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Question 1

What is the moment of inertia for a solid cylinder or disc about its symmetry axis?

Answer 1

I = (1/2) MR²

M is the mass and R is the radius.

Question 2

What is the moment of inertia for a solid cylinder about its central diameter?

Answer 2

I = (1/4) MR²

This is based on the distribution of mass along the diameter.

Question 3

What is the moment of inertia for a hoop about its symmetry axis?

Answer 3

I = MR²

The mass is concentrated at a fixed distance from the axis.

Question 4

What is the moment of inertia for a hoop about its diameter?

Answer 4

I = (1/2) MR²

This considers the mass distribution along the diameter.

Question 5

What is the moment of inertia for a solid sphere?

Answer 5

I = (2/5) MR²

A solid sphere has its mass distributed throughout its volume.

Question 6

What is the moment of inertia for a thin spherical shell?

Answer 6

I = (2/3) MR²

The mass is distributed on the surface of the shell.

Question 7

What is the moment of inertia for a rod about its center?

Answer 7

I = (1/12) ML²

M is the mass and L is the length of the rod.

Question 8

What is the moment of inertia for a rod about its end?

Answer 8

I = (1/3) ML²

This accounts for the mass distribution from the end point.