Final answer:
To find the equivalent resultant force and couple moment at point O, calculate the individual moments and net force, with torques determined by cross products, and sum these to obtain the resultant torque and net force.
Step-by-step explanation:
The question pertains to finding an equivalent resultant force and couple moment at point O when a force F is applied. With F set to 20 lb or 20 N (as specified), to replace the force system, one must compute the moments produced by the forces about point O and then determine the net force acting on the system by vector addition of the individual forces. The torque or couple moment is found by taking the cross product of the position vector (from the point O to the point of application of the force) and the force vector itself, which gives a measure of the turning effect produced by the force about point O. If multiple forces are acting at different points on a body, like a flywheel, their torques can be calculated individually and then summed (algebraically) to obtain the net torque about the axis.
For the largest magnitude of torque, one should apply the force perpendicularly to the lever arm, which corresponds to a 90° angle with respect to the arm, as sin(90°) = 1 and gives the maximum value for the torque.