A disc is rotating with constant angular velocity `omega` in anticlockwise direction. An insect sitting at the centre (which is origin of our co-ordinate system) begins to crawl along a radius at time `t = 0` with a constant speed V relative to the disc. At time `t = 0` the velocity of the insect is along the X direction.
(a) Write the position vector `(vec(r))` of the insect at time ‘t’.
(b) Write the velocity vector `(vec(v))` of the insect at time ‘t’.
(c) Show that the X component of the velocity of the insect become zero when the disc has rotated through an angle `theta` given by `tan theta = (1)/(theta)`.

Answer

(a) `vec(r) = vt [cos (omegat)hati + sin (omegat)] hatj`
(b) `vec(V_(p)) = V [cos (omegat) - omegat sin (omegat)]`
`hati + V [sin (omegat) + omegat cos (omegat)] hatj`