Symmetry principle

Definition

The symmetry principle states that the center of mass of a symmetric object lies along the axis of symmetry. This principle simplifies calculations for moments and centers of mass in symmetric regions.

5 Must Know Facts For Your Next Test

1. The symmetry principle can significantly reduce the complexity of integration when determining moments and centers of mass.
2. For an object with bilateral symmetry, its center of mass will lie on the line or plane of symmetry.
3. In problems involving multiple objects, each object's symmetry must be considered individually to locate the overall center of mass.
4. The use of symmetry allows one to determine certain coordinates (usually the $x$ or $y$ coordinate) without performing integration.
5. Common shapes where the symmetry principle is applied include rectangles, circles, and ellipses.

Review Questions

• How does the symmetry principle simplify finding the center of mass for symmetric objects?
• What is the significance of an axis or plane of symmetry in determining moments?
• Give an example where applying the symmetry principle could eliminate the need for integration.

Related terms

Center of Mass: The point at which an object's mass is considered to be concentrated for purposes of analyzing translational motion.

Moment: A measure of the tendency to cause rotation about a specific point or axis; calculated as force times distance.

Axis of Symmetry: A line through a shape such that each side is a mirror image across this line.