How to calculate acceleration...?

Question

Hope I can visualize this for you, it might be difficult. There is a (hard, solid) rod which is connected to an axle on one end (allowing it to swing freely around in a complete circle). I know that when the rod is at a steeper angle (almost vertical), the rods acceleration is less than when it is horizontal. How can you calculate the difference in acceleration between different angles? I'm not looking for a perfect calculation (mass is unimportant or 1, and length doesn't matter), I'm just sort of looking to see if the difference (or acceleration of acceleration) is linear or exponential?

Answer 1

I think you are looking at the acceleration of the rod at different points as you move it from vertical to horizontal position through angle A

(0<A<90 )

Let the length of the rod be L  

If the far tip moves in circular path with linear speed V we have acceleration a as

a= V^2/R or

a=R w^2

w- angular speed with which the shaft rotates.

since

R= L sin(A)

a= L sin(A) w^2

Does that help?