Moment of Inertia
Moment of inertia is a measure of the difficulty of spinning something around. It depends on how the weight is balanced and how close it is to the center-line. Such as in case of merry-go-round when it is rotating, if all the kids sit near the middle, spinning becomes easier. But if they try to spin this to the edges, it gets more and more difficult. It is because the moment of inertia is higher when the mass is located far from the center. Consequently, the moment of inertia provides an answer to the question of how objects rotate and how they react to forces that try to either speed them up or slow them down. The moment of inertia formula is given as
I = ∑miri2
where,
- I is moment of inertia
- m is mass of particle
- r is distance from axis of rotation
Perpendicular Axis Theorem
Perpendicular Axis Theorem, also known as the perpendicular axes rule, is a theorem in physics that relates the moments of inertia of a two-dimensional object about three perpendicular axes. It is one of those very fundamental physics principles that we use to understand how the object in question changes its rotational path perpendicular to the plane of its symmetry. The perpendicular axis theorem is useful in simplifying calculations of moments of inertia for objects with known moments of inertia about axes lying in their plane.
Through this article, we will simplify the Perpendicular Axis Theorem for better understanding, learn proof of it and compare it with the Parallel Axis.
Table of Content
- What is the perpendicular axis theorem?
- Moment of Inertia:
- Difference between Perpendicular Axis Theorem and Parallel Axis Theorem:
- Application of Perpendicular Axis Theorem:
- Conclusion:
- Frequently Asked Questions(FAQs)