Question

A clay vase on a potter's wheel experiences an angular acceleration of 5.69 rad/s2 due to the application of a 16.0-n m net torque. find the total moment of inertia of the vase and potter's wheel.

Answer 1

The equivalent of the Newton's second law for rotational motions is:
$\tau = I \alpha$
where
$\tau$ is the net torque acting on the object
$I$ is its moment of inertia
$\alpha$ is the angular acceleration of the object.

Re-arranging the formula, we get
$I= \frac{\tau}{\alpha}$
and since we know the net torque acting on the (vase+potter's wheel) system, $\tau=16.0 Nm$, and its angular acceleration, $\alpha = 5.69 rad/s^2$, we can calculate the moment of inertia of the system:
$I= \frac{\tau}{\alpha}= \frac{16.0 Nm}{5.69 rad/s^2} =2.81 kg m^2$