[Physics] How torque and friction cause wheel to roll

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I apologize if this question has been answered before, but I did not find the explanation that I needed.

If a torque is applied to a wheel situated on a frictional surface, what forces cause the wheel to roll?

I know that if P is the contact point, the static frictional force counteracts the torque, making P stationary with respect to the surface.

What are the forces that cause the translation motion and how can I compute them?

EDIT:
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I know that in order for it to roll, the acceleration at point P should be equal to the translational acceleration.

Best Answer

You can always imagine torque as being represented by two opposing forces at either side of the object. In this case imagine the torque being generated by two forces of magnitude F at the top and bottom of the disk, the top one pointing forwards and the bottom one, backwards.

In order to generate torque $\tau$, these two forces must be of magnitude $\frac{\tau}{2r}$, where $r$ is the radius of the disk. This is so that $2Fr=\tau$.

Now the force at the bottom is counteracted by friction (of magnitude $\frac{\tau}{2r}$) leaving the top force unopposed and generating the forward motion.

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