Moments
- 1. TURNING EFFECTS OF FORCES (MOMENTS!) Introduction: Hey guys! How are you? Today we are going to study a really interesting topic i.e. Moments. Okay so you open and close doors everyday in your life, right? So that’s the turning effect you create. Definition: What is moment? The moment of a force is the product of the force and the perpendicular distance from the pivot to the line of action of force. Moment of force = F x s Where F is the force (in N) and s is the perpendicular distance from pivot (in m). The SI unit of the moment of force is the newton metre (N m) and it is a vector quantity. Let’s make it more clearer. At which part of the door, A or B, is the least effort required to open it? A larger force is needed if the force is applied nearer the hinge (i.e. B) and a smaller force is needed if the force is applied further away from the hinge. Why is that so? We know that in both cases, same moment will turn the door. Keeping this in mind, we shall conclude that decreasing the distance from the hinge (pivot) will automatically need a greater force in order to create the same magnitude of moment. Conversely, increasing the distance from the pivot requires a lesser force to create the same moment. Got the concept? Let’s move on! We know that moment is a vector quantity, so..what is it’s direction? It is a turning effect so it must be either clockwise or anti-clockwise about the pivot. So to describe the moment completely, we need: 1. The magnitude of the moment in N m; 2. The direction of the moment: clockwise or anti-clockwise. Principle of Moments: This will make every question a piece of cake for you! So here we go: the principle of moments states that when a body is in equilibrium, the sum of clockwise moments about the pivot is equal to the sum of anti-clockwise moments about the same pivot.
- 2. Let us solve this question together to find the value of F when the body is in equilibrium, and you’ll be clear of how to solve such a question. First, determine the clockwise forces and the anti-clockwise forces. Let’s learn a simple way of doing that! Just turn the head of the arrow of force F towards the pivot and keep turning it in a circular direction. What direction do you get? Umm..it’s anti-clockwise! Now for the 5 N force, turn the arrow head towards the pivot and you’ll see it turns in clockwise direction. More practice will make it easier for you. As we learnt that anticlockwise moments are equal to clockwise moments for a body in equilibrium, we can form an equation easily: Anti-clockwise moments = Clockwise moments F1 x s1 = F2 x s2 F (0.25) = 5 ( 0.5) F = 2.5 / 0.25 F = 10 N Easy, isn’t it? But even if you get harder questions, you can solve them easily if your concepts are clear. Let’s do another question before moving on. It asks to find the value of d when the body is in equilibrium. Okay so let’s apply the principle of moments: Anti-clockwise moments = Clockwise moments F1 x s1 = F2 x s2 10 (6) = 30 (d) 60 / 30 = d d = 2 m Yeah you’re right, it’s that easy! Q1: Find the force F in the following case if the body is in equilibrium.
- 3. Conditions for Equilibrium: So the question is when is equilibrium reached? We have discussed in the earlier tutorial on Forces that for a stationary object and for an object moving with constant velocity, resultant force is zero. And we have just learnt from the Principle of Moments that if an object is not turning, it is in , equilibrium, that is, resultant moment is zero. To summarize it, equilibrium is reached when: 1. The resultant force acting is zero, or you can the forces are balanced. 2. The resultant moment about the pivot is zero, that is, the Principle of Moments must be applicable on the given situation (as we did in the questions). Types of Equilibrium: 1. Stable equilibrium ● occurs when an object is placed in such a position that any disturbance effort would raise its centre of gravity ● the centre of gravity still falls in its base so it returns to its original position (as an anti-clockwise moment is created as shown above by the arrow) 2. Unstable equilibrium ● occurs when an object is placed in such a position that any disturbance effort would lower its centre of gravity ● the centre of gravity no longer falls in its base so it topples over to fall into a more stable position (a clockwise moment is created shown by an arrow above) 3. Neutral equilibrium
- 4. ● occurs when an object is placed in such a position that any disturbance effort would not change the level of its centre of gravity ● no such moment is created The following diagrams will make it more clear: Take a look at the above diagram, in (a), the block is in stable equilibrium and it won’t topple. In (b), the wooden block is disturbed and an anti-clockwise moment will cause it to return to its original position as the centre of gravity still falls in its base. While in ( c), the centre of gravity does not fall in its base so it topples over as a clockwise moments is created. It’s not that difficult, just be clear of centre of gravity and how moment is created Q2: Now examine the following diagram to see what will happen in (b). Centre of Gravity: Any idea of what centre of gravity is? Let me explain. Centre of gravity of an object is the point through which its whole weight appears to act. Let’s consider a metre rule, it’s uniform that means it has equal thickness throughout. So where will its entire weight act? In the centre of course i.e. 50 cm mark. Okay that was easy. Now how will you find the centre of gravity of an irregular thing like this:
- 5. Not that simple it is, but once we learn the method, it will turn out to be easy for any possible weird shape you can think of. The method goes like this: Firstly hang the shape somewhere with a pin as shown. And with the pin, hang a thread with a weight hanging on it which will keep the thread straight (it’s a paper clip in this case). Now draw a line in-line with the thread on the shape. Now repeat the procedure with another two or three points where you will hang the thread and draw lines. The point where the lines intersect is the centre of gravity the shape. Try it at home, cut a weird shape and carry the procedure, once you get the centre point of intersection (i.e. centre of gravity), try balancing the shape on that point on your finger and you will see that it balances on none other point but the centre of gravity. Interesting, isn’t it?
- 6. Answers: Q1. 6.4 N Q2. The wooden block will topple over because the centre of gravity no longer falls in its base.
- 7. Answers: Q1. 6.4 N Q2. The wooden block will topple over because the centre of gravity no longer falls in its base.