Physics/ Math people

[John G]

I was trying to figure out the optimal Force output of our kicker by doing some math. If you increase the weight at the end, then the torque needed is higher, speed lower, and vice versa. So after trying to do the math, I had some questions ( i have taken calcI, but not calc based physics yet).

If you have a position formula and take the first derivative, you get linear velocity, the second derivative is linear acceleration. How would you compute this for a rotational device such as a pendulum or a kicker?

And how would you come up with one position formula for a device like that if x = cosQ * r and y = -sinQ * r ( r being the arm length)(Q = degrees in radians)?

Thanks.