While sitting in a swivel chair, you push against the floor with your heel to make the chair spin. The 6.7 N frictional force is applied at a point 39 cm from the chair's rotation axis, in the direction that causes the greatest angular acceleration.
If that angular acceleration is 1.8 rad/s², what is the total moment of inertia about the axis of you and the chair?

I = 1.4kgm²

Explanation:

The rotational motion is caused by the frictional force, which generates a torque on the system. As there is no other force that creates a torque, this can be expressed in the equation of rotational motion below:

And , where r is the distance from the point of application and the rotation axis, and f is the magnitude of the frictional force. This is because the frictional force is applied in the direction that causes the greatest angular acceleration (this is, 90°) and . Then, we have that:

Plugging in the given values, we obtain:

In words, the total moment of inertia is equal to 1.4kgm².