Tangential and centripetal acceleration problem

[r_swayze]

A windmill starts from rest and rotates with a constant angular acceleration of 0.25 rad/s2. How many seconds after starting will the magnitude of the tangential acceleration of the tip of a blade equal the magnitude of the centripetal acceleration at the same point?

I don't exactly know where to start with this problem. Wouldnt I need the radius to solve for the tangential acceleration as well as the centripetal acceleration?

 

[Delphi51]

It might work out without r. Give it a try! I suggest you begin with putting that condition into symbols:
tangential acceleration = centripetal acceleration
rα = v²/r (pardon the poor alpha character after the first r)
Fill in the details and see if the r's cancel out!

 

[Andrew Mason]

A windmill starts from rest and rotates with a constant angular acceleration of 0.25 rad/s2. How many seconds after starting will the magnitude of the tangential acceleration of the tip of a blade equal the magnitude of the centripetal acceleration at the same point?

I don't exactly know where to start with this problem. Wouldnt I need the radius to solve for the tangential acceleration as well as the centripetal acceleration?

No. You have to work it out to see why.

What is the tangential acceleration (convert angular acceleration to tangential acceleration - use r for the radius).

Now, write out the expression for centripetal acceleration of a mass located at the tip in terms of angular speed.

At what speed does the centripetal acceleration equal the tangential acceleration?

AM

 

[r_swayze]

I don't see how the r's can cancel out with ra = v^2/r

And how can I covert angular acceleration to tangential acceleration?

 

[Delphi51]

It was rα = v²/r where the 2nd character is an alpha, angular acceleration.
No r's cancel at this point, but you are given that α = .25 and of course v = rω.
Since it is constant angular acceleration, you can also get a value for ω as a function of time . . . just keep working on that equation with these details and see what happens.