Question

Question #33405

Answer 1

The Moment of Inertia of a rigid body is defined as function of the amount of torque required to rotate that body around a particular axis. This is a simple consequence of Newton's Laws. Angular momentum, much like linear momentum is always conserved. In analogy to Newton's First Law, we might say that an object which is not spinning will stay not spinning unless acted upon by an external torque. This also applies to the predilection of object which is spinning to keep spinning.

Here is a simple explanation of a Moment of Inertia:
A pencil can be easily rotated about an axis along it's center from the tip to the eraser. But it take more torque to spin it about its center perpendicular to this axis. The moment of inertia about an axis perpendicular to the lead is higher than the moment of inertia about an axis along the lead.

What would it mean for an object to have a negative Moment of Inertia? This would imply that the torque applied to spin it in one direction would spin it in the opposite direction. The angular acceleration `alpha` is in direct proportion to the applied torque `tau` and inversely proportional to the object's Moment of Inertia `I`.

`alpha = tau/I`

Moment of Inertia, like mass, cannot be negative. Consider the implications of negative mass to Newton's Second Law.

`a = F/m`

A force `F` in one direction would cause mass `m` to accelerate `a` in the opposite direction.