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.