Rotational Kinetic Energy Calculator
Calculate the kinetic energy stored in a rotating object from its moment of inertia and angular velocity.
How it works
- 1Enter the moment of inertia I (kg·m²) — a measure of how mass is distributed around the rotation axis.
- 2Enter the angular velocity ω (rad/s) — how fast the object is spinning.
- 3The calculator applies KE = ½·I·ω² and shows the rotational kinetic energy in joules and kilojoules.
Use cases
- Mechanical engineering — energy stored in flywheels and rotating machinery.
- Physics education — verifying calculations and exploring how energy scales with spin rate.
- Robotics and motor design — kinetic energy in spinning actuators and wheels.
Frequently asked questions
What is the formula for rotational kinetic energy?
KE = ½·I·ω², where I is the moment of inertia in kg·m² and ω is the angular velocity in rad/s, giving joules. For example, I = 0.5 kg·m² and ω = 10 rad/s give KE = ½ × 0.5 × 10² = 25 J.
How does rotational KE compare to linear kinetic energy?
It is the rotational analogue of ½mv²: moment of inertia I replaces mass m, and angular velocity ω replaces linear velocity v. Both measure the energy of motion — one rotational, one translational.
Why does energy scale with ω² and not just ω?
Kinetic energy depends on the square of velocity, so doubling ω quadruples the energy. Going from 5 to 10 rad/s (with I = 0.5 kg·m²) raises KE from 6.25 J to 25 J — a 4× increase, which is why high-speed flywheels store so much energy.
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