Table of Contents
Pendulum Energy
A pendulum continuously converts between kinetic energy (energy of motion) and gravitational potential energy (energy of height). At the highest point of its swing, all energy is potential and velocity is zero. At the lowest point, all energy has been converted to kinetic and velocity is maximum. At intermediate positions, energy is shared between both forms.
This energy conservation principle, first clearly articulated by Huygens, makes the pendulum an excellent demonstration of the law of conservation of energy. In an ideal pendulum with no friction or air resistance, the total mechanical energy remains constant throughout the swing.
Energy Formulas
Energy at Different Positions
| Position | KE | PE | Velocity |
|---|---|---|---|
| Top (release) | 0 | Maximum | 0 |
| Middle | ~50% total | ~50% total | Moderate |
| Bottom | Maximum | 0 | Maximum |
Frequently Asked Questions
Why does a real pendulum eventually stop?
Air resistance and friction at the pivot convert mechanical energy into heat. Each swing, a small amount of energy is lost to these non-conservative forces. The total mechanical energy decreases gradually, reducing the amplitude until the pendulum stops. In a grandfather clock, the escapement mechanism adds energy each swing to compensate for these losses.
At what angle is KE equal to PE?
KE equals PE when the height is exactly half the maximum height: h = h₀/2. This occurs at angle θ where cos(θ) = (1 + cos(θ₀))/2. For a 30° release angle, this occurs at about 21.5 degrees.