- #1

Karagoz

- 52

- 5

- Homework Statement
- What's the source of increase in rotational energy of a carousel when two persons in that carousel move into centrum, assuming the angular momentum is conserved?

- Relevant Equations
- w: angular speed

I: inertia

Rotational energy: 1/2 * I * w^2

A carousel has the shape of a circular disc with radius 1.80 m and a mass of 300 kg. There are two people with masses of 30 and 45 kg out on the edge while carousel rotates with the angular speed 0.6 rad / s.

The people move towards the center of the carousel

Calculations show that the rotational energy increase after these two people move towards the center of the carousel. It's calculated by this:

The first question is: what will be the angular velocity now. The angular velocity will be 0.9 rad/s.

Since angular momentum is conserved: Inertia_0 * w_0 = Inertia_1 * w_1

Inertia_0 = 729 (when the persons are at the edge)

Inertia_1 = 486 (when the persons are in the centrum)

w_0 = 0.6 rad/s (as mentioned above)

w_1 = Inertia_0*w_0 / Inertia_1 = 0.9 rad/s.

The second question is the change in rotational energy. That's simple:

1/2*Inertia_1*w_1 - 1/2*Inertia_0*w_0 = 65 j.

But the question I can't answer is, what's the source of that energy?

In this link where they show a similar example (the example is a rotating ice dancer pulling her hands inwards and increasing her rotational energy):

https://opentextbc.ca/universityphysicsv1openstax/chapter/11-2-conservation-of-angular-momentum/

They say the following:

It says the source of the additional rotational kinetic energy is the work required to pull her arms inward.

And does total energy increases? Or only rotational kinetic energy?

The people move towards the center of the carousel

Calculations show that the rotational energy increase after these two people move towards the center of the carousel. It's calculated by this:

The first question is: what will be the angular velocity now. The angular velocity will be 0.9 rad/s.

Since angular momentum is conserved: Inertia_0 * w_0 = Inertia_1 * w_1

Inertia_0 = 729 (when the persons are at the edge)

Inertia_1 = 486 (when the persons are in the centrum)

w_0 = 0.6 rad/s (as mentioned above)

w_1 = Inertia_0*w_0 / Inertia_1 = 0.9 rad/s.

The second question is the change in rotational energy. That's simple:

1/2*Inertia_1*w_1 - 1/2*Inertia_0*w_0 = 65 j.

But the question I can't answer is, what's the source of that energy?

In this link where they show a similar example (the example is a rotating ice dancer pulling her hands inwards and increasing her rotational energy):

https://opentextbc.ca/universityphysicsv1openstax/chapter/11-2-conservation-of-angular-momentum/

They say the following:

The source of this additional rotational kinetic energy is the work required to pull her arms inward. Note that the skater’s arms do not move in a perfect circle—they spiral inward. This work causes an increase in the rotational kinetic energy, while her angular momentum remains constant. Since she is in a frictionless environment, no energy escapes the system. Thus, if she were to extend her arms to their original positions, she would rotate at her original angular velocity and her kinetic energy would return to its original value.

It says the source of the additional rotational kinetic energy is the work required to pull her arms inward.

**There's work required to pull her arms inward, but there's also work required to pull her arms outward too. How come when the work of her pulling her arms inwards the rotational kinetic energy increases, but the work of her extending her arms outward decreases the rotational kinetic energy?**

I can't understand how it works. How does the rotational kinetic energy increase?I can't understand how it works. How does the rotational kinetic energy increase?

And does total energy increases? Or only rotational kinetic energy?