Angular Acceleration

Larger Inertia Reduces Alpha

With the same torque, larger inertia changes spin more slowly. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Larger inertia gives a smaller alpha

The same 12 newton meter torque acting on inertia 12 gives alpha 1 per second squared.

α=12/12=1 per second squared\alpha=12/12=1\ \mathrm{per\ second\ squared}
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

The torque did not change

Only inertia changed: alpha goes from 2 down to 1.

2>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