An engineer places a small sample of a material on a horizontal disk whose surface is made of another material and then rotates the disk from rest with a constant angular acceleration of 4 rad/s2. assuming that the coefficient of static friction between the sample and disk is 0.2, what is the angular velocity of the disk at the time instant when the sample starts slipping on the disk?

When a vertical beam of light passes through a transparent medium, the rate at which its intensity i decreases is proportional to i(t), where t represents the thickness of the medium (in feet). in clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity i0 of the incident beam. what is the intensity of the beam "10" feet below the surface? (give your answer in terms of i0. round any constants or coefficients to five decimal places.)