1. What is Reduced Mass?

The reduced mass (μ) is an effective inertial mass appearing in the two-body problem of Newtonian mechanics. It represents the "equivalent" mass of a system when two masses interact through a central force.

2. How Does the Calculator Work?

The calculator uses the reduced mass formula:

Where:

• \( m1 \) — Mass of first object (kg)
• \( m2 \) — Mass of second object (kg)
• \( \mu \) — Reduced mass (kg)

Explanation: The reduced mass is always less than or equal to the smaller of the two masses. When one mass is much larger than the other, the reduced mass approaches the smaller mass.

3. Importance of Reduced Mass

Details: Reduced mass simplifies two-body problems into equivalent one-body problems. It's crucial in orbital mechanics, molecular vibrations, quantum mechanics, and other areas of physics where two masses interact.

4. Using the Calculator

Tips: Enter both masses in kilograms. The calculator will compute the reduced mass, which will always be less than either individual mass.

5. Frequently Asked Questions (FAQ)

Q1: What's the physical significance of reduced mass?
A: It allows the two-body problem to be treated as a single mass moving relative to the center of mass, simplifying calculations.

Q2: How does reduced mass relate to center of mass?
A: The reduced mass appears in the equations of motion relative to the center of mass frame.

Q3: What happens when one mass is much larger than the other?
A: The reduced mass approaches the value of the smaller mass (e.g., Earth-Sun system: μ ≈ mass of Earth).

Q4: Where is reduced mass commonly used?
A: In calculating vibrational frequencies of diatomic molecules, orbital mechanics, and quantum mechanical systems.

Q5: Can reduced mass be greater than either mass?
A: No, it's always less than or equal to the smaller of the two masses.