Question

When a fan is at its highest setting, the fan blade is rotating at 150 Hz. When the fan is turned down to its next lowest setting, the fan blade uniformly decelerates at 12 cycles/s2 until it reaches 60 Hz. Through how many cycles does the fan blade rotate over this interval

Answer 1

Step-by-step explanation:

150(2π) = 300π rad/s

60(2π) = 120π rad/s

-12(2π) = -24π rad/s²

ωf² = ωi² + 2αθ

θ = (ωf² - ωi²) / 2α

θ = ((120π)² - (300π)²) / 2(-24π)

θ = -75600π²/ -48π

θ = 1575π

θ = 1575π / 2π = 787.5 cycles