Question

For a system of particles, if the external net force acting on the system is zero, the system's center of mass is:

• A. at rest
• B. moving at a constant velocity
• C. accelerating
• D. rotating

Hint:

This is a statement of the conservation of momentum for a system. If the net external force is zero, the total momentum of the system (\(M\vec{v}_{CM}\)) is conserved.

Answer 1

The Correct Option is B

Step 1: Recall Newton's second law for a system of particles. The net external force \(\vec{F}_{net, ext}\) acting on a system is equal to the total mass \(M\) of the system times the acceleration of its center of mass \(\vec{a}_{CM}\). \[ \vec{F}_{net, ext} = M \vec{a}_{CM} \]
Step 2: Apply the given condition. We are given that the net external force is zero, \(\vec{F}_{net, ext} = 0\). \[ 0 = M \vec{a}_{CM} \]
Step 3: Solve for the acceleration of the center of mass. Since the total mass \(M\) is not zero, the acceleration of the center of mass must be zero. \[ \vec{a}_{CM} = 0 \]
Step 4: Interpret the result. Zero acceleration means that the velocity of the center of mass, \(\vec{v}_{CM}\), does not change. This means the center of mass moves at a constant velocity. Being "at rest" is a special case of moving at a constant velocity where the constant velocity is zero. Option (2) is the more general and correct statement.