Center of mass

Definition

The center of mass is the point in an object or system where all its mass can be considered to be concentrated for the purpose of analyzing translational motion. It is the weighted average position of all the mass in the system.

5 Must Know Facts For Your Next Test

1. The center of mass of a system can be found using the formula $\vec{R} = \frac{1}{M} \sum_{i} m_i \vec{r}_i$, where $M$ is the total mass, $m_i$ are individual masses, and $\vec{r}_i$ are their positions.
2. In uniform gravitational fields, the center of mass coincides with the center of gravity.
3. For symmetrical objects with uniform density, the center of mass lies at their geometric center.
4. The motion of an object's center of mass can be described using Newton's second law: $\vec{F}_{net} = M \vec{a}_{cm}$, where $\vec{F}_{net}$ is the net external force and $\vec{a}_{cm}$ is the acceleration of the center of mass.
5. The velocity and acceleration of a system's center of mass can be determined by taking time derivatives of its position vector.

Review Questions

• What formula is used to calculate the position of a system's center of mass?
• How does Newton's second law apply to the motion of an object's center of mass?
• Where does the center of mass lie in a uniformly dense symmetrical object?

Related terms

Linear Momentum: The product of an object's mass and its velocity, represented as $\vec{p} = m \vec{v}$.

Collision: An event where two or more bodies exert forces on each other for a relatively short time.

Translational Motion: Movement that changes an object's position without rotating it about any axis.