Which statement correctly relates external forces to the acceleration of a system's center of mass?

Which statement correctly relates external forces to the acceleration of a system's center of mass?

• A. The net external force equals the total mass times the acceleration of the center of mass: F_ext = M a_cm.
• B. Internal forces determine a_cm regardless of external forces.
• C. External forces only affect rotation, not translation of a_cm.
• D. Work done by external forces equals the change in kinetic energy of the center of mass.

Answer: (A)

The key idea is that how a system moves as a whole is set by external forces, not by forces inside the system. Newton’s second law for a system says the sum of external forces acting on the system equals the total mass M times the acceleration of the center of mass, so F_ext = M a_cm. This means the center of mass accelerates in response to the net external push or pull, as if all the mass were concentrated at that point. Internal forces (the forces between parts of the system) cancel out when you add them up, so they don’t determine the center-of-mass acceleration. They can shuffle energy and motion between parts, but the overall translation of the system is driven by external forces. External forces can also impart rotation, but that doesn’t negate the translation: the center of mass still follows a_cm = F_ext / M under the net external force. The statement about work is a bit imprecise; the work done by external forces changes the total kinetic energy of the system, not solely the kinetic energy of the center of mass.

The key idea is that how a system moves as a whole is set by external forces, not by forces inside the system. Newton’s second law for a system says the sum of external forces acting on the system equals the total mass M times the acceleration of the center of mass, so F_ext = M a_cm. This means the center of mass accelerates in response to the net external push or pull, as if all the mass were concentrated at that point.

Internal forces (the forces between parts of the system) cancel out when you add them up, so they don’t determine the center-of-mass acceleration. They can shuffle energy and motion between parts, but the overall translation of the system is driven by external forces.

External forces can also impart rotation, but that doesn’t negate the translation: the center of mass still follows a_cm = F_ext / M under the net external force. The statement about work is a bit imprecise; the work done by external forces changes the total kinetic energy of the system, not solely the kinetic energy of the center of mass.