- #1
hermes1908
- 4
- 0
Homework Statement
I am trying to derive the formula [tex]a_r=\frac{v^2}{r}[/tex] for uniform circular motion (for personal understanding, this is not an assignment). But am having some difficulty. I have seen other proofs, but I want to know why my approach is wrong.
The Attempt at a Solution
Since we are considering uniform circular motion, we assume the tangential and angular accelerations are 0, and the magnitude of the velocity of the particle at any point is the same. Adding the two vectors shown in attached picture, gives us the magnitude of the change in velocity (sqrt(2)*v) over a distance of ∏/2. Since the angular displacement of the particle is ∏/2 we can find the amount of time that has passed by [tex]\frac{\frac{\pi}{2} r}{v}[/tex]. Now simply taking the velocity and dividing it by the derived time expression should yield the magnitude of the radial acceleration, but as you can see it gives [tex]\frac{2\sqrt{2}v^2}{\pi r}[/tex]. My answer is close to what is expected so I suspect my mistake is mathematical in nature, but I can't seem to figure out what it is.