Question

Three uniform rods each of mass m and length l are joined to form an equilateral triangle in horizontal plane as shown. Find angular impulse required to rotate the triangle about an axis passing through A and perpendicular to the plane of triangle, with constant angular speed.

Answer 1

The moment of inertia of a single rod about an axis passing through its center and perpendicular to it is

$\frac{1}{12}M{L}^2$

That of each side of the equilateral triangle about an axis passing through the triangle's center and perpendicular to its plane is

$\frac{1}{12}M{L}^2+M{\left(\frac{L}{2\sqrt{3}}\right)}^2=\frac{1}{6}M{L}^2$

(by the parallel axis theorem).

The moment of inertia of the triangle about this axis is

$3\times \frac{1}{6}M{L}^2=\frac{1}{2}M{L}^2$