# Calculate Angular Acceleration of Cooling Fan | 850 rev/min to Stop

• vinny380
In summary, the fan's angular acceleration can be calculated using the equation 2 \alpha \Delta \theta = \omega_f^2 - \omega_i^2, where \omega_i is the initial angular velocity and \omega_f is the final angular velocity when the fan stops. The time it takes for the fan to stop can be calculated using the equation a = \frac{\Delta \omega}{\Delta t}, where a is the acceleration, \Delta \omega is the change in angular velocity, and \Delta t is the time it takes for the fan to stop. To find the change in angular velocity, we can use the equation 2\pi f = \omega, where f is the frequency of the fan.
vinny380
Question: A cooling fan is turned off when it is running at 850 rev/min. It turns 1500 revolutions before it comes to a stop.
A. What is the fan's angular acceleration?
B. How long does it take for the fan to come to a stop?

I am pretty stumped with this question. I know that I have to use the equation a= omega (angular velocity)/ time ...and angular velocity= Change in theta/time ...but i am not sure how to go about the problem ...can anyone help?

You said it: $$\alpha = \frac{\Delta \omega}{\Delta t}$$
Be careful though. 850rev/min is the frequency, NOT the angular velocity. But these are related by $$2\pi f = \omega$$.

thanks Euclid ... so I got an angular velocity of 5340 rev/sec ...but how would I figure out the time since a= change in angular velocity/time

i am really confused... i don't even know if i got the angular velocity right ... 5340 revolutions per second seems so much ...

?

Firstly, angular velocity is in units of 1/s or rad/s, not rev/sec.

Secondly, sorry for misleading you, I read the question wrong. You want to use the equation:

$$2 \alpha \Delta \theta = \omega_f^2 - \omega_i^2$$

How many radians does 1500 revolutions correspond to?

would 1500 revolutions = 3000 radians? or am i totally off

i know that the acceleration must be negative ... considering wf=0 ... and -w1^squared= 2Atheta

## 1. How do you calculate angular acceleration?

To calculate angular acceleration, you need to know the change in angular velocity and the time it takes to change. The formula is: angular acceleration = (final angular velocity - initial angular velocity) / time. In this case, the final angular velocity is 0 (since the fan is stopping), the initial angular velocity is 850 rev/min, and the time is not specified. So, the angular acceleration cannot be calculated with the given information.

## 2. What is the initial angular velocity of the cooling fan?

The initial angular velocity of the cooling fan is 850 rev/min, as stated in the question.

## 3. How long will it take for the cooling fan to stop?

To determine the time it takes for the cooling fan to stop, you need to know the angular acceleration. However, since the angular acceleration cannot be calculated with the given information, the time it takes to stop cannot be determined.

## 4. Can the angular acceleration of the cooling fan be negative?

Yes, the angular acceleration of the cooling fan can be negative. A negative angular acceleration means that the fan is slowing down or decelerating.

## 5. How does the angular acceleration of the cooling fan affect its stopping time?

The angular acceleration of the cooling fan is directly proportional to its stopping time. This means that a higher angular acceleration will result in a shorter stopping time, while a lower angular acceleration will result in a longer stopping time. However, the exact relationship between angular acceleration and stopping time cannot be determined without knowing the time it takes for the fan to stop.

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