Physics tangential speed of a ceiling fan

[lina29]

An electric ceiling fan with blades of diameter 0.720 m is rotating about a fixed axis with an initial angular velocity of 0.240 rev/s. The angular acceleration is 0.899 rev/s^2.

C- What is the tangential speed of a point on the tip of the blade at time t = 0.201 s?

D- What is the magnitude of the resultant acceleration of a point on the tip of the blade at time t = 0.201 s?

I am currently stuck on part c. I though in order to find the tangential speed I would use v=rw which would be (.720/2)(.240)(2pi)=.543

However, it says the answer is incorrect

 

[cepheid]

The problem is that you're using the original ω at t = 0. But the rotation speed is not constant, due to the angular acceleration. It is increasing. First you need to figure out what ω is at t = 0.201 s, and then use v = ωr.

 

[lina29]

For c I got .952 which was correct.

For part d I know I need to find the sqrt of the centripetal acceleration^2 + tangential acceleration^2

For centripetal acceleration I use the tangential speed^2/R->(.952)^2/.36=2.518

For tangential acceleration I use the radius^angular acceleration->.36^.899=.399

so the sqrt of 2.518^2+.399^2=2.549

Would that be correct?
I'm on my last attempt so I'd like to be positive before I put it in

 

[cepheid]

Umm, no, for the tangential acceleration, it should be:

a_tang = rα

where α is the angular/rotational acceleration.

Hence (a_tang)² = r²α²

Your expression for the centripetal (a.k.a radial) acceleration looks fine.