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Moment of a force: vector Formulation
The cross product:
Moment of Force F around point O:MO
Calculating the moment using rectangular components
Resultant moment:Mro
Moment of a force about a specified axis a-a:Ma
O: any point on a-a
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.
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FAQs on Moment of a Force (Vector Formulation) - Engineering Mechanics for Mechanical Engineering
| 1. What is the definition of moment of a force in vector formulation? |  |
| 2. How is the moment of a force calculated in vector form? | |
Ans. To calculate the moment of a force in vector form, you need to take the cross product of the force vector and the position vector from the axis of rotation. The magnitude of the moment is given by the product of the magnitudes of the two vectors and the sine of the angle between them.
| 3. What is the significance of the direction of the moment of a force? | |
Ans. The direction of the moment of a force is determined by the right-hand rule. If you curl the fingers of your right hand in the direction of the force vector, then your thumb points in the direction of the moment vector. The direction of the moment indicates whether the rotation caused by the force is clockwise or counterclockwise.
| 4. How does the moment of a force affect rotational equilibrium? | |
Ans. In rotational equilibrium, the sum of the moments of all the forces acting on an object is zero. This means that the clockwise moments are balanced by the counterclockwise moments. If the moment of a force is not zero, it will cause the object to rotate.
| 5. Can the moment of a force be negative? | |
Ans. Yes, the moment of a force can be negative. A negative moment indicates that the rotation caused by the force is in the opposite direction compared to the conventionally defined positive direction. The sign of the moment depends on the orientation or position of the force relative to the axis of rotation.
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