# What is the Moment of Inertia for a Door Rotating Around a Vertical Axis?

• JMUkid
In summary, the problem involves finding the moment of inertia of a 32kg door with a width of 107 cm, rotating around a vertical axis 10 cm inside the door. Using the parallel axis theorem, the moment of inertia is calculated by adding the moment of inertia at the center of mass (1/3(32)(107)^2) to the product of the mass (32kg) and the squared distance from the center of mass to the axis of rotation (10cm)^2.
JMUkid

## Homework Statement

A 32kg door that is 107 cm wide. What is the moment of inertia 10 cm inside the door with rotation around a vertical axis?

L=Iω

## The Attempt at a Solution

I=1/3mL^2
I= Icm+ md^2

1/3(32)(107)^2
Im not sure what to do after I find the I center of mass

Your question is confusing.Give more details.Whether the door is rotating in vertical plane or horizontal plane??

It is rotating around a vertical axis

JMUkid said:
It is rotating around a vertical axis
But in which plane?
I mean that whether the door is on floor and rotating about vertical axis or in an erect position rotating about vertical axis.Moment of inertia in both cases is different.

It seems fair to assume from the question that the door is mounted to a vertical pole 10cm from its longest edge and parallel to that edge.
JMUkid you should try doing a search for the "parallel axis theorem" :)

## What is the moment of inertia of a door?

The moment of inertia of a door refers to the door's resistance to changes in its rotational motion. It is a measure of how difficult it is to rotate the door around its hinges.

## How is the moment of inertia of a door calculated?

The moment of inertia of a door can be calculated by multiplying the mass of the door by the square of its distance from the axis of rotation. This can be expressed mathematically as I = mr^2, where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation.

## Why is the moment of inertia important for doors?

The moment of inertia is important for doors because it affects how easily the door can be opened and closed. A door with a larger moment of inertia will require more force to rotate, making it more difficult to open and close.

## How does the shape of a door affect its moment of inertia?

The shape of a door can greatly affect its moment of inertia. A door with a larger width and height will have a larger moment of inertia than a door with a smaller width and height, even if they have the same mass. Additionally, the distribution of the door's mass can also impact its moment of inertia.

## Can the moment of inertia of a door be changed?

Yes, the moment of inertia of a door can be changed by altering its mass or shape. For example, adding weight to the door or changing its dimensions can affect its moment of inertia. However, the axis of rotation must remain the same for an accurate calculation of the moment of inertia.

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