1. What is Center of Mass?

The center of mass is the average location of the mass of a system. For simple systems, it's the balance point where the weighted relative position of the distributed mass sums to zero.

2. How Does the Calculator Work?

The calculator uses the center of mass formula:

Where:

• \( R \) — Center of mass position (length units)
• \( m_i \) — Mass of individual objects (kg)
• \( r_i \) — Position of individual objects (length units)
• \( M \) — Total mass of the system (kg)

Explanation: The formula calculates the weighted average of all positions, where the weights are the masses at each position.

3. Importance of Center of Mass

Details: The center of mass is crucial in physics for analyzing motion, stability, and rotational dynamics. It's used in engineering, astronomy, and biomechanics.

4. Using the Calculator

Tips: Enter comma-separated values for masses and positions. Both lists must have the same number of values. Example: masses "5,10,15" with positions "1,2,3".

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Use consistent units - kg for mass and any length unit (meters, cm, etc.) for positions, but the same unit for all positions.

Q2: Can I use this for 2D or 3D systems?
A: This calculator is for 1D systems. For 2D/3D, you need to calculate x, y, and z components separately.

Q3: What if masses are negative?
A: Physical masses can't be negative. The calculator will give a result but it may not be physically meaningful.

Q4: How does center of mass relate to center of gravity?
A: They are the same in uniform gravitational fields. In non-uniform fields, they may differ.

Q5: What's the center of mass of empty system?
A: Mathematically undefined (division by zero). Physically meaningless for zero mass systems.