From the instant the force is applied , we should use two formulas to help us understand what physics is at play.
So we want to know how force is related to acceleration, and specifically centripital acceleration. Luckily , physics is described by mathematics , which have very specific, and strict rules, and definitions.
Let’s understand general force first,
Force = massxacceleration
re-arranging , acceleration = Force / mass
Providing force , is non zero, we will have acceleration (tangential) over time , so let’s break down the centripital formula in the same way,
Centripetal acceleration is the rate of change of tangential velocity.
Then if we are now looking at “a change” in the tangential velocity vector , at time = 0 , there is no change , as we need two points in time to find a difference.
velocity is distance over time = d/ t
so we need Fc = mac = m v^2/ r = m*angularFrequency^2*r
Hence , the question you need to ask is,
Has the tangential velocity changed over time ? Has the direction of travel changed?
When we consider calculus , and taking a derivative , what we are doing is finding the instantaneous rate of change. So providing you have non-zero figures , you will have non-zero centrifugal acceleration.
Hopes this helps you get started thinking about how to approach your problem