Question

An anemometer for measuring wind speed consists of four metal cups, each of mass m = 131 g, mounted on the ends of four essentially massless rods of length R= 0.31 m. The rods are at right angles to each other and the structure rigidly rotates at f = 12 rev/s. Treat the cups as point masses. 1) What is the moment of inertia of the anemometer about the axis of rotation?

Answer 1

The total moment of inertia is the sum of m r² for each point mass, that is the sum of each point mass times the square of its distance from the axis.

Because the rods are massless, they do not contribute to the moment of inertia of the system.

The problem reduces to four point masses of m = 0.131 kg rotating at a distance of R = 0.31 m around an axis of rotation.

The speed of rotation is irrelevant to calculating the moment of inertia.

The moment of inertia is then:

I = 4 m r²

= 4 (0.131 kg)(0.31 m)²

= 0.050 kg.m²