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Pendulum Energy Equation:
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Pendulum energy refers to the potential energy stored in a pendulum system at its maximum displacement. For a simple pendulum, this energy is calculated based on mass, gravitational acceleration, length, and the angular displacement from the vertical position.
The calculator uses the pendulum energy equation:
Where:
Explanation: This equation calculates the maximum potential energy of a pendulum at its highest point, which equals the total mechanical energy of the system (assuming no energy losses).
Details: Calculating pendulum energy is essential for understanding oscillatory motion, designing pendulum-based systems (like clocks), and studying energy conservation in physics experiments.
Tips: Enter mass in kilograms, gravitational acceleration in m/s² (Earth's gravity is approximately 9.81 m/s²), length in meters, and angle in radians. All values must be positive.
Q1: Why is the angle measured in radians?
A: Radians are the natural unit for angular measurement in physics calculations, particularly when using trigonometric functions in equations.
Q2: What is the typical range for pendulum angles?
A: For small angle approximations (sinθ ≈ θ), angles should be less than about 0.35 radians (20 degrees). This calculator works for all angles up to π radians (180 degrees).
Q3: Does this equation account for energy losses?
A: No, this calculates the theoretical maximum potential energy. Real pendulums lose energy to air resistance and friction.
Q4: Can I use degrees instead of radians?
A: You'll need to convert degrees to radians first (radians = degrees × π/180) before using this calculator.
Q5: What if my pendulum isn't simple?
A: This equation is for ideal simple pendulums. Compound or physical pendulums require more complex calculations involving moment of inertia.