Angular acceleration changes only after both torque and inertia sources close. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Base torque over inertia gives alpha two

Torque 12 newton meters divided by inertia 6 gives angular acceleration 2 per second squared.

α=12/6=2\alpha=12/6=2
Angular acceleration source rowBoth torque and inertia sources feed the alpha check.r=1 mr=3 mF=4 Nm=6 kgr=1 mI=6 kg*m^2r=3 mF=4 Ntau=12 N*malpha=2 1/s^2

Doubling torque doubles alpha

Torque 24 newton meters divided by inertia 6 gives angular acceleration 4 per second squared.

α=24/6=4\alpha=24/6=4
Angular acceleration source rowBoth torque and inertia sources feed the alpha check.r=1 mr=6 mF=4 Nm=6 kgr=1 mI=6 kg*m^2r=6 mF=4 Ntau=24 N*malpha=4 1/s^2

Doubling torque and inertia returns alpha two

Torque 24 newton meters divided by inertia 12 gives angular acceleration 2 per second squared.

α=24/12=2\alpha=24/12=2
Angular acceleration source rowBoth torque and inertia sources feed the alpha check.r=2 mr=6 mF=4 Nm=3 kgr=2 mI=12 kg*m^2r=6 mF=4 Ntau=24 N*malpha=2 1/s^2