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.

 

[rwisz]

.

I would like to clarify that the tangential speed of a point on the tip of the blade is not constant and varies with time. Therefore, in order to find the tangential speed at a specific time t = 0.201 s, we need to use the equation v = rω, where r is the radius of the blade and ω is the angular velocity at that specific time.

Using the given values, we can calculate the tangential speed at t = 0.201 s as v = (0.720/2)(0.240 rev/s)(2π) = 0.544 m/s. Therefore, the tangential speed of the point on the tip of the blade at t = 0.201 s is 0.544 m/s.

For part D, we need to find the magnitude of the resultant acceleration of a point on the tip of the blade at time t = 0.201 s. This can be calculated using the formula a = rα, where r is the radius of the blade and α is the angular acceleration at that specific time.

Substituting the given values, we get a = (0.720/2)(0.899 rev/s^2) = 0.323 m/s^2. Therefore, the magnitude of the resultant acceleration of a point on the tip of the blade at t = 0.201 s is 0.323 m/s^2.

I hope this helps clarify the confusion and provides the correct answers for parts C and D. Remember, as scientists, it is important to use the correct equations and units in order to obtain accurate results.