A smooth bead B of mass 0.3 kg is threaded on a light inextensible string of length 0.9m. One end of the string is attached to a fixed point A, and the other end of the string is attached to a fixed point C which is vertically below A. The tension in the string is TN, and the bead rotates with angular speed ω rad s^-1 in a horizontal circle about the vertical axis through A and C.

i. Given that B moves in a circle with centre C and radius 0.2m, calculate ω, and hence find the kinetic energy of B.

ii. Given instead that angle ABC= 90°, and that AB makes an angle tan^-1(1/2) with the vertical, calculate T and ω.