Moment of inertia help, please

[*best&sweetest*]

This should be simple but I'm not sure whether I'm doing it right or not...
I have a rod rotating about its edge #1. Rod's length is L and its mass is M. There is a point mass m on the rod, 3/4 L away from the edge #1, and on the other edge (#2) there is a sphere of radius R and mass m1. I need to find the moment of inertia of the whole system. I know that I need to use parallel axis theorem for the point mass, but what should I do with the sphere?
Is it I = (1/3) ML^2 + m (0.75L)^2 + m1*(L)^2 + (2/5)m1*R^2
or I = (1/3)ML^2 + m (0.75L)^2 + (2/5)m1*R^2?
I think it is the first option, but I'm not sure.
Thank you!

 

[PhanthomJay]

This should be simple but I'm not sure whether I'm doing it right or not...
I have a rod rotating about its edge #1. Rod's length is L and its mass is M. There is a point mass m on the rod, 3/4 L away from the edge #1, and on the other edge (#2) there is a sphere of radius R and mass m1. I need to find the moment of inertia of the whole system. I know that I need to use parallel axis theorem for the point mass, but what should I do with the sphere?
Is it I = (1/3) ML^2 + m (0.75L)^2 + m1*(L)^2 + (2/5)m1*R^2
or I = (1/3)ML^2 + m (0.75L)^2 + (2/5)m1*R^2?
I think it is the first option, but I'm not sure.
Thank you!

Option 1 loooks correct, but actually, you used the parallel axis theorem for the sphere, not the point mass, which is correct.

 

[kyle8921]

I would suggest reviewing the definition of moment of inertia and the parallel axis theorem to ensure you are using the correct equations and understanding the concepts correctly. It is important to accurately represent the physical properties and dimensions of the system in your calculations.

In this case, the moment of inertia for the rod would be (1/3)ML^2, and for the point mass it would be m(0.75L)^2. However, for the sphere, the moment of inertia would be (2/5)m1R^2, not m1L^2. This is because the sphere is rotating about its own center of mass, not about the edge of the rod.

Therefore, the correct equation for the moment of inertia of the entire system would be I = (1/3)ML^2 + m(0.75L)^2 + (2/5)m1R^2. It is important to note that the moment of inertia of the point mass and the sphere cannot be combined into one term, as they are rotating about different axes.

I would also suggest double-checking your calculations to ensure you are using the correct units and that your final answer makes physical sense. If you are still unsure, it may be helpful to consult with a colleague or refer to a trusted resource for further clarification.

Remember, accuracy and attention to detail are crucial in scientific calculations. Good luck!