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!