Pendulum Problem: Solving for Angular Velocity (ω)

[vysero]

Homework Statement

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?

Homework 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.

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]

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.

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

 

[Nickie]

I would say that you have correctly used the conservation of energy principle to solve this problem. Your formula for the final angular velocity, ω, is also correct. The angular equivalent to mgh is 1/2(mr^2)ω^2, also known as the rotational kinetic energy. Your math and formula are both correct, so you have solved the problem correctly. However, I would suggest showing more steps in your solution to make it easier for others to follow and understand your reasoning. Additionally, it would be helpful to include units in your equations to make sure your calculations are dimensionally consistent. Good job on solving the problem!