Inspiring Calculation of Blade Revolutions
Calculating the revolutions of a fan blade as its angular velocity decreases involves using the equation:
Δθ = θi + ωit + (1/2)αt^2
where:
Δθ is the change in angular position,
θi is the initial angular position,
ωi is the initial angular velocity,
α is the angular acceleration,
t is the time taken for the change in angular velocity.
First, we find the angular acceleration:
α = (ωf - ωi) / t
After calculating, we find that the angular acceleration is -46.08 rad/s^2.
Using the formula for angular displacement, we get:
Δθ = 1500 rev/min * (2π rad/1 rev) * (1 min/60 s) * 2.5 s - (1/2) * (-46.08 rad/s^2) * (2.5)^2 = 39.9 rev
Hence, the fan blade undergoes 40 revolutions during the 2.5 seconds, which is not listed in the given options!
I hope this explanation inspires you to explore more about angular velocity and acceleration in physics!