STUDY4MECHANICAL for Mechanical Engineers

Moment and couple are two important concepts found in mechanics. They both terms describe the effect and cause of rotation in the system of forces , particle systems, and rigid bodies too.  What is a moment of a force? The turning effect produced by a force applied to a rotational system or on the body at a distance from the axis of rotation is called the moment of force . The moment of a force is the product of the force and the perpendicular distance of the point, about which the moment is required and the line of action of the force. What is a couple OR moment of a couple?   In mechanics, a couple refers to two equal and opposite forces, whose line of action is different from a couple . The couple also called a force couple or pure moment.  Points of difference between moment and couple are discussed below. So let us check out some key differences between them to know more about it.  Difference between moment and couple: ...

Couple:  The couple is a system of two forces that are equal in magnitude, opposite in direction and have a line of action are parallel.  Moment of a couple: Moment of a couple is the product of the magnitude of one of the forces that make up the couple and the perpendicular distance between their parallel lines of action. It is a measure of the capacity of the couple to cause rotation. 

Definition of a couple in Mechanics: In mechanics, a couple refers to two equal and opposite forces, whose line of action is different from a couple. The couple also called a force couple or pure moment.  Moment of couple The perpendicular distance between L and M of the two equal and opposite forces is known as the arm of the couple. The magnitude of the couple is the product of one of the forces and the arm of the couple.  Mathematically, Moment of couple = LM × F A little analysis can show that a couple produces no translational motion but a couple produces a body rotation motion that acts on it.

Definition of parallel forces: A parallel force is a situation in which two forces of equal magnitude act whose line of action is parallel to each other within the same plane are said to be a parallel force.  Example -  A see-saw Types of parallel forces: Like parallel forces  If the parallel forces act in the same direction then these forces are known as, like parallel forces.  Unlike parallel forces  If the parallel forces act in the opposite direction then these forces are known as, unlike parallel forces. 

Varignon's theorem also called the principle of moments.  Varignon's Principle: Varignon's principle states that if a number of concurrent forces acting on a particle are in equilibrium, then the algebraic sum the moments that each force creates about a single point will be equal to the moment of their resultant force about the same point.   Varignon's Theorem From the above figure, F1 and F2 are two concurrent forces and their resultant is R. The moment produced by R with respect to a moment center O is R × d. The moment produced by the force F1 and F2 is respectively F1 × d1 and F2 × d2.  As per varignon's therorem R d = F1 d1 + F2 d2 Notes: This theorem initially stated for two concurrent forces, but, it is true for any system of forces and any number of concurrent or coplanar forces.  One of the practical applications of this theorem is to find the unknown reactions when a system is known to be in equilibrium under...

The turning effect produced by a force applied to a rotational system or on the body at a distance from the axis of rotation is called the moment of force. The moment of a force is the product of the force and the perpendicular distance of the point, about which the moment is required and the line of action of the force.  Moment of force Mathematically, the moment of force F1 about point 2 = F1 × d  The unit of moment of force depends on the units of force and perpendicular distance. If the unit of force is in newtons and the perpendicular distance in meters, then the unit of the moment will be Newton-meter (N-m). 

When two or more than two forces of different magnitude and different directions act on the body they form a system of forces. Depending upon plane and direction the different types of system of forces categorize are following below.  System of forces: Coplanar forces If all the forces in the system lie in a single plane or whose line of action lies on the same plane are known as coplanar forces.  Concurrent forces  The forces that are meet at one point or if the line of action of all the forces in a system passes through a single point are known as concurrent forces.  Coplanar concurrent forces The forces that are meet at one point and their line of action also lie on the same plane are known as coplanar concurrent forces.  Coplanar parallel forces  The forces are parallel to each other and lie in the single plane are known as coplanar parallel forces.   Coplanar like parallel forces The forces are ...