If a system experiences only internal forces and there are no external forces, what is the acceleration of the center of mass?

If a system experiences only internal forces and there are no external forces, what is the acceleration of the center of mass?

• A. a_cm = ΣF_ext / M
• B. a_cm = sum of internal forces / M
• C. a_cm = 0
• D. a_cm equals external acceleration

Answer: (C)

When there are only internal forces and no external forces, the total external force on the system is zero. Newton’s second law for the center of mass tells us that F_ext = M a_cm, where M is the total mass. With F_ext = 0, it follows that M a_cm = 0, so a_cm = 0. This means the center of mass moves with a constant velocity (it could be moving, or at rest, but its speed and direction don’t change). Internal forces can rearrange how mass and internal energy are distributed, but they cannot change the overall motion of the center of mass in the absence of external pushes.

When there are only internal forces and no external forces, the total external force on the system is zero. Newton’s second law for the center of mass tells us that F_ext = M a_cm, where M is the total mass. With F_ext = 0, it follows that M a_cm = 0, so a_cm = 0. This means the center of mass moves with a constant velocity (it could be moving, or at rest, but its speed and direction don’t change). Internal forces can rearrange how mass and internal energy are distributed, but they cannot change the overall motion of the center of mass in the absence of external pushes.