There is a fixed half cylinder of radius R on a horizontal table. A uniform rod of length `2R` leans against it as shown. At the instant shown, `theta = 30^(@)` and the right end of the rod is sliding with velocity `v`.

(a) Calculate the angular speed of the rod at this instant.
(b) Find the vertical component of the velocity of the centre of the rod at this instant.

Answer

(a) `omega = (v)/(2 sqrt3R)`
(b) `v_(y) = (v)/(4) (darr)`