Electric ceiling fan

1. teenholiday

4
1. The problem statement, all variables and given/known data
An electric ceiling fan is rotating about a fixed axis with an initial angular velocity of 0.290 rev/s. The angular acceleration is 0.888 rev/s^2. Its blades form a circle of diameter 0.740 m.

Through how many revolutions has the blade turned in the time interval 0.208 s from Part A?

2. Relevant equations

theta (t) = theta (0) + w (0) t+ .5 at^2

3. The attempt at a solution

ngular velocity = .475 rev/ sec

.475 rev/s * .208 s = .0988 rev

2. alphysicist

2,249
Hi teenholiday,

Why didn't you use the equation you have listed under "Relevant equations" in your post?

(In your work, you found the final velocity, and then you found the number of revolutions it would have taken if it had been rotating at that final velocity the entire time; but I don't think that is what's happening in this problem.)

3. HallsofIvy

40,367
Staff Emeritus
How did you arrive at this? You were told that the initial angular velocity was .290 rev/s and the angular velocity is NOT a constant!

That is assuming a constant angular velocity which is not true. I'm with alphysicist: why not use the formula by have under "relevant equations"?

You could also use a different method: in general, with constant acceleration, the average velocity is just the arithmetic average of the initial velocity and the final velocity. You are told that the initial velocity is .475 rev/sec. It it accelerates at 0.888 rev per second per second for .208 seconds, how much will the angular velocity increase by? So what will be the final angular velocity? And then what is the average velocity? Using that average angular velocity, how many revolutions will be made in .208 seconds? You might try using both methods and see if you get the same answer.

4. teenholiday

4
^^

thanks for the alternative method.

i had tried using the relevant equation, but i must have been tired or something, because i kept on getting the wrong answer.

i got it now though. thanks.