How Do You Calculate the Moment of Inertia for an Off-Center Pivot?

[cyclemun]

Homework Statement

A 20 kg solid door is 220 cm tall, 93 cm wide.

Homework Equations

What is the door's moment of inertia for rotation about a vertical axis inside the door, 14 cm from one edge?

The Attempt at a Solution

I know that if the pivot point is at the edge of the door, the equation is 1/3ML^2, but I don't know how to find the formula for this question...

 

[berkeman]

Hint: Think of the door as two doors, joined at the axis 14cm in...

 

[djeitnstine]

Oops thinking of angular momentum

 

[bziegler]

Do you know how the equation for the pivot point of the edge of the door is calculated?
It is done by using the moment of inertia of an axis thru the center of the door plus M * R^2 where R is the perpendicular distance between the two axes. You can confirm this equation by starting with the moment of inertia of a thin rectangular plane thru the center and adding the M * R^2 to get the moment of inertia of a thin rectangular plane on the edge.

BTW: The equation you have for the pivot point at the edge of the door is wrong (rather, incomplete). You need to have another term for the length of the door.

 

[berkeman]

Moment of inertia is L = I \omega I meaning inertia and omega meaning angular velocity

Might be a typo. L is angular momentum, and I is the Moment of Inertia. Just follow the PF Library link that was automatically added to your term moment of intertia:

https://www.physicsforums.com/library.php?do=view_item&itemid=31

 

[bziegler]

Hint: Think of the door as two doors, joined at the axis 14cm in...

Or you could do that :P

 

[djeitnstine]

Might be a typo. L is angular momentum, and I is the Moment of Inertia. Just follow the PF Library link that was automatically added to your term moment of intertia:

https://www.physicsforums.com/library.php?do=view_item&itemid=31

After I reread the question I caught my mistake...thanks