Students analyzing a rigid body in static equilibrium often choose different points…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Students analyzing a rigid body in static equilibrium often choose different points about which to calculate torques, yet they obtain consistent physical predictions.
Consider a uniform horizontal bar of length L and weight W that is supported at its left end by a pin hinge and at its right end by an unknown upward force F. The system is at rest in a vertical plane.
(a) Describe, in words, why any point can be selected as a pivot when applying the condition for rotational equilibrium of a body that is not accelerating.
(b) Write the torque equation about the hinge and solve for the magnitude of the upward force F in terms of W and L.
(c) Repeat the calculation in part (b) using a pivot located at the bar’s center. Show explicitly that the resulting expression for F is identical to that obtained in part (b).
(d) Reflect on your results and explain how they support the statement you made in part (a).