Velocity Of Center Of Mass — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Velocity of Center of Mass General systems of particles, collisions, and decomposing rigid body motion into translation and rotation. Define position of center of mass: R cm = (Σ m i r i) / M. Differentiate position with respect to time to get velocity. Apply linearity of the derivative operator: v cm = dR cm/dt = (Σ m i v i) / M. Masses must be positive. Valid for inertial reference frames. Believing v cm is simply the arithmetic average of velocities (v1+v2)/2 without accounting for mass differences. Ignoring the vector nature (signs) of velocities when calculating the sum.