# Inertia, Momentum, Rotation

• JB83
In summary: You need to calculate the moment of inertia of the system consisting of the board and the children, using Steiner's theorem. To do so, take the total mass of the children and multiply it by their distance from the rotation axis.
JB83
I am stuck on the first part of this question. I thought that I could add the Inertias for child 1 + child 2 + board and that would give me the answer. I used I=mr^2 for the children with the r being L/2 and 1/12*(mass)*(width^2 + length^2). as the I for the board. However I am not getting the right answer. Also I am unsure of how to calculate the angular momentum of the system Any help would be appreciated

Two children, each with mass m = 10.5 kg, sit on opposite ends of a narrow board with length L = 4.8 m, width W = 0.18 m, and mass M = 6.2 kg. The board is pivoted at its center and is free to rotate in a horizontal circle without friction. What is the rotational inertia of the board plus the children about a vertical axis through the center of the board?

What is the magnitude of the angular momentum of the system if it is rotating with an angular speed of 2.28 rad/s?

While the system is rotating, the children pull themselves toward the center of the board until they are half as far from the center as before. What is the resulting angular speed?

JB83 said:
I am stuck on the first part of this question. I thought that I could add the Inertias for child 1 + child 2 + board and that would give me the answer. I used I=mr^2 for the children with the r being L/2 and 1/12*(mass)*(width^2 + length^2). as the I for the board. However I am not getting the right answer. Also I am unsure of how to calculate the angular momentum of the system Any help would be appreciated

Two children, each with mass m = 10.5 kg, sit on opposite ends of a narrow board with length L = 4.8 m, width W = 0.18 m, and mass M = 6.2 kg. The board is pivoted at its center and is free to rotate in a horizontal circle without friction. What is the rotational inertia of the board plus the children about a vertical axis through the center of the board?

What is the magnitude of the angular momentum of the system if it is rotating with an angular speed of 2.28 rad/s?

While the system is rotating, the children pull themselves toward the center of the board until they are half as far from the center as before. What is the resulting angular speed?

Well, for the first part, simply use Steiner's theorem on the system consisting of the board and the childern. You must add the mass of each child separately multiplied with its squared distance from the axis of rotation to the moment of inertia of the board, which you can find here: http://www.physics.uoguelph.ca/tutorials/torque/Q.torque.inertia.html" .

For the second part of the problem, with the children pulling themselves towards the center, here's a hint: there is no external torque - so what is conserved?

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JB83 said:
I am stuck on the first part of this question. I thought that I could add the Inertias for child 1 + child 2 + board and that would give me the answer. I used I=mr^2 for the children with the r being L/2 and 1/12*(mass)*(width^2 + length^2). as the I for the board. However I am not getting the right answer. . . .
You have the right approach for I. If you do not post your answer, there is no way we can check to see if you did the calculation correctly.

## 1. What is inertia?

Inertia is the tendency of an object to resist changes in its state of motion. This means that an object will maintain its current velocity and direction unless acted upon by an external force.

## 2. How is momentum defined?

Momentum is a measure of an object's motion and is defined as the product of its mass and velocity. It is a vector quantity, which means it has both magnitude and direction.

## 3. What is rotational inertia?

Rotational inertia, also known as moment of inertia, is the measure of an object's resistance to rotational motion. It depends on the object's mass, distribution of mass, and the axis of rotation.

## 4. How does rotational inertia affect rotation?

Rotational inertia affects the speed at which an object rotates. Objects with a larger rotational inertia will rotate slower than objects with a smaller rotational inertia, even if they have the same applied torque.

## 5. Can rotational inertia be changed?

Yes, rotational inertia can be changed by altering the distribution of mass in an object or by changing the axis of rotation. This can be seen in activities such as ice skating, where skaters can change their rotational inertia by extending or retracting their arms.

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