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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.
Solution
According to the diagram, where weight of the door acts along the negative y-axis.
Torque is not produced by weight about the y-axis.
Because the direction of weight is parallel to the y-axis (axis of rotation).
A force can produce torque only along the direction normal to itself because f = r × F. So when the door is in the xy-plane, the torque produced by gravity can only be along ±z-direction never about an axis passing through the y-direction.
Hence, the weight will not produce any torque about the y-axis.
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