Calculating Distance and Acceleration of a Wind Turbine Blade Tip

[dmoney123]

Homework Statement

During a sustained wind the blades on a two blade horizontal–axis wind turbine is
turning with an angular velocity of 5 rad/s. If initially the blades have an angular velocity of 2
rad/s, determine the distance point P on the tip of the blade has traveled in 3.0 seconds. Also,
what is the magnitude of the acceleration of this point when t = 3.0 seconds.

Point P is the Tip of the blade. Radius is 4.55m.

Homework Equations

[/B]
where w=omega (angular velocity in rad/s)

w=v/r

L=Iw

The Attempt at a Solution

[/B]
Initially we have 2rad/s

wr=v

2rad/s * 4.55m=9.1 m/s

5rad/s *4.55m= 22.75m/s

I don't understand how to answer the question considering there is no information given on how fast it accelerates to 5rad/s. Does it instantly go to 5rad/s

Any insight?

 

[haruspex]

It's not well worded but I think you are supposed to take the 5 m/s as the limiting speed as the duration of the sustained stronger wind tends to infinity. If so, you need to reason out how the angular velocity will increase with time. It will not be constant acceleration. Any ideas?