The vacuum cleaner’s armature shaft S rotates with an angular acceleration of α = 4ω3/4 ra...

The vacuum cleaner’s armature shaft S rotates with an angular acceleration of α = 4ω3/4 rad/s2, where ω is in rad/s. Determine the brush’s angular velocity when t = 4 s, starting from ω0 = 1 rad/s, at θ = 0. The radii of the shaft and the brush are 0.25 in. and 1 in., respectively. Neglect the thickness of the drive belt.