Acooling fan is turned off when it is running at 850 rev/min. it turns 1500 revolutions before it comes to a stop. (a) what was the fan's angular acceleration, assumed constant? (b) how long did it take the fan to come to a complete stop?

The fan's angular acceleration assumed constant is -0.42rad/s²

The time it takes the fan to come to a complete stop is 211.90secs

In order to get the fan's angular acceleration, we will use the equation of rotation is expressed as:

ω² = ω₀² + 2 α θ where;

ω is the final angular velocity

ω₀ is the initial angular velocity

α  is the angular acceleration

θ is the angle

Since the body comes to rest, hence ω = 0

θ = 1500 x 2 x π

θ = 9424.78 rad

Substitute the given parameters to get the angular acceleration

b) Next is to get the time it takes for the fan to stop

Hence the time it takes the fan to come to a complete stop is 211.90secs

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The angular acceleration of fan is .

The fan will take 5.36 seconds to stop completely.

Given data:

The number of rotation made by fan per minute is, .

The number of revolutions is, .

(a)

The angular displacement made by the fan is,

And, angular speed at initial is,

Now, apply the third rotational equation of motion as,

Thus, the angular acceleration of fan is .

(b)

Applying the first rotational equation of motion to obtain the time taken to stop as,

Thus, the fan will take 5.36 seconds to stop completely.

Learn more about the rotational equation of motion here:

link

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