Learning Forum

[kremella]

Why does the total sum of forces acting on a system always have to be equal to zero?

[Keyur Kanade]

Hi!

The total sum of forces acting on a system is equal to zero only if it is not accelerating i.e. it is in a static equilibrium. This is a consequence of the conservation of linear momentum law.

[kremella]

Thank you for the answer. Could you please explain what linear momentum is? And how does it lead to the condition that when a body is in static equilibrium the sum total of all forces acting on it should be zero?

[Keyur Kanade]

The linear momentum is defined as p=mv, where p is the linear momentum, m is the system mass, and v is the velocity. We can have conservation of linear momentum as long as the linear momentum stays constant in time. If you differentiate both sides of the above equation wrt time you would get dp/dt = m*dv/dt = m*a. Since dp/dt=0 for an isolated system for the momentum to be conserved, then m*a=force=0 i.e. net force on an isolated system has to be equal to 0.