The magnitude of displacement of a particle moving in a circle of radius a with constant angular speed `omega` varies with time `t` as

Explanation

`vec(L) = vec(r) xx vec(p)`
As linear momentum `(vec(p))` is along the tangent, hence `vec(r) xx vec(p) = rp hat(n)`, where `hat(n)` is the unit vector perpendicular to the plane of the circle.
`rArr" "|vec(L)| = mvr = m omega r^(2)`