Center of Mass

http://youtu.be/VrflZifKIuw

Definition

• “The center of mass (or mass center) is the mean location of all the mass in a system”

• Marked with:

Examples

• The center of mass of a two-particle system lies on the line connecting the particles (or, more precisely, their individual centers of mass). The center of mass is closer to the more massive object

• The center of mass of a ring is at the center of the ring (in the air).

More Examples

• The center of mass of a solid triangle lies on all three medians and therefore at the centroid, which is also the average of the three vertices.

Applications• Objects rotate around their center of mass• http://youtu.be/DY3LYQv22qY• A projectile’s center of mass will follow a

parabolic path.• If an object’s center of mass is outside it’s base

of support, it will topple.

Forces and center of mass• If a force is placed on an object in line with it’s

c.m. if moves without rotation.

• A force on an object which is not in line with it’s c.m. tends to rotate the object.

Toppling Rule of Thumb

• If the CG of the object is above the area of support, the object will remain upright.

• If the CG is outside the area of support the object will topple.

A look at Stability

• Stable equilibrium: when for a balanced object a displacement raises the CG (to higher GPE so it tends to go back to the lower U).

• Unstable equilibrium: when for a balanced object a displacement lowers the CG (lower GPE).

• Neutral equilibrium: when the height of the CG does not change with displacement.

Stability

Hons only.