Moments & equilibrium of rigid bodies

Thread starter phospho
Start date Oct 21, 2012
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bodies Equilibrium Moments Rigid bodies

In summary, a moment of a rigid body is a measure of the tendency of a force to cause rotation, determined by the magnitude of the force and the distance from the point/axis. The equilibrium of a rigid body is determined by analyzing the forces and moments, where a sum of zero for both indicates equilibrium. The center of mass is the average position of the mass, while the center of gravity is where the weight can be considered to act. A rigid body cannot be in equilibrium if it is accelerating, as it must have a constant velocity. Changing the point of application of a force does not change the magnitude of the moment, but can change its direction. The moment is always perpendicular to the plane of motion and passes through the point of

Oct 21, 2012

phospho

The underlined red part: I don't particularly understand where they got this from?
The yellow highlight: Why are they finding the vertical distance, instead of the perpendicular distance?

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Oct 21, 2012

voko

The underlined red part follows from the definition of moment about a point. In the yellow part, what would the "perpendicular" distance be?

1. What is a moment of a rigid body?

A moment of a rigid body is a measure of the tendency of a force to cause rotation about a specific point or axis. It is calculated by multiplying the magnitude of the force by the perpendicular distance from the point/axis to the line of action of the force.

2. How is the equilibrium of a rigid body determined?

The equilibrium of a rigid body is determined by analyzing the forces and moments acting on the body. If the sum of all forces acting on the body is zero and the sum of all moments about any point is also zero, then the body is in equilibrium.

3. What is the difference between the center of mass and center of gravity of a rigid body?

The center of mass is the average position of the mass of a body, while the center of gravity is the point at which the weight of the body can be considered to act. For symmetrical objects with uniform density, the center of mass and center of gravity are at the same point.

4. Can a rigid body be in equilibrium if it is accelerating?

No, a rigid body cannot be in equilibrium if it is accelerating. In order for a body to be in equilibrium, it must have a constant velocity or zero acceleration.

5. How does changing the point of application of a force affect the moment of a rigid body?

Changing the point of application of a force does not change the magnitude of the moment of a rigid body, but it can change the direction of the moment. The moment of a force is always perpendicular to the plane of motion of the force and passes through the point of application.