Center of Mass

1. Center of Mass http://youtu.be/VrflZifKIuw

2. Definition • “The center of mass (or mass center) is the mean location of all the mass in a system” • Marked with:

3. 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).

6. 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.

9. 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.

15. 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.

17. 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.

18. 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.

19. Stability

25. Hons only.