Question

The three 200 g masses in the figure (Figure 1) are connected by massless, rigid rods.  

Part A

What is the triangle's moment of inertia about the axis through the center?  

Express your answer to two significant figures and include the appropriate units.  

Part B

What is the triangle's kinetic energy if it rotates about the axis at 6.0 rev/s?  

Express your answer to two significant figures and include the appropriate units.

Answer 1

Answer 2

Let r be the distance in m of each mass from the centroid of the triangle.

r = (2/3)*median

r = (2/3)[sq rt(0.40^2 - 0.20^2)]

r = 0.231 m

We know that:

The moment of inertia, I of the system of particles is given by

I = 3*0.200*(0.231^2)

I = 0.032 kg m^2

w = 2*pi*5.4 = 33.929 rad/s

Kinetic energy, KE of the system is:

KE = 0.5*I*w^2

KE = 18.42 J