# If a cylinder skids what can we say about the work of friction on it

A cylinder skids on a rough horizontal plane and we know that a frictional force will act on it. What can we say about the work done by friction?

I believe that the frictional force is forward, the displacement of skidding element is forward therefore the work should be positive.

But from another post I've come to know that the work done by friction will be negative , otherwise we run into inconsistency. But how can that be,how can friction do negative work here?

I'd be grateful if someone helped me.

• Friction will always oppose relative motion , how can work done by it be positive? Commented Jan 10, 2021 at 10:36
• When it's slipping with $\omega r>V_{cm}$ the velocity of contact point is backwards so the force will be forward Commented Jan 10, 2021 at 10:55

## 1 Answer

I believe that the frictional force is forward.

Why? This is only true $$v_{com}<\omega R$$.

Note that work done is defined as :

$$dW=F\cdot ds$$

where $$ds$$= Point of application of force. It is not the displacement of centre of mass.

In the case of skidding , friction will always try to oppose the relative motion of the point of contact and the ground . Thus it will act in the opposite direction of the motion of point of contact. hence , work done by friction is negative in case of skidding.

NB body can move forward and the work done by friction still can be negative.

I hope this helps.

• Thank you, but imho it's the opposite of ' $Vcom>ωR$ Commented Jan 10, 2021 at 12:08
• @YasirSadiq if vcom > wR then point of contact will have a forward velocity. To oppose that friction will act in backward direction. Commented Jan 10, 2021 at 12:10
• Agreed......... Commented Jan 10, 2021 at 12:10