Sage-Tips

Why is the moment of a couple independent?

It is independent of the axis because it work with the average of the distance and works along line of center of mass of the body.

Does the moment of a couple change with a change in the position of the point about which it is causing a rotation?

The moment of force changes with the change in the axis of rotation while the moment of a couple about any axis is constant. The magnitude of the moment of a force about the given axis depends on the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation.

What is couple show that the moment of couple is same irrespective of the point of rotation of the body?

It is the product of one of the forces of couple and perpendicular distance between the forces of couple. The perpendicular distance between the forces of couple is independent of the point of rotation of the body. Hence, we conclude that the moment of couple is same irrespective of the point of rotation of the body.

Does the moment of a couple depend on the point about which you take the moment?

In this case to prove the point that the moment of a couple is constant and does not depend upon the point about which we take the moment. The position vectors at these points are →r1and→r2 with respect to the origin O. As it is the moment of a couple the forces acting at point P and Q will be given as −→F,→F.

Why is the moment of couple independent of axis of rotation?

The magnitude of the moment of couple or torque is equal to the product of one of the forces and the perpendicular distance between the lines of action of the two forces. The calculation is not linked with the axis of rotation. Hence it is independent of the position of the axis of rotation.

Why is the moment of a couple independent of the axis of rotation even if tax is fixed?

Let q and p be the perpendicular distances of the axis of rotation from the forces F and F F → and – F → respectively. In this case, the rotation of F is anticlockwise, while that of F is clockwise (from the top view). As a result, their individual torques are oppositely directed.

What is the difference between couple and moment?

What is the difference between Moment and Couple? Moment of force is the measure of turning effect of a force about a point. A couple consists of two equal and opposite forces acting with two different but parallel lines of action.

What is couple and moment of couple?

Couple is a pair of equal and opposite forces with different line of action. Moment of Couple is the rotational effect produced by a couple. It is a vector quantity. Its unit and dimension are same as that of.

What is moment of couple?

: the product of either of the forces of a couple by the perpendicular distance between them.

What is the translator effect of couple?

A couple consists of two parallel forces that are equal in magnitude, opposite in sense and do not share a line of action. It does not produce any translation, only rotation. The resultant force of a couple is zero. BUT, the resultant of a couple is not zero; it is a pure moment.

What are the factors on which moment of force depends?

Solution: Factors on which moment of force depends are: (i) The magnitude of the force applied. (ii) The distance of line of action of the force from the axis of rotation.

What does the moment of force depends on?

Moment of force depends on two factors: (i) Magnitude of force applied. (ii) Distance of line of action of the force from the axis of rotation.

Is moment of couple independent of choice of point of rotation?

Your assertion that “torque or moment of couple independent of choice of point of rotation” is only true either (1) of a system of forces F → i at positions R → i that sum to nought or (2) you shift your torque computing centre along a vector parallel to any nonzero nett force. Otherwise your assertion is not true.

What is the moment of a a couple?

A couple is defined as: ” Two parallel forces with the same magnitude but opposite in direction separated by a perpendicular distance d “, and the moment of the couple is: F ∗ d. In the right sketch the points of F 1, F 2 are B, A and are at distance r = 2m (Arm of the lever) from the point of rotation O (Fulcrum of the lever).

What is the resultant force of a couple moment?

A special case of moments is a couple. A couple consists of two parallel forces that are equal in magnitude, opposite in sense and do not share a line of action. It does not produce any translation, only rotation. The resultant force of a couple is zero. BUT, the resultant of a couple is not zero; it is a pure moment.

Does moment of force depend on reference point?

The moment of a force is only defined with respect to a certain point P (it is said to be the “moment about P “) and, in general, when P is changed, the moment changes. However, the moment (torque) of a couple is independent of the reference point P: Any point will give the same moment.