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When a block is stationary on an inclined plane, the frictional force on the base of the block has a torque about the center of gravity of the block. However, the block does not rotate. Which force provides the opposing torque to that of friction? This opposing torque cannot be from gravity, since both components of the gravitational force on the block (parallel and perpendicular to the plane) pass through the center of gravity of the block and have no torque about it. Where does the opposing torque come from in order to keep the block from rotating? enter image description here

Toba
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  • I believe that it would make more sense if don't break the weight into it's components and instead mark the resultant of the Normal reaction and friction.Then consider it's line of action.This might help you understand why the block doesn't rotate. – AfiJaabb Jun 12 '20 at 19:40
  • The normal force can provide the necessary torque. https://physics.stackexchange.com/questions/314729/does-the-normal-reaction-shift-when-a-force-is-applied/314849#314849 – BowlOfRed Jun 12 '20 at 19:41
  • But the normal force is also acting through the center of gravity of the block so it has no torque about it. – Toba Jun 12 '20 at 20:11
  • No, the normal force is distributed over all the surface of contact between the block and the inclined plane. – GCLL Jun 13 '20 at 00:00
  • But the normal forces distributed over the surface of contact sum up to give a resultant single normal force acting through the center of gravity of the body. – Toba Jun 13 '20 at 01:05

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The torque due to friction here is balanced by torque due to normal reaction because the point of action of normal reaction changes.It changes due to torque due to friction, which tilts the block a little and the normal reaction does not act along the center of gravity enter image description here

The block looses some points of contact and thus normal reaction shifts downwards due to toppling effect of friction which inturn balances the torque due to friction.

Muzammil ahmed
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  • Thanks a lot Muzammil. Very good answer; introductory physics texts should emphasize that the normal reaction does not always act through the centre of gravity of a body. Most introductory texts I've come across assume it to act through the centre of gravity and do not consider cases where it doesn't. – Toba Aug 30 '20 at 00:37
  • @Thorbah you can tick the satisfied option if you are satisfied with my answer.If not others may write anwers to help you. – Muzammil ahmed Aug 31 '20 at 01:25