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Question

A door is hinged at one end and is free to rotate about a vertical axis (Figure). Does its weight cause any torque about this axis? Give reason for your answer.
1793806_97449e235bfa4a2aa4c9a18d213f74b3.png

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Solution

Here axis of rotation of door is along Yaxis and door is in xy plane and force F can be applied along ±zaxis, the torque is experience by door. So a force can produce torque only along axis in the direction normal to force. Force due to gravity of door is parallel to the axis of rotation. So cannot produce torque along yaxis. Gravity due to door is along yaxis. So it can rotate the door in axis along ±zaxis.
Hence the weight of door cannot rotate the door along yaxis.

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