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Wednesday, 13 November 2019

MOMENT OF FORCE IN ENGINEERING MECHANICS

We have started a new topic in our previous post i.e. engineering mechanics. We have seen there the basics of engineering mechanics such as concept of force systemprinciple of transmissibility of forces and its limitations, classification of force system, body force and surface force in mechanics.  

Now, we will be interested to understand here the moment of force in engineering mechanics  with the help of this post. 

Moment of a force in mechanics 

As we have studied earlier that the effect of a force on a body or object will be the combination of translation motion i.e. linear motion and rotational motion. Only translation or only rotational motion will be in exceptional cases. 

Moment of force 

Moment of force is basically defined as the measure of the tendency of the force to rotate the body about the point of interest. 

Let us consider the following figure where a force F is acting at a point on the body. Let us think that we need to find out the moment of this force F about a point P which is an arbitrary point on the body as displayed here in following figure. 


Let us assume that r is the positional vector of the force F with respect to the arbitrary point P.
Therefore, we can write down the equation to find out the rotary or rotational effect of force F about the arbitrary point P as mentioned here. 


Above equation is representing the moment of force in vector form. Let us now find out the magnitude of the moment of force. 

Moment of force = Force x Perpendicular distance from the pivot point to the line of action of the force

Unit of moment of force = Unit of force x unit of distance 
Unit of moment of force = N x m  
Unit of moment of force will be N-m in SI system. 

Sign convention for moment of force 

We need to consider and visualize physically how the force is trying to rotate the object. In order to find out the sign of moment or moment of force i.e. positive or negative moment, we use the concept of right-hand thumb rule. 

If force is trying to rotate the object in anti-clock wise direction, moment of force will be taken as positive. 

Let us see here the following figure, when we will close the finger in anti-clock wise direction, thumb will be in upward direction and it will be the indication for positive moment of force in our sign-convention for moment of force.

Similarly, if force is trying to rotate the object in clock wise direction, moment of force will be taken as negative. 

Therefore, we need to take care the sign conventions for moment of force and we must note it here that moment of force will be always expressed with its magnitude, unit of measurement and sense of rotation i.e. positive or negative sign. 

Important notes 

There are few very important points that we need to keep in our mind while dealing with the moment of force. 
  1. Like force, Moment of force is also a vector quantity. 
  2. Moment of force and force are sliding vectors. 
  3. Anti-clock wise rotation or counter clock wise rotation about the pivot will be taken as positive. 
  4. Clock wise rotation about the pivot will be taken as negative. 
  5. Moment of force will be considered as the function of magnitude of the force and the moment arm. 
  6. Unit of moment of force will be N-m in SI system. 

Therefore, we have seen here the basics of moment of force, unit of moment of force, equation to determine the moment of force and finally we have also seen the sign conventions used to express the moment of force with the help of this post.  

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Further we will find out, in our next post, varignon's theorem in engineering mechanics.  

Reference:  

Engineering Mechanics, By Prof K. Ramesh 
Image courtesy: Google 

Also read 


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