Mechanics-Chapter 5-Moments

Thomas Marshall
Mind Map by Thomas Marshall, updated more than 1 year ago
Thomas Marshall
Created by Thomas Marshall over 4 years ago
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A chapter overview on Maths Mechanics-Moments

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Mechanics-Chapter 5-Moments
1 Equations
1.1 Force of Moment=Perpendicualr distance from Pivot X Force
1.1.1 P=FD
1.1.1.1 Remember this must include a direction (Clockwise or Anticlockwise)
1.1.1.1.1 If not perpendicular the use the equation
1.1.1.1.1.1 P=F X Dsinθ
2 We can find the sum of multiple moments around a point by taking one from the other. EG A force 3N acting clockwise with a perpendicular distance of 5m and a force 10N with a perpendicular distance of 2m acting anticlockwise are acting on the point P. Find the resultant force.
2.1 So we know that one is 5X3 and the other is 2X10. So if we take one and mius it from the other = (2X10)-(5X3)= we get a force of 5NM. We know this will be anticlockwise as that was the number we took away from.
2.1.1 So the answer is 5NM anticlockwise.
2.1.1.1 If you are unsure what way it will be moving then that's easy. First, what was the first force you used. Is it clockwise or anticlockwise? If it's positive it will be that one negative the opposite one.
2.1.1.1.1 If it is not perpendicular the just use Dsinθ X F for each moment like stated in the equations section.
2.2 Still draw a diagram for these as it will help. I have not as it is a simple diagram and you should be able to draw it without my help on that
3 When something is in equilibrium its resultant force =0. This means we can solve the reaction force at any point by finding just one point
3.1 For example- A uniform rod AB of length 5m and weight 20N is resting on two points C and D. Such that C is 1m from A and 3m from D. Find the reaction at C and D.
3.1.1 We know RC + RD = 20. So if we consider the moments about point C we get 20 X 1.5 = RC X 3. We know this as the clockwise moments = the anticlockwise moments. 30=3RC. RC=10
3.1.1.1 If more forces are involved just add them to each side.
3.1.1.1.1 When we have a non-uniform rod it is the same bu the point of mass is not in the middle.
3.1.1.1.1.1 This therefore only changes your diagram and just move the Weight/mass to where it should and change the distances. Everything will stay the same.
3.1.1.1.1.1.1 If you don't have the mass then just rearrange the formula to help you find it.
3.2 Start by drawing a diagram like the one below. This will help a lot.
4 Draw a diagram everytime it will help a lot.
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