Pendulum Energy Conservation
Converts the potential energy at the top of the swing (mgh) into kinetic energy at the bottom (½mv²)
The equation
What it solves
Converts the potential energy at the top of the swing (mgh) into kinetic energy at the bottom (½mv²). Gives the maximum speed from the swing height, or vice versa, without needing to know the angle explicitly.
When to use it
Finding the speed at the bottom of a pendulum swing, or the height reached given a launch speed. Works for any conservative swing, not just small angles.
When NOT to use it
Assumes no energy losses — invalid if the problem mentions friction at the pivot or air resistance. Also does not give the instantaneous speed at intermediate points without knowing the height at that point.
Common mistakes
Forgetting to compute h correctly: for a pendulum of length L at angle θ₀, h = L(1 − cos θ₀), not L·sin θ₀ or L·θ₀. Canceling the mass m and then not recognizing that the result is independent of mass. Using the full string length L instead of the height h.