Centripetal acceleration and tangential acceleration

[Maxo]

When having a circular acceleration motion, we have both tangential acceleration and centripetal acceleration.

The tangential acceleration is a_T=r*α where α=1/2*(ω_f-ω₀). So we can see tha a_T is dependent on both the initial angular velocity ω₀ and the final ω_f).

For centripetal acceleration, we instead have a_C=r*ω_f².

My question is, how come the centripetal acceleration is only dependent on the final angular velocity, and not the initial?
Is there a physical explanation for this?

 

[dauto]

First: α isn't 1/2*(ω_f-ω₀). The correct equation is α = (ω_f-ω₀)/(t_f-t₀).

Second: The equation above is the expression for the AVERAGE angular acceleration. If the circular motion is UNIFORMLY accelerated than you can use the average angular acceleration to calculate the tangential speed since angular acceleration is constant, otherwise you have to use the instantaneous angular acceleration - say α_f and the expression for tangetial acceleration becomes a_Tf = r α_f

 

[Maxo]

Ok thanks for the correction. But I still wonder why the centripetal acceleration is only dependent on the final angular velocity, and not the initial angular velocity. Is there a physical explanation for this?

 

[namanjain]

centripetal acceleration is caused to continue circular motion so at every point. so at that point it has to accelerate the mass toward center so as to change it direction.
now for at the point it has angular velocity omega then centripetal acceleration will vary with that only