What is the moment of inertia?
The rotational equivalent of mass — it measures resistance to angular acceleration. I = Σmᵢrᵢ² for a discrete system.
Rotational Kinetic Energy Calculator
KE_rot = ½Iω²
Calculate rotational kinetic energy from moment of inertia and angular velocity. KE = ½Iω².
Calculate
Enter values above to calculate
How it calculates
1
KE_rot = ½ × I × ω²
2
I in kg·m², ω in rad/s
3
Result in joules
Formula
KE_rot = ½Iω²
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| KE_rot | Rotational kinetic energy | J |
| I | Moment of inertia | kg·m² |
| ω | Angular velocity | rad/s |
How to Use This Calculator
This rotational kinetic energy 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 KE_rot = ½Iω² 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 flywheel: I = 2 kg·m², ω = 10 rad/s. Find KE.
Step 1: KE = ½ × 2 × 10²
Step 2: KE = 1 × 100
Answer: KE = 100 J
Common Mistakes
- ω in rad/s, not rpm — convert: ω = rpm × 2π/60
- Total KE of rolling object = ½mv² + ½Iω²
- I depends on shape: solid cylinder = ½MR², thin ring = MR²
Related
Frequently Asked Questions
How do I convert rpm to rad/s?
ω (rad/s) = rpm × 2π/60. For example, 3000 rpm = 314 rad/s.