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The torque is dependent upon the direction of the lever arm and the direction of the force, so you can't neglect sign or direction (the latter is what you have neglected).
The reason why the torque is in the same direction for both is because you are applying the force in the same direction with relation to the lever arm.
dE_logics said:Yeah I was thinking about that, but it's just a distance...I mean, its just a displacement...it's like taking a measured section of a scale...that doesn't have a direction.
"Moment independent of direction of force" refers to the concept that the rotational effect, or moment, of a force applied to an object is the same regardless of the direction in which the force is applied. This means that the magnitude of the moment is not affected by the direction of the force, only its distance from the pivot point.
The direction of force does not affect the moment, only the distance from the pivot point does. This is because the moment is a product of the magnitude of the force and the distance between the force and the pivot point, not the direction of the force.
The concept of moment independent of direction of force is important in physics because it allows us to calculate the rotational effect of a force on an object without having to consider the direction in which the force is applied. This simplifies calculations and makes it easier to analyze and predict the behavior of objects under the influence of various forces.
Yes, there are some exceptions to this concept. One example is when the force is applied at the pivot point itself, in which case the moment would be zero regardless of the magnitude of the force. Additionally, if the object is not rigid and can deform, the direction of the force may affect the moment.
The moment can still be calculated for a force that is not perpendicular to the object by using the perpendicular distance from the pivot point to the line of action of the force. This distance is known as the lever arm, and it is used in the moment equation: M = F x d, where M is the moment, F is the magnitude of the force, and d is the perpendicular distance from the pivot point to the line of action of the force.