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Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE) PDF Download

Moment of a force: Scalar Formulation

 The magnitude of the moment of a force:

MO: Magnitude of the moment of F around point O

d: Perpendicular distance from O to the line of action of F

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Note: moving a force along its line of action does not change its moment

Note: M0 =Fd =Fr sin (θ) =rF⊥

Direction of the moment in 2-D:The direction of the moment is given by the right hand rule: Counter Clockwise (CCW) is out of the page, Clockwise (CW) is into the page.

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Calculating the moment in 2-D using components: Moments add together as vectors. Select a positive direction (CCW or CW), then calculate each moment and add them using the proper sign for each term. For example:

M0 =-Fx d1 + Fy d2 CCW positive 

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Moment of a force: vector Formulation

The cross product: 

Moment of Force F around point O:MO

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Calculating the moment using rectangular components

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Resultant moment:Mro

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Moment of a force about a specified axis a-a:Ma

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

O: any point on a-a

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE)

Note:The moment of a couple does not depend on the point one takes the moment about. In other words, a moment of a couple is the same about all points in space.

The document Moment of a Force (Scalar Formulation) | Engineering Mechanics - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Engineering Mechanics.
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FAQs on Moment of a Force (Scalar Formulation) - Engineering Mechanics - Civil Engineering (CE)

1. What is the scalar formulation of the moment of a force?
Ans. The scalar formulation of the moment of a force is the magnitude of the force multiplied by the perpendicular distance from the point of rotation to the line of action of the force.
2. How is the moment of a force different from the force itself?
Ans. The moment of a force is a measure of the tendency of a force to rotate an object around a specific point, while the force itself is a vector quantity that represents a push or pull on an object.
3. Can the moment of a force be negative?
Ans. Yes, the moment of a force can be negative if the force tends to rotate an object in the opposite direction compared to the chosen positive direction for calculating moments.
4. How is the moment of a force calculated in practical applications?
Ans. In practical applications, the moment of a force is calculated by multiplying the magnitude of the force by the perpendicular distance from the point of rotation to the line of action of the force.
5. Why is understanding the moment of a force important in engineering and physics?
Ans. Understanding the moment of a force is crucial in engineering and physics as it helps in designing structures, analyzing the stability of objects, and predicting how objects will behave under the influence of external forces.
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