Moment of Inertia Door

In summary, the data for the width and mass of the door are necessary, while the data for the height is unnecessary for calculating the moment of inertia for rotation on its hinges. The appropriate formula to use is I = \int r^2 \rho dA, where r is the perpendicular distance to the hinge, \rho is the density of the door, and dA is the area differential. Alternatively, if using known formulas for rotational inertia, the moment of inertia for a door about an edge is the same as that of a rod about one end. The formula to use in this case is I = (mass * (width^2 + thickness^2)) / 12.
  • #1
Jacob87411
171
1
A uniform, thin, solid door has a height of 2.2 m, a width of 0.87 m, and a mass of 23 kg. Find its moment of inertia for rotation on its hinges.

Are any of the data unnecessary?
the width of the door is unnecessary
the mass of the door is unnecessary
no; all of the data is necessary
the height of the door is unnecessary

First off, the height of the door should be unnecessary since the distance in moment of inertia is perpendicular to the force being applied? Second I'm having problems finding what I equation to use for a door about the hinge?
 
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  • #2
[tex]I = \int r^2 \rho dA[/tex]
Here r is the perpendicular distance to the hinge, \rho is the (surface) density of the door, and dA is the area differential.
The height of the door will come into the area differential.
 
  • #3
Are you sure, the correct answer said the height wasnt needed?
 
  • #4
The height is not needed. If you do the integral that Euclid gave, using the mass density [itex]\rho[/itex], the height will drop out of the answer.

Are you supposed to solve this using calculus? If so, set up the integral.

Or are just supposed to get the answer using known formulas for the rotational inertia of common shapes? If so, since height doesn't matter, what formula would apply?
 
  • #5
Its not supposed to use calculus...I wasn't sure which moment of inertia would apply..i was thinking maybe 1/3MR^2 but not sure
 
  • #6
Jacob87411 said:
...i was thinking maybe 1/3MR^2
That's the one. Since height doesn't matter, the moment of inertia of a door about an edge is the same as that of a rod about one end.
 
  • #7
The Formula to use is

I= (mass*((width^2)+(thickness^2)))/12
 
  • #8
Adam Lakehead said:
The Formula to use is

I= (mass*((width^2)+(thickness^2)))/12
Eh... no. (And you're 5 years too late anyway!)
 

1. What is "Moment of Inertia Door"?

The moment of inertia door refers to the measure of the door's resistance to changes in its rotational motion. It takes into account the door's mass, distribution of mass, and shape.

2. How is the moment of inertia of a door calculated?

The moment of inertia of a door can be calculated using the formula I = mr^2, where I is the moment of inertia, m is the mass of the door, and r is the distance from the axis of rotation to the door's center of mass.

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

The moment of inertia of a door is affected by its mass, shape, and distribution of mass. A heavier door will have a larger moment of inertia, while a door with more mass concentrated farther away from the axis of rotation will have a larger moment of inertia.

4. How does the moment of inertia of a door affect its movement?

The moment of inertia of a door affects its rotational movement, as it determines how easily the door can be rotated. A door with a larger moment of inertia will require more force to rotate, while a door with a smaller moment of inertia will require less force.

5. How can the moment of inertia of a door be changed?

The moment of inertia of a door can be changed by altering its mass, shape, or distribution of mass. For example, adding weight to the door or moving the hinges closer to the edge of the door will increase the moment of inertia, while reducing the mass or moving the hinges closer to the center of the door will decrease the moment of inertia.

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