1. What is the Tension in a Pendulum?

Definition: This calculator computes the tension force in a pendulum string or rod based on the mass, gravitational acceleration, and angle from vertical.

Purpose: It helps physics students and engineers understand and calculate the forces acting in pendulum systems.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( T \) — Tension force (Newtons, N)
• \( m \) — Mass of the pendulum bob (kilograms, kg)
• \( g \) — Gravitational acceleration (m/s², typically 9.81 on Earth)
• \( \theta \) — Angle from vertical (degrees)

Explanation: The tension is calculated as the component of gravitational force acting along the pendulum's supporting string or rod.

3. Importance of Tension Calculation

Details: Understanding pendulum tension is crucial for designing stable pendulum systems, analyzing harmonic motion, and solving physics problems.

4. Using the Calculator

Tips: Enter the mass in kg, gravitational acceleration (default 9.81 m/s²), and angle from vertical (0-90 degrees). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why does the angle affect tension?
A: As the angle increases, more of the gravitational force goes into the tangential component, reducing the tension in the string.

Q2: What's the tension at 0 degrees (vertical)?
A: At θ=0°, cos(0°)=1, so T=mg - the tension equals the full weight of the pendulum bob.

Q3: Does this formula work for any pendulum?
A: This is the static tension formula. For swinging pendulums, additional terms would be needed to account for centripetal force.

Q4: What units should I use?
A: Use kg for mass, m/s² for gravity, and degrees for angle. The result will be in Newtons (N).

Q5: How does mass affect tension?
A: Tension is directly proportional to mass - doubling the mass doubles the tension.