Conservation of Angular Momentum

A point mass m at radius r has moment of inertia I = mr². With no external torque about the fixed axis, its signed angular momentum L = Iω stays constant. A radial actuator can change rotational kinetic energy without exerting torque about that axis. Energy conservation for the rotating mass alone is therefore not assumed.

Native experiment

Open Conservation of Angular Momentum. Use these exact labelled raw controls; results update on each valid edit, while invalid inputs replace the calculation with a visible error.

1. Set Mass m = 1, Initial radius r0 = 2, Final radius r = 1 and Initial angular speed omega0 = 1. Check L = 4, final angular speed 4 and work 6 J.
2. Set Mass m = 2, Initial radius r0 = 1, Final radius r = 2 and Initial angular speed omega0 = 3. Read inertias 2 and 8, angular momentum 6, final speed 0.75 rad/s, energies 9 and 2.25 J and work −6.75 J.
3. Set Mass m = 3, Initial radius r0 = 1, Final radius r = 1 and Initial angular speed omega0 = -2. Read L = −6, final angular speed −2 and both energies 6 J; clockwise direction is retained.
4. Set Initial angular speed omega0 = 0. Angular momentum, both energies, final angular speed and work are all 0; no rotation arrows are shown.
5. Set Initial radius r0 and Final radius r both to 1.5, Mass m = 2 and Initial angular speed omega0 = -4. Final angular speed equals −4, both energies are 36 J and work is 0.
6. Set Final radius r = 0. The actual domain error replaces results; no infinite spin or hidden result is supplied. Restore r = 0.5, set r0 = 3, m = 5 and omega0 = 4. Read final angular speed 144 rad/s, final energy 12960 J and work 12600 J.
7. Pan the diagram and choose Reset view. The four inputs remain unchanged. Clear Mass m, inspect the error, then restore 1 to recover the comparison.