The wheel of a water mill with a diameter of 4m makes 30 revolutions in 2 minutes.

The wheel of a water mill with a diameter of 4m makes 30 revolutions in 2 minutes. Determine the speed of rotation of the wheel?

Initial data: D (diameter of a wheel of a water mill) = 4 m; t (wheel rotation time) = 2 min; N (number of wheel revolutions in time t) = 30 revolutions.

SI system: t = 2 min = 2 * 60 s = 120 s.

1) Determine the frequency of rotation of the wheel of the water mill: ν = N / t = 30/120 = 0.25 rev / s.

2) Linear speed of the water mill wheel: V = 2 * Π * R * ν = 2 * Π * 0.5D * ν = 2 * 3.14 * 0.5 * 4 * 0.25 = 3.14 m / s …

3) The angular speed of the water mill wheel: ω = 2 * Π * ν = 2 * 3.14 * 0.25 = 1.57 rad / s.