# Ceiling Fan Blade Acceleration and Angle Calculation

• eiriyuki
You use the average angular acceleration when solving for θ. You need to find the angular velocity at a given point in time.f

#### eiriyuki

1. The blades of a ceiling fan have a radius of 0.318 m and are rotating about a fixed axis with an angular velocity of +1.48 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of +2.22 rad/s2. After 0.394 s have elapsed since the switch was reset, what is (a) the total acceleration (in m/s2) of a point on the tip of a blade and (b) the angle between the total acceleration and the centripetal acceleration (See Figure)?

http://edugen.wiley.com/edugen/courses/crs2216/art/qb/qu/c08/w1590int.gif

## Homework Equations

I tried using equation $$\omega$$$$_{2}$$ = $$\omega$$$$^{2}_{o}$$ + 2$$\alpha$$$$\theta$$

## The Attempt at a Solution

This is the first time I have used the forums and I'm having a hard time putting in equations and things, so I apologize if the format is silly. I solved for theta in the above equation and my answers were 3.6509 (part a) rev and 14.153 (part b). I do not know if this is right, and if it is, I am not sure how to convert it into degrees so I can figure the position on the wheel.

This is the first time I have used the forums and I'm having a hard time putting in equations and things, so I apologize if the format is silly. I solved for theta in the above equation and my answers were 3.6509 (part a) rev and 14.153 (part b).

Why did you solve for θ? You don't have ω2. You need to find ω2.

Use the other equations of rotational motion.

Also, how does the tangential acceleration aT relate to the angular acceleration α?

How does the centripetal acceleration relate to ω2?

Wow, that is silly. I put my work for another problem I was having trouble with.

For this problem I used, total a=$$\sqrt{(rw^{2})^{2} + (r\alpha)^{2}}$$

I worked out the problem and got 0.99m/s$$^{2}$$, which was incorrect.

What value did you use ω?

What value did you use ω?

That's where you went wrong. You need to use the final angular velocity. It started out at 1.48 rad/s and then allowed to accelerate at 2.22 rad/s for 0.394s. How would you find the final angular velocity given the information?

That's where you went wrong. You need to use the final angular velocity. It started out at 1.48 rad/s and then allowed to accelerate at 2.22 rad/s for 0.394s. How would you find the final angular velocity given the information?

Would I use average angular acceleration?

w - w0 / t - t0