A fixed torque produces larger alpha when inertia is smaller. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Large inertia changes spin slowly

The same checked torque is 12 newton meters. Dividing by inertia 12 gives angular acceleration 1 per second squared.

α=12/12=1\alpha=12/12=1
Angular accelerationTorque divided by inertia sets alpha.r=3 mF=4 Nr=2 mr=3 mF=4 Ntau=12 N*mm=3 kgr=2 mI=12 kg*m^2alpha=1 1/s^2

Half the inertia gives twice the alpha

The same checked torque is 12 newton meters. Dividing by inertia 6 gives angular acceleration 2 per second squared.

α=12/6=2\alpha=12/6=2
Angular accelerationTorque divided by inertia sets alpha.r=3 mF=4 Nr=1 mr=3 mF=4 Ntau=12 N*mm=6 kgr=1 mI=6 kg*m^2alpha=2 1/s^2

Small inertia gives the largest alpha

The same checked torque is 12 newton meters. Dividing by inertia 3 gives angular acceleration 4 per second squared.

α=12/3=4\alpha=12/3=4
Angular accelerationTorque divided by inertia sets alpha.r=3 mF=4 Nr=1 mr=3 mF=4 Ntau=12 N*mm=3 kgr=1 mI=3 kg*m^2alpha=4 1/s^2