Two masses, m1 and m2, are connected by a light rod of length L. Calculate the m

Question

Two masses, m1 and m2, are connected by a light rod of length L. Calculate the moment of inertia I of the system with respect to the axis going through mass m1 perpendicularly to the direction of L. Same for m2. Same for the axis going through the center of mass. Which of the results is the smallest?
Two masses, m1 and m2, are connected by a light rod of length L. Calculate the moment of inertia I of the system with respect to the axis going through mass m1 perpendicularly to the direction of L. Same for m2. Same for the axis going through the center of mass. Which of the results is the smallest?

Explanation / Answer

1. axis going through mass m1

I = m2*L^2

2. axis going through mass m2

I = m1*L^2

3. axis going through the center of mass

Center of mass of two objects will be:

let x be from m1, so

x = (m2*L)/(m1+m2)

and, I = m1*(x)^2 + m2*(L-x)^2

I could have simplified for you provided m1 = m2 or some values, this is also needed to determine which will be smallest.

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