Center of Gravity Calculator

Center of Gravity Formula:

\[ CG = \frac{\sum (m_i \times x_i)}{\sum m_i} \]

Center of Gravity (CG):

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1. What is Center of Gravity?

The center of gravity (CG) is the average location of the weight of an object. It's the point where the total weight of the body may be considered to be concentrated.

2. How Does the Calculator Work?

The calculator uses the center of gravity formula:

\[ CG = \frac{\sum (m_i \times x_i)}{\sum m_i} \]

Where:

\( CG \) — Center of gravity position
\( m_i \) — Mass of each component
\( x_i \) — Position of each component

Explanation: The equation calculates the weighted average of positions based on mass distribution.

3. Importance of CG Calculation

Details: Knowing the center of gravity is crucial for stability analysis in engineering, vehicle design, architecture, and physics applications.

4. Using the Calculator

Tips: Enter masses in kg (comma separated) and their corresponding positions in meters (comma separated). The number of masses and positions must match.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Masses should be in kilograms (kg) and positions in meters (m), though any consistent units will work.

Q2: Can I use this for 2D or 3D objects?
A: This calculates the CG along one axis. For 2D/3D, you would need to calculate CG separately for each axis.

Q3: What if my object has uniform density?
A: For uniform density objects, the center of gravity coincides with the geometric center.

Q4: How does CG affect stability?
A: Lower CG increases stability. Objects tip when CG moves outside the base of support.

Q5: What's the difference between CG and center of mass?
A: They are the same when gravity is uniform, but differ in non-uniform gravitational fields.