1. What is Pendulum Angle?

The pendulum angle (θ) is the angular displacement of a pendulum from its equilibrium position. It can be calculated from the pendulum's velocity, length, and gravitational acceleration.

2. How Does the Calculator Work?

The calculator uses the pendulum angle formula:

Where:

• \( \theta \) — Pendulum angle in radians
• \( v \) — Velocity of the pendulum (m/s)
• \( g \) — Acceleration due to gravity (9.8 m/s² on Earth)
• \( L \) — Length of the pendulum (m)

Explanation: The formula calculates the angle by taking the arcsine of the ratio between the velocity and the square root of gravity multiplied by length.

3. Importance of Pendulum Angle Calculation

Details: Calculating pendulum angle is essential in physics experiments, clock mechanisms, and any application involving pendulum motion. It helps predict the pendulum's behavior and energy state.

4. Using the Calculator

Tips: Enter velocity in m/s, length in meters, and gravity in m/s² (9.8 for Earth). All values must be positive numbers. The calculator will return the angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the maximum valid angle for this calculation?
A: The formula is valid for angles where the small-angle approximation holds (typically < 15°). For larger angles, more complex equations are needed.

Q2: Why does gravity affect the pendulum angle?
A: Gravity determines the restoring force that brings the pendulum back to equilibrium, thus affecting how velocity translates to angular displacement.

Q3: What happens if the velocity input is too high?
A: The calculator will show an error because the ratio v/√(gL) must be ≤ 1 for a real solution (pendulum can't have enough energy to go vertical).

Q4: Can I use this for a pendulum on another planet?
A: Yes, just input the appropriate gravitational acceleration for that planet.

Q5: How does length affect the pendulum angle?
A: Longer pendulums will have smaller angles for the same velocity, as the velocity is distributed over a larger arc length.