Question

A heavy flywheel rotating on its central axis is slowing down because of friction in its bearings. At the end of the first minute of slowing, its angular speed is 0.68 of its initial angular speed of 260 rev/min. Assuming a constant angular acceleration, find its angular speed (rev/min) at the end of the second minute.

Answer 1

ω₂ = 93.6 rev / min

Step-by-step explanation:

ω₀ = 260 rev / min

ω₁ = 0.68*ω₀ = 0.68*(260 rev / min) = 176.8 rev / min

ω₂ = ?

t₁ = 1 min

t₂ = 2 min

We can apply the equation:

ω₁ = ω₀ + α*t₁ ⇒ α = (ω₁ - ω₀) / t₁

⇒ α = (176.8 rev / min - 260 rev / min) / 1 min = - 83.2 rev / min²

then we can use the same formula, knowing the angular acceleration:

ω₂ = ω₀ + α*t₂ ⇒ ω₂ = (260 rev / min) + (- 83.2 rev / min²)*(2 min)

⇒ ω₂ = 93.6 rev / min