Pendulum problem

vysero

1. The problem statement, all variables and given/known data
A small object of mass m, on the end of a light rod, is held horizontally at a distance r from a fixed support. The object is then released. What is the angular velocity, ω, of the mass when the object is at the lowest point of its swing?



2. Relevant equations
This is my problem. I believe it is a conservation of energy problem so:
PEi + KEi = PEf + KEf however I am not sure what the angular equivalent to mgh is.



3. The attempt at a solution
mgr = (1/2)(mr)^2(w)^2
2g = r(w)^2
(2g/r)^1/2=w

Which is the correct answer but I am not sure about my math or my formula, did I do this problem the right way or did I just get lucky?

SHISHKABOB

Well, there isn't really an angular equivalent to mgh, you just need to use some trigonometry to find the change in height of the pendulum.

In this case it's really easy since the pendulum mass starts horizontal and they want to know its angular velocity at the bottom of its swing. Therefore it's trivial to say that the change in height is equal to the length of the pendulum.

vysero

So I did do this problem right? I assumed that r or the length of the pendulum was h.

SHISHKABOB

yeah that's a reasonable assumption to make, and if your answer agrees with the one in the book (I think that's what you said) then yes you did the problem right