# Angular velocity tank receiving cereal

• Granger
In summary, the cylindrical container, initially with a moment of inertia of 2.0 kgm^2, is rotating at 20 revolutions per minute on its axis. As it receives cereal at a rate of 0.5 kg-1, its radius being 0.40m, the angular velocity after 10 seconds can be calculated using the conservation of angular momentum. After the cereal has settled, the total moment of inertia can be calculated by summing the container's and the cereal's moment of inertia.
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...

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

scottdave said:
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?

scottdave
Granger said:
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".

scottdave

## 1. What is angular velocity?

Angular velocity is a measure of the rate at which an object is rotating or moving around a central point or axis. It is usually measured in radians per second (rad/s) or revolutions per minute (rpm).

## 2. How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angle (in radians) by the change in time. It can also be calculated by dividing the linear velocity (in meters per second) by the radius (in meters) of the circular motion.

## 3. How is angular velocity related to cereal pouring into a tank?

In the context of cereal pouring into a tank, the angular velocity would represent the rate at which the tank is rotating as the cereal is being poured in. This can affect the dispersion and distribution of the cereal within the tank.

## 4. Why is angular velocity important in this scenario?

Angular velocity is important in this scenario because it can affect the overall efficiency and effectiveness of the cereal pouring process. A higher angular velocity may result in faster pouring and better mixing of the cereal, while a lower angular velocity may result in slower pouring and uneven distribution of the cereal.

## 5. How can angular velocity be controlled in this situation?

Angular velocity can be controlled in this situation by adjusting the speed of the rotating tank or by changing the radius of the tank. Additionally, the angle at which the cereal is poured into the tank can also affect the angular velocity.

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