The cyclist was driving at a speed of 25.2 km / h. How many revolutions did a wheel with a diameter

The cyclist was driving at a speed of 25.2 km / h. How many revolutions did a wheel with a diameter of 10 cm make in 10 minutes?

Data: V (speed at which the cyclist was riding) = 25.2 km / h; D (wheel diameter) = 10 cm; t (movement time) = 10 min.

SI system: V = 25.2 km / h = 25.2 * 1000/3600 = 7 m / s; D = 10 cm = 0.1 m; t = 10 min = 10 * 60 s = 600 s.

We express the number of wheel revolutions from the formula: V = 2 * Π * R / T, where R (wheel radius) = 0.5 * D and T (rotation period) = t / N.

V = 2 * Π * 0.5 * D / (t / N) = Π * D * N / t and N = V * t / (Π * D).

Calculation: N = V * t / (Π * D) = 7 * 600 / (3.14 * 0.1) = 13,378 revolutions.