Hello Bobbin

A bobbin rolls without slipping on a horizontal surface so that the velocity vv of the end of the thread (point AA) is directed along the horizontal. A board hinged at point BB leans against the bobbin making an angle 2x2x with the horizontal. The inner and outer radii of the bobbin are rr and RR respectively.

If the angular velocity ww of the board can be expressed in terms of xx as kv(sinx)2r+R\dfrac{kv(\sin x)^{2}}{r+R}, find the magnitude of kk.

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