal acceleration

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