A student pushes a rectangular classroom door that is hinged along one vertical edge.
(i) State the mathematical expression for the magnitude of the turning moment (torque) produced when a force F acts at a distance r from the hinge making an angle θ with the line AB drawn from the hinge to the point of application of the force.
(ii) Using the expression obtained in part (i), explain qualitatively why the turning effect is greatest when the force is applied perpendicular to the door surface.
(iii) Sketch a rough graph of the dimensionless ratio Frτ versus θ for 0∘≤θ≤180∘, clearly marking the angle at which the curve attains its maximum value.
a. State the mathematical expression for the magnitude of the turning moment (torque) produced when a force F acts at a distance r from the hinge making an angle θ with the line AB drawn from the hinge to the point of application of the force.