text: The total acceleration to cause the block to slip is .53g, or 5.194 m/s^2.\n\nThe tangential acceleration is alpha*r = .50*.30 = .15 m/s^2 = At\nThe radial acceleration is r*w^2, where w = .5(alpha)t^2, so Ar = .30*.5*.50*t^2  Ergo, we have \n\n5.194 = root(.15^2 + .005625t^4)  Solving for t,\n\nt = 5.506 sec