1. What is Pendulum Tension?

The tension in a pendulum is the force exerted by the string or rod that keeps the mass moving in a circular arc. It has two components: the gravitational component (mg cosθ) and the centripetal component (mv²/r).

2. How Does the Calculator Work?

The calculator uses the pendulum tension formula:

Where:

• \( T \) — Tension in the string (N)
• \( m \) — Mass of the pendulum bob (kg)
• \( g \) — Acceleration due to gravity (m/s²)
• \( θ \) — Angle from vertical (degrees)
• \( v \) — Tangential velocity (m/s)
• \( r \) — Length of pendulum string (m)

Explanation: The first term accounts for the gravitational force component along the string, while the second term accounts for the centripetal force needed for circular motion.

3. Importance of Tension Calculation

Details: Understanding pendulum tension is crucial for designing pendulum systems, analyzing pendulum motion in physics, and ensuring the string/rod can withstand the maximum forces.

4. Using the Calculator

Tips: Enter mass in kg, gravity in m/s² (9.81 on Earth), angle in degrees (0-90), velocity in m/s, and length in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the tension at the bottom of the swing?
A: At θ=0°, cosθ=1, so T = mg + mv²/r. This is typically the maximum tension point.

Q2: How does angle affect tension?
A: Tension decreases as angle increases because the cosθ term becomes smaller.

Q3: What happens when velocity is zero?
A: The tension equals just the gravitational component (mg cosθ), which is the minimum tension.

Q4: Can this be used for conical pendulums?
A: Yes, the same formula applies to conical pendulums moving in horizontal circles.

Q5: What's the relationship between length and tension?
A: Longer pendulums typically have lower velocities, which may reduce the centripetal component of tension.