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Calculators / Science / Rolling kinetic energy
Rolling kinetic energy calculator
Combine translational and rotational energy for an object rolling without slip.
On this page
Total energy13.5J
Rotational energy4.5J
Angular speed15rad/s
Calculator controls
How to calculate
Combine translational and rotational energy for an object rolling without slip.
Total energy = m*v^2/2+i*(v/r)^2/2 J; Rotational energy = i*(v/r)^2/2 J; Angular speed = v/r rad/s
Worked example
Mass (kg): 2; Centre speed (m/s): 3; Moment of inertia (kg·m²): 0.04; Rolling radius (m): 0.2.
Total energy: 13.5 J; Rotational energy: 4.5 J; Angular speed: 15 rad/s.
Assumptions and limits
Assumes angular speed equals centre speed divided by radius. Enter moment of inertia about the rolling axis; slipping needs a different angular-speed input.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Combine translational and rotational energy for an object rolling without slip.
When this tool is useful
Total energy = m*v^2/2+i*(v/r)^2/2 J; Rotational energy = i*(v/r)^2/2 J; Angular speed = v/r rad/s
Understanding your inputs
| Input | What to enter |
|---|---|
| Mass (kg) | Enter a number of at least 0 and no more than 1000000000000. |
| Centre speed (m/s) | Enter a number of at least 0 and no more than 1000000000000. |
| Moment of inertia (kg·m²) | Enter a number of at least 0 and no more than 1000000000000. |
| Rolling radius (m) | Enter a number of at least 1e-12 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Assumes angular speed equals centre speed divided by radius. Enter moment of inertia about the rolling axis; slipping needs a different angular-speed input.
How is the result calculated?
Total energy = m*v^2/2+i*(v/r)^2/2 J; Rotational energy = i*(v/r)^2/2 J; Angular speed = v/r rad/s