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MotionLab
The spinning counterpart to ½mv² — rotational KE depends on moment of inertia and angular velocity.
Just as a moving object has KE = ½mv², a spinning object has rotational KE = ½Iω². The moment of inertia I plays the role of mass (how hard it is to spin up), and angular velocity ω replaces linear velocity. A rolling object has both types simultaneously.
Flywheels exploit ½Iω² for energy storage — by spinning a heavy disk at high speed, significant energy is stored mechanically. Modern flywheel batteries use carbon-fiber rotors spinning at 60,000+ RPM in a vacuum, storing enough energy to power a house for hours.
Rotational KE (J)
25
KE = ½Iω²
What you entered
Angular velocity in RPM
10 × 60 / (2π)= 95.493 RPMRotational KE = ½Iω²
0.5 × 0.5 × 10²= 25 JResult
Rotational KE (J): 25
A body with I = 0.5 kg·m² spinning at 10 rad/s (95.5 RPM) has 25 J of rotational kinetic energy.