A constant force F acts on a horizontal uniform ruler AB at point A.
Case 1. The ruler is pivoted at the end B.
Case 2. Ruler is not pivoted.
(a) In which case is the moment of force greater? (Case 1 or Case 2)
(b) Give a reason for your answer in (a) above.
(c) In which case does the ruler exhibit both translational and rotational motion simultaneously? (Case 1 or Case 2)
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(a) The moment of force is greater in Case 1.
(b) Reason — The moment of a force is the product of the force and the perpendicular distance of its line of action from the axis of rotation.
In Case 1, the ruler turns about the pivot at the end B, so the perpendicular distance of the force F at A from the axis is the whole length AB.
In Case 2, the ruler is free, so it turns about its centre of gravity which lies at the middle of the uniform ruler. Hence the perpendicular distance is only $\frac{\text{AB}}{2}$.
Since the force F is the same in both cases and the perpendicular distance in Case 1 is twice that in Case 2, the moment of force is greater in Case 1.
(c) The ruler exhibits both translational and rotational motion simultaneously in Case 2, because the ruler is free to move, so the force makes its centre of gravity move forward (translational motion) and at the same time turns the ruler about the centre of gravity (rotational motion).