Angular velocity tank receiving cereal

[Granger]

Homework Statement

The cylindrical container, when empty, has the moment of inertia of 2.0 Kgm^2 around the axis of rotation. It is rotating freely on its axis 20 revolutions per minute, when it begins to receive cereal, which falls vertically along its axis at the rate of 0.5 kg-1. The radius of the container is 0.40m. Calculate the angular velocity after 10 seconds.

Homework Equations

$$ \tau = I \alpha $$
$$ L = I \omega$$
Conservation of angular momentum

The Attempt at a Solution

I am a bit lost with this problem.
At first I thought about using conservation of angular momentum
$$L_i=L_f $$

$$I_i= 2.0 kgm^2$$
$$\omega _i = 2\pi /3$$

My problem is how can I get the final rotational inertia. The only thing I know is that the new mass is the first one + 5 kg (0.5 * 10s) and that the radius is 0.40 m.
But I don't know the expression of the rotational inertia...

 

[scottdave]

After it has settled, you should be able to consider the grain as a uniform cylindrical disc, rotating with the bin.

 

[Granger]

After it has settled, you should be able to consider the grain as a uniform cylindrical disc, rotating with the bin.

And then the total rotational inertia should be the sum of the container one and the disk one?

 

[jbriggs444]

And then the total rotational inertia should be the sum of the container one and the disk one?

Yes. Though I would be more comfortable if you had said "moment of inertia" rather than "rotational inertia".