Symmetry principle

Definition

The symmetry principle states that if a system or shape has symmetry, its center of mass will lie along the axis of symmetry. In other words, symmetric objects have their centers of mass located on lines or planes that divide them into mirror-image halves.

5 Must Know Facts For Your Next Test

1. For an object with symmetrical properties, the center of mass lies on the axis or plane of symmetry.
2. The symmetry principle simplifies the calculation of moments and centers of mass for symmetric objects.
3. Symmetry can reduce multi-dimensional integration problems to simpler one-dimensional ones.
4. In applying the symmetry principle, only consider those axes or planes that truly divide the object into equal halves.
5. When dealing with composite shapes, each part's symmetry can be used to calculate the overall center of mass.

Review Questions

• How does the symmetry principle help in finding the center of mass?
• What happens to the complexity of integration when an object exhibits symmetry?
• Can you apply the symmetry principle to objects that are not perfectly symmetrical? Why or why not?

Related terms

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

Moment: A measure of the tendency of a force to rotate an object about a point or axis.

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