What is moment of inertia?
The rotational analogue of mass — resistance to angular acceleration. For a point mass, I = mr².
Moment of Inertia (Point Mass) Calculator
I = mr²
Calculate the moment of inertia of a point mass. I = mr² — rotational inertia about an axis at distance r.
Calculate
Enter values above to calculate
How it calculates
1
For a point mass: I = m × r²
2
m in kg, r (distance to axis) in metres
3
Result in kg·m²
Formula
I = mr²
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| I | Moment of inertia | kg·m² |
| m | Mass | kg |
| r | Distance from rotation axis | m |
How to Use This Calculator
This moment of inertia (point mass) calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula I = mr² is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
A 2 kg point mass 0.5 m from the axis. Find moment of inertia.
Step 1: I = m r²
Step 2: I = 2 × (0.5)²
Step 3: I = 2 × 0.25
Answer: I = 0.5 kg·m²
Common Mistakes
- Extended bodies use shape formulas: solid cylinder ½MR², thin rod about end ⅓ML²
- I depends on the axis chosen — the parallel-axis theorem shifts it
- r is the perpendicular distance to the rotation axis
Related
Frequently Asked Questions
What is the parallel-axis theorem?
I = I_cm + Md², which gives the moment of inertia about any axis parallel to one through the centre of mass at distance d.