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Energy on a pendulum
Beginner
Energy swaps between kinetic at the bottom and potential at the top.
pendulumAt the top of the swing the bob has maximum U and zero K; at the bottom maximum K. The speed at the bottom is v = √(2gL(1 − cosθ)).
L = 1 m, θ = 60°: v ≈ 3.13 m/s.
The tension does no work because it's perpendicular to motion.
In more detail
A pendulum exchanges potential and kinetic energy. At the highest points it has maximum potential energy and zero kinetic energy, and at the lowest point the reverse is true.
Real-world uses
- Clocks use pendulum energy exchange to keep a steady beat.
- Swings in playgrounds demonstrate energy transfer as they rise and fall.
- A clock pendulum swings between two heights, trading energy between kinetic and potential forms each half-cycle.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Where is the speed greatest?
At the lowest point, where potential energy is smallest and kinetic energy is greatest.
Does a pendulum keep swinging forever?
Not in practice, because friction and air resistance remove energy.
Where is the pendulum fastest?
At the lowest point, where its potential energy is smallest and its kinetic energy is greatest.
Related topics in Work, Energy & Power
Equilibrium types · Conservation of mechanical energy · Energy conservation in free fall · Energy in spring-mass systems · Roller coaster and loops · Energy loss to friction