Solution: Question 12
Diagram: Pseudo Force Action
In the inertial frame, the body has an acceleration \( a \). Therefore, the net external force is not zero (\( \Sigma F = ma \)).
(a) The body is NOT in translational equilibrium.
In the non-inertial frame, the body is in total equilibrium. This means the sum of real torques plus the pseudo-force torque is zero.
The pseudo force \( -m\vec{a} \) acts effectively at the Center of Mass (COM).
Since the pseudo force acts through the COM, its torque about the COM is zero. Consequently, the sum of real external torques about the COM must also be zero. This holds true regardless of the frame.
(b) Net torque about mass centre is a null vector.
The torque of the pseudo force is zero about any point lying on its line of action (the line passing through COM parallel to acceleration). Thus, the net torque of real forces about any such point is also zero.
(c) Net torque about any point collinear with the line of acceleration is a null vector.
