Four particles, each of mass 0.20 kg, are placed at the vertices of a square wit

Question

Four particles, each of mass 0.20 kg, are placed at the vertices of a square with sides of length 0.56 m. The particles are connected by rods of negligible mass. This rigid body can rotate in a vertical plane about a horizontal axis A that passes through one of the particles. The body is released from rest with rod AB horizontal, as shown in the figure. (a) What is the rotational inertia of the body about axis A? (b) What is the angular speed of the body about axis A at the instant rod AB swings through the vertical position?

Explanation / Answer

The moment of intertia (or the rotational inertia) is

   So:   I = 0.2 *0.562   + 0.2 *0.562   + 0.2 * 0.7922 =   0.251 kg m2

The square loses potential energy as it drops, and gains KE.

So lost PE is   2mgh = 2 * 0.2 *9.8 * 1.12 = 4.39 Joules

So this must be the KE when AB is vertical. We know

    KE = (1/2) I 2     or

   2    =   2 K / I = 2 * 4.39 / 0.251=35

so          =   5.92  rad/sec

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