$[15]$ A uniform circular disk is spinning with an angular velocity $\backslash (\backslash$Omega $\backslash )$ about a diameter when a point $\backslash ($ P $\backslash )($not on the diameter about which the disk is spinning$)$ on its rim is suddenly fixed by a ball and socket joint. Prove that the subsequent velocity of the center is equal to $\backslash (1/5\backslash )$ of the velocity of the point P immediately before the fixing.