Kinetic Energy of a Pendulum Calculator
Calculate pendulum kinetic energy, potential energy, and motion parameters using physics principles
Pendulum Energy Calculator
Mass of the pendulum bob
Length from pivot to center of mass
Height above lowest point
Maximum height reached during swing
Current velocity of the pendulum
Acceleration due to gravity (m/s²)
Energy Analysis Results
Energy Conservation: E_total = KE + PE = constant
At maximum height: All energy is potential (PE = mgh_max, KE = 0)
At bottom: All energy is kinetic (KE = ½mv_max², PE = 0)
Energy Conservation Analysis
Example Calculation
Wrecking Ball Pendulum
Mass: 1000 kg (1 ton wrecking ball)
Length: 10 m (crane cable length)
Maximum height: 3 m above lowest point
At bottom position: Height = 0 m
Energy Calculations
Total Energy: E = mgh_max = 1000 × 9.81 × 3 = 29,430 J
Maximum Velocity: v_max = √(2gh_max) = √(2 × 9.81 × 3) = 7.67 m/s
At bottom: KE = 29,430 J, PE = 0 J
At top: KE = 0 J, PE = 29,430 J
Pendulum Motion Phases
Release Point
Maximum height, zero velocity
All potential energy
Descending
PE converts to KE
Velocity increases
Bottom Point
Maximum velocity, zero height
All kinetic energy
Ascending
KE converts back to PE
Velocity decreases
Energy Conservation
Total Energy
E = KE + PE = constant
Kinetic Energy
KE = ½mv²
Potential Energy
PE = mgh
Maximum Velocity
v_max = √(2gh_max)
Physics Tips
Energy is conserved in ideal pendulum motion
Maximum velocity occurs at the bottom
Period depends only on length and gravity
Real pendulums lose energy to air resistance
Understanding Pendulum Energy
What is a Pendulum?
A pendulum is a weight (called a bob) hanging from a pivot point that can swing freely. In the mathematical pendulum approximation, we ignore friction and the mass of the string/rod, focusing on the physics of energy transformation.
Energy Conservation Principle
The total mechanical energy of a pendulum remains constant during its motion. Energy continuously transforms between kinetic energy (energy of motion) and potential energy (energy due to height).
Applications
- •Pendulum clocks for timekeeping
- •Wrecking balls for demolition
- •Seismometers for earthquake detection
- •Amusement park rides
Key Formulas
Energy Equations
- Kinetic Energy: KE = ½mv²
- Potential Energy: PE = mgh
- Total Energy: E = KE + PE = constant
- Maximum Velocity: v_max = √(2gh_max)
Motion Parameters
- Period: T = 2π√(L/g)
- Frequency: f = 1/T
- Angular Displacement: θ = arccos((L-h)/L)
Note: These equations assume no friction or air resistance. Real pendulums gradually lose energy due to these factors.