Please explain centripetal acceleration?

[St@rbury]

can some1 please explain centripical acceleration? i don't get it at all

 

[BerryBoy]

It is the acceleration a body feels when following a circular trajectory, towards the centre of that circle.

Imagine modelling the a particle's position as:
$$x = r \cos \omega t$$ and $$y = r \sin \omega t$$
This is simply circular motion at a radius r.

By differentiating twice you find the acceleration:
$${\partial^2 x} / {\partial t^2} = - \omega^2 r \cos \omega t$$ and $${\partial^2 y} / {\partial t^2} = - \omega^2 r \sin \omega t$$

Which is a vector that points towards the centre of the circle, this is centripetal acceleration.

Does this help?? :P

Sam

 

[malty]

This isn't a rigourous explanation but I hope it helps; here goes:

If an object is moving in a circular motion with a constant speed we refer to the motion as being uniform circular motion. Now if we take the velocity at any instant i.e the instantaneous velocity, we find that in order for the object to maintain its circular motion the direction in which it is traveling is ALWAYS tangential to the circle. For this reason, the velocity is NEVER constant, and there is no component of acceleration parallel to the path at any instant because if this was the case the speed would increase. So for the speed to remain constant the acceleration must ALWAYS be in the direction perpendicular to the instantaneous velocity i.e towards the centre of the cirlce.