CENTER OF MASS AND MOMENTUM!

The center of mass is the point at which Newton's 2nd Law applies: ΣFext = Mtotacm

rcm = (1/M)Σi miri.

rcm = (1/M)∫r dm.







An object can be fully supported at a point below or above the center of mass, no matter how it extends beyond the point of support. For a uniform object, the center of mass is at the geometrical center of the object.



Define P = Σi mivi. Then ΣFext = dP/dt.

If no external forces act on a system, P is a constant vector! That is,

THE TOTAL MOMENTUM OF THE SYSTEM IS CONSERVED!



SYSTEM KINETIC ENERGY!

Kinetic energy is a scalar, so that if we have a large number of individual masses, mi , each with speed vi , the total kinetic energy is simply the ordinary sum of all the individual kinetic energies, namely K = Σi (1/2) mi vi2 .

Total Momentum!

Impulse!

Collisions in General!

Head-On Collisions!

Center of Mass and Orbits!

Next!