[SOLVED] Physics moment of inertia help?

Question

physics moment of inertia.

Three 210 g masses are connected to form an equilateral triangle with side lengths of 40 cm. The angle in between the masses is 60 degrees.

What is the triangles moment of inertia about the axis through the center?

What is the triangles kinetic energy if it rotates at 5.2 rev/s?

Answer 1

The Best Answer for the moment of inertia.

If the side length is 40 cm, then the height is

h = 40cm * √3/2 = 34.6 cm

(from years of looking at equilateral triangles)

The center is 1/3 of the way up the height, so the top is

r = (2/3)*34.6cm = 23 cm

away from the center. That means that all three corners are 23 cm from the center.

Then I = 3mr² = 3 * 0.21kg * (0.23m)² = 0.033 kg·m²

5.2rev/s * 2πrad/rev = 32.7 rad/s, so

KE = ½Iω² = ½ * 0.033kg·m² * (32.7rad/s)² = 18 J

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