# Moment of inertia of door rotation

• sp3sp2sp
In summary, the moment of inertia for a 23 kg solid door with dimensions 220 cm x 95 cm, rotating about a vertical axis 17 cm from one edge, is 3.87 kg*m^2. This is calculated using the equation I = I_cm + MR^2, with a distance of 0.17 m (half the width minus 17 cm) used for R. The calculated value is also confirmed through integration.
sp3sp2sp

## Homework Statement

A 23 kg solid door is 220 cm tall, 95 cm wide. What is the door's moment of inertia for rotation about a vertical axis inside the door, 17 cm from one edge?

I = I_cm + MR^2

## The Attempt at a Solution

I = I_cm + MR^2

I = (1/12)(23kg)(0.95m)^2 + (23kg)((.95m/2) -.17m)^2

I = 1.73 +2.14 = 3.87kg*m^2
If this is wrong then I am not sure I am using right value for R. I am using the distance from the center of mass for the door which i think is middle of door. So .17m from edge would be .95/2 - .17 = .305 = R

thanks for any help

That looks completely correct to me.

I checked it with integration of mr^2 across the width of the door and got the same answer.

## 1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in rotational motion. It is the product of an object's mass and the square of its distance from the axis of rotation.

## 2. How is moment of inertia calculated for a rotating door?

The moment of inertia for a rotating door can be calculated by multiplying the mass of the door by the square of its distance from the hinge point. This value will also depend on the shape and distribution of the door's mass.

## 3. What factors affect the moment of inertia of a door?

The moment of inertia of a door will be affected by its mass, shape, and distribution of mass. A door with a larger mass or a more spread out distribution of mass will have a higher moment of inertia.

## 4. How does the moment of inertia affect the ease of opening and closing a door?

A higher moment of inertia means that more force is required to change the rotation of the door. This can make it more difficult to open and close the door, especially if the door is heavy or has a large moment of inertia.

## 5. 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, shape, or distribution of mass. For example, removing weight from the door or changing its shape can decrease the moment of inertia and make it easier to open and close.

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