Windmill rotates with constant ang. accel. What time does Tangetial = Centripetal

[IAmPat]

Homework Statement

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.

Homework Equations

Vt = Tangetial Speed = r * w
At = Tangetial Acceleration = r * $$\alpha$$
Ac = Centripetal Acceleration = w²/r

The Attempt at a Solution

Not sure where to start with this one because I don't know the radius of the windmill.

At = Ac
$$\alpha$$ * r = w²/r
0.25*r = w²/r

 

[Undoubtedly0]

Greetings! Good start. You are right in saying that the tangential and centripetal accelerations will be equal when

$$a_{cen} = a_{tan}$$

$$\frac{v^2}{R} = R\alpha$$

But since v = Rω,

$$\frac{(R\omega)^2}{R} = R\alpha$$

$$\omega^2 = \alpha$$

Now just use the fact the $$\omega = \alpha t$$ to solve for time, $$t$$.