An airplane propeller slows from 14 rad/s to 1.3 rad/s as the propeller completes 14 revolutions. Find the angular acceleration of the propeller assuming that it is a constant value.
To find the angular acceleration of the propeller, we can use the equation:
angular acceleration (α) = (final angular velocity (ωf) - initial angular velocity (ωi)) / time (t)
First, let's convert the number of revolutions to radians:
1 revolution = 2π radians
So, 14 revolutions = 14 * 2π radians = 28π radians
The initial angular velocity (ωi) is 14 rad/s, and the final angular velocity (ωf) is 1.3 rad/s.
Now, we need to find the time (t) it takes for the propeller to complete this change in angular velocity. We can use the formula:
ωf = ωi + αt
Substituting the known values:
1.3 rad/s = 14 rad/s + αt
Simplifying:
-12.7 rad/s = αt
Now, we can substitute the value of t into our equation for angular acceleration:
α = (1.3 - 14) rad/s / (-12.7 rad/s)
Simplifying:
α = -12.7 rad/s / -12.7 rad/s
α = 1 rad/s^2
Therefore, the angular acceleration of the propeller is 1 rad/s^2.