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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.
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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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