Centripetal acceleration and circular motion

[GeneralOJB]

My question is about the centripetal acceleration formula |a| = ω^2*r. If we keep the angular speed constant then why does increasing the radius increase the centripetal acceleration? I don't find this intuitive because the velocity vector is being turned by the same amount each second, if ω is constant.

Also is there an intuitive way to think about how the units (m/s^2) relate to circular motion?

 

[rcgldr]

The linear velocity = ω * r. If r increases, then so does the linear velocity. Using the other form for centripetal acceleration:

|a| = ω^2 * r = v^2 / r

If r increases by a factor "c" and ω remains constant, then:

|a| = ω^2 * c * r = (c * v)^2 / (c * r) = c * v^2 / r

 

[AlephZero]

If ω is constant, the particle has to get from one side of the circle to the other in the same amount of time, ∏ω seconds.

The distance traveled "across the circle" is proportional to r, so it makes sense that the acceleration has to be bigger when r is bigger.