An airplane propeller slows from 14 rad/s to 1.3 rad/s as the propeller completes 14 revolutions. Find the angular acceleration of

Question

the propeller when it is a constant value.

Answer 1

We can use the formula for angular acceleration:

α = (ωf - ωi) / t

where ωi is the initial angular velocity, ωf is the final angular velocity, and t is the time taken to change between the two velocities.

In this case, ωi = 14 rad/s, ωf = 1.3 rad/s, and the propeller completes 14 revolutions, or 28π radians, during this time. So we have:

t = 28π / (ωi - ωf)
t = 28π / (14 rad/s - 1.3 rad/s)
t ≈ 6.39 s

Now we can use the formula to find the angular acceleration when the propeller is at a constant velocity:

α = (ωf - ωi) / t
α = (1.3 rad/s - 14 rad/s) / 6.39 s
α ≈ -2.04 rad/s²

We get a negative value for the angular acceleration because the propeller is slowing down. If it were speeding up, we would get a positive value.