Rotational Kinetic Energy Calculator (KE = ½Iω²)
Rotational Kinetic Energy Calculator (KE = ½Iω²)
Rotational kinetic energy is the energy an object has due to spinning, analogous to linear kinetic energy but using moment of inertia in place of mass and angular velocity in place of linear velocity. Choose which variable to solve for, enter the other two, and this calculator computes the result with a full step-by-step solution.
- KE = ½Iω², where I is the moment of inertia (kg·m²) and ω is the angular velocity (rad/s) - e.g. I=4 kg·m², ω=3 rad/s gives KE = ½×4×3² = 18 J.
- Moment of inertia depends on both mass and how it's distributed around the axis - a solid disk and a hoop of the same mass and radius have different moments of inertia, and therefore different rotational kinetic energy at the same spin rate.
- A spinning flywheel stores energy exactly like this formula describes - which is why flywheels are used for mechanical energy storage in some vehicles and power grids.
What is the formula for rotational kinetic energy?
KE = ½Iω², where I is the moment of inertia and ω is the angular velocity in radians per second.
How does rotational kinetic energy differ from linear kinetic energy?
Linear KE = ½mv² uses mass and linear velocity; rotational KE = ½Iω² uses moment of inertia (which accounts for how mass is distributed) and angular velocity.
Rotational Kinetic Energy Calculator (KE = ½Iω²)
Rotational kinetic energy is the energy an object has due to spinning, analogous to linear kinetic energy but using moment of inertia in place of mass and angular velocity in place of linear velocity. Choose which variable to solve for, enter the other two, and this calculator computes the result with a full step-by-step solution.
- KE = ½Iω², where I is the moment of inertia (kg·m²) and ω is the angular velocity (rad/s) - e.g. I=4 kg·m², ω=3 rad/s gives KE = ½×4×3² = 18 J.
- Moment of inertia depends on both mass and how it's distributed around the axis - a solid disk and a hoop of the same mass and radius have different moments of inertia, and therefore different rotational kinetic energy at the same spin rate.
- A spinning flywheel stores energy exactly like this formula describes - which is why flywheels are used for mechanical energy storage in some vehicles and power grids.
What is the formula for rotational kinetic energy?
KE = ½Iω², where I is the moment of inertia and ω is the angular velocity in radians per second.
How does rotational kinetic energy differ from linear kinetic energy?
Linear KE = ½mv² uses mass and linear velocity; rotational KE = ½Iω² uses moment of inertia (which accounts for how mass is distributed) and angular velocity.