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

In summary, the question is asking for the moment of inertia of a 20 kg solid door, with measurements of 220 cm tall and 93 cm wide, rotated about a vertical axis 14 cm from one edge. The correct equation to use would be the moment of inertia of an axis through the center of the door plus the product of the mass and the perpendicular distance between the two axes. This can be confirmed by starting with the moment of inertia of a thin rectangular plane through the center and adding the product of the mass and the square of the distance between the two axes.
  • #1
cyclemun
9
0

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...
 
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  • #2
Hint: Think of the door as two doors, joined at the axis 14cm in...
 
  • #3
Oops thinking of angular momentum
 
  • #4
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.
 
  • #5
djeitnstine said:
Moment of inertia is [tex]L = I \omega[/tex] 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
 
  • #6
berkeman said:
Hint: Think of the door as two doors, joined at the axis 14cm in...

Or you could do that :P
 
  • #7

1. What is the inertia of a rotating door?

The inertia of a rotating door refers to the tendency of a rotating door to resist changes in its motion. It is a measure of the door's resistance to being accelerated or decelerated.

2. How does the inertia of a rotating door affect its motion?

The inertia of a rotating door affects its motion by making it harder to start or stop rotating. This means that more force is needed to open or close the door, compared to a non-rotating door.

3. How is the inertia of a rotating door calculated?

The inertia of a rotating door is calculated by multiplying the mass of the door by the square of its distance from the axis of rotation. This is known as the moment of inertia and is represented by the symbol I.

4. What factors affect the inertia of a rotating door?

The inertia of a rotating door is affected by the mass and shape of the door, as well as its distance from the axis of rotation. The farther the door is from the axis, the greater its inertia will be.

5. How can the inertia of a rotating door be reduced?

The inertia of a rotating door can be reduced by decreasing its mass or by moving it closer to the axis of rotation. This will make it easier to open and close the door as less force will be needed to overcome its inertia.

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