A cooling fan is turned off when it is running at 880 . It turns 1300 revolutions before it comes to a stop.
What was the fan's angular acceleration, assumed constant?
How long did it take the fan to come to a complete stop?
What are the units that go with the number 880? rpm?
-0.57
To determine the angular acceleration of the cooling fan, we need to use the formula:
θ = ω_i * t + (1/2) * α * t^2
where:
- θ is the total angular displacement (1300 revolutions in this case)
- ω_i is the initial angular velocity (880 revolutions per minute)
- α is the angular acceleration (what we're trying to find)
- t is the time it takes for the fan to come to a stop
First, let's convert the initial angular velocity from revolutions per minute to revolutions per second:
ω_i = 880 revolutions/minute * (1 minute/60 seconds) = 14.67 revolutions/second
Now, let's convert the total angular displacement to radians:
θ = 1300 revolutions * 2π radians/revolution = 2600π radians
Next, let's substitute these values into the formula:
2600π = (14.67 * t) + (1/2 * α * t^2)
We can simplify this equation to:
1300π = 7.335t + (0.5αt^2)
Since the angular acceleration is assumed to be constant, we can treat α as a constant and solve this equation as a quadratic equation.
To find the angular acceleration (α), we'd need more information. However, we can proceed to find the time it takes for the fan to come to a complete stop.
At the point when the fan comes to a complete stop, its final angular velocity would be 0. Therefore, we can set ω_f (final angular velocity) to 0 in the formula:
0 = ω_i + αt
Substituting the value of ω_i (14.67 revolutions/second) and rearranging the equation, we get:
αt = -14.67
Since we don't know the specific value of α, we can't solve for t. We would need more information to calculate the time it takes for the fan to come to a complete stop.