Moment of Inertia of a Ring About a Tangent
This simulation demonstrates the calculation of the moment of inertia of a ring about an axis tangent to the ring using the parallel axis theorem.
Ring
Diameter (Axis)
Tangent (Axis)
Radius (Distance between axes)
Moment of inertia about diameter (Idia):
½MR²
Distance between axes (R):
R (radius of ring)
Using parallel axis theorem:
I = Idia + MR²
Moment of inertia about tangent:
I = ½MR² + MR² = ³⁄₂MR²
Understanding the Problem
We need to calculate the moment of inertia of a ring about an axis that is tangent to the ring (in the plane of the ring).
The tangent is parallel to one of the diameters of the ring, and the distance between these two parallel axes is R (the radius of the ring).
Key Concepts and Formulas
1. Moment of inertia of a ring about its diameter: Idia = ½MR²
2. Parallel Axis Theorem: I = Icm + Md²
Where:
- Icm = moment of inertia about center of mass axis
- M = mass of the object
- d = distance between the two parallel axes
3. Calculation: Itangent = Idia + MR² = ½MR² + MR² = ³⁄₂MR²
