Can you think of a body that has the same moment of inertia for all possible axes? If so, give an example, and if not, explain why this is not possible. Can you think of a body that has the same moment of inertia for all axes passing through a certain point? If so, give an example and indicate where the point is located.
Solution 9DQ Moment of inertia is a property of an object which depends on the axis of rotation. By the use of symmetry, we can calculate it very easily for different objects. The most symmetric thing so far we know is a sphere. It’s moment of inertia is same for all possible axis passing through it’s centre. But for any other axes, it is not true. The moment of inertia is, I = m r . i i i If the change of axis does not affect the mass distribution to any point times the square of position vector, then it would be same. We saw that it could not happen even for the most symmetric object. So, it is not true. There is no such object whose moment of inertia would be same for any chosen axis. For sphere, all the axes passing through it’s centre, the moment of inertia is same.