Question

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?

Answer 1

Answer:

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:

$\tau_f =I\alpha$

And $\tau_f=rf$, 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 $rf\sin90\°=rf$. Then, we have that:

$rf=I\alpha\\\\\implies I=\frac{rf}{\alpha}$

Plugging in the given values, we obtain:

$I=\frac{(0.39m)(6.7N)}{1.8rad/s^{2} } =1.4kgm^{2}$

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