# Looks are sceptical!

Classical Mechanics Level 5

A disc of radius $$\text R$$ is spun to an angular speed $$\omega$$ about its axis and then imparted a horizontal velocity of magnitude $$\omega\text R/4$$ at $$t = 0$$ with its plane remaining vertical.

The coefficient of friction between the disc and the plane is $$\mu$$. The sense of rotation is anticlockwise and linear speed is in forward direction. Find the time taken by the disc to return to its initial point.

Details and Assumptions:

• If your answer is $$\text T$$. Then define $$f = \mu g\text T/\omega R$$, where $$g$$ is the acceleration due to Gravity on earth.

• If $$f = a/b$$ for positive co-prime integers $$a,b$$.

Find the value of $$a+b$$.

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