Center of Mass

What is Center of Mass?
The center of mass (CM) of a body is the point where the whole mass of the body can be thought to be concentrated for the purpose of motion analysis.

In simple words – It’s the balance point of an object .

Examples in Daily Life:

• A cricket bat balances at its center of mass.
• When you toss a stick in the air, it spins around its CM.
• Gymnasts and divers control their CM to perform flips.

Center of Mass for a System of Particles

If a system has n particles with masses m1,m2,...,mn​ and positions x1,x2,...xn​:

Along x-axis:

Along y-axis:

Along z-axis:

Special Cases:

• Uniform rod: CM at midpoint.
• Uniform sphere: CM at center.
• Ring: CM at geometric center.

Difference Between Center of Mass and Center of Gravity:

• Center of Mass: Depends only on mass distribution.
• Center of Gravity: Depends on both mass distribution and gravity.

Summary:

The center of mass is the point where the mass of an object is considered to be concentrated. It helps in analysing motion and balance.