Velocity of centre of mass

Intermediate

Equals total momentum divided by total mass.

Key relationv_cm = P/M

v_cm = Σmv/M = P/M. If net external force is zero, v_cm is constant, even when parts explode.

Worked example

A firework explodes at the top of its path; the centre of mass continues along the parabola.

Common mistake

Internal forces can't change v_cm.

In more detail

The velocity of the centre of mass is the total momentum divided by the total mass. If the system is isolated, this velocity is constant.

Analysing an exploding projectile, where the fragments scatter but the centre of mass keeps its path.
Calculating the motion of two skaters pushing apart on ice.
A rocket's centre of mass moves like a particle with the total momentum, which simplifies the motion of the whole system.

Does the centre of mass always move in a straight line?

Only if there is no net external force, such as gravity.

How is it related to momentum?

Total momentum equals total mass times the velocity of the centre of mass.

Can the centre of mass accelerate without external forces?

No. Its acceleration is set only by the net external force, so with none it moves at constant velocity.