Center of mass

Definition

The center of mass is the point in a body or system of bodies where the entire mass can be considered to be concentrated for the purpose of analyzing translational motion. It is the average location of all the mass in a system.

5 Must Know Facts For Your Next Test

1. The center of mass of a uniform circular object, like a wheel, is at its geometric center.
2. In a gravitational field, the center of mass coincides with the center of gravity if the field is uniform.
3. The motion of an object can often be simplified by considering only the motion of its center of mass.
4. For complex systems, such as multi-body systems, the center of mass can be calculated using $\vec{R} = \frac{1}{M} \sum m_i \vec{r}_i$, where $M$ is the total mass and $\vec{r}_i$ are position vectors.
5. An object's stability and balance depend on whether its center of mass falls within its base.

Review Questions

• What happens to an object's balance if its center of mass shifts outside its base?
• How do you calculate the center of mass for a system comprising multiple masses?
• Why does considering only an object's center of mass simplify analyzing its motion?

Related terms

Uniform Circular Motion: Motion in a circular path with constant speed.

Newton’s Universal Law of Gravitation: $F = G \frac{m_1 m_2}{r^2}$ describes how every particle attracts every other particle with a force proportional to their masses and inversely proportional to the square of their separation distance.

Center Of Gravity: The point where gravitational force can be considered to act on an object.