Let a particle moves with constant angular speed ω along a circular path of radius 'a'. The foot of the perpendicular drawn from the position of the particle on the diameter of circular path executes S.H.M.
When the particle moves from position P1 to P2 in time t, the displacement of Q (foot of the perpendicular drawn from the position of the particle on the diameter of the circle) executing SHM from ΔOP2 is given as
or, OQ = OP2 sinθ
y = a sinθ
As θ = ωt
The equation of the particle in SHM,
y = a sin ωt
and Velocity, v = dy/dt = d/dt (a sin ωt)
or, v = aw cos ωt
