Four forces act in the x–y plane on a small rigid plate whose centre of mass is located at the origin O. The forces are applied at the following points and act for a short interval:
• F1=(5+2t)N along the +y-direction at the point (0.30 m, 0).
• F2=8N along the −x-direction at the point (0, 0.20 m).
• F3=4N along the −y-direction at the point (−0.25 m, 0).
• F4=6N along the +x-direction at the point (0, −0.15 m).
Here t is the time in seconds measured from the instant the forces start acting.
(i) Derive the expression for the instantaneous net torque about the origin O as a function of time t, clearly indicating the sign convention for clockwise and anticlockwise torques.
(ii) Calculate the magnitude and sense of the net torque at t=2s.
(iii) Determine the net torque of the same four forces at t=2s about the point P located at (0.20 m, 0) and compare its value with that obtained about O.
(iv) Briefly explain why the net torques about O and P differ in numerical value for the same system of forces.