M1: Chapter 5 Moments Dr J Frost Last modified: 2 nd April 2014 Learning Objectives: Understand what is meant by the moment of a force. Use moments to solve problems involving unknown lengths, forces and masses.

Intro This is a door Why do you think the handle is put on the other side of the door from the hinge? Increasing the distance of the force applied from the point of rotation increases the ‘turning effect’ of the force. ? If I double the distance of my finger from the hinge, what happens to the force required to keep the door open? As the distance doubles, the force required halves (we’ll see why). ?

Moments about a point perpendicular distance 10m m = 70kg ? ? 

Moments - Examples 123 ? ? ? We see what force is acting perpendicularly. 4 ? 5 ?

Summing moments We can also find the overall moment by summing them – just treat one of the directions (clockwise or anticlockwise) as negative. 1 ? 2 ? 3 ? 4 ? (Rod is light)

Exercise ?? ?

This whole chapter in a nutshell… 10m m = 70kg  If a rigid body is in equilibrium then: The resultant force in any direction is 0. The sum of the moments about any point is 0. a b 2m i.e. Forces up = forces down i.e. Clockwise moments = anticlockwise moments

Example 10m m = 70kg m = ? 2m Lewis and Tom are on a uniform seesaw of mass 20kg, where the pivot is not central. Lewis weighs 70kg and is 10m from the pivot. Tom is 2m from the pivot. The seesaw is horizontal. Determine the reaction force at the pivot of the seesaw. Determine how heavy Tom is. Bro Tip: First draw on forces. Click to Brosketch Lewis Tom ? ? Hint: Choose a suitable point to take moments about.

Moments about which point? 10m m = 70kg m = ? 2m Lewis Tom Key Point: You can choose different points to take your moments about, depending on which variable we wish to ‘ignore’. ? ?

Test Your Understanding A uniform rod of mass 20kg is supported at each end so that it is horizontal. The bar is 4m long and a mass of 10kg is placed 1m from one end. Find the magnitude of the reactions at each support. A uniform rod of mass 20kg is supported at each end so that it is horizontal. The bar is 4m long and a mass of 10kg is placed 1m from one end. Find the magnitude of the reactions at each support. ? Working ? Diagram Q

Finding centre of mass ? Working ? Diagram Q

Exam Questions On provided hand-out. (Solutions on following slides)

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?? Hint: When the beam is on the verge of tilting about P, there is no reaction force at Q. ?

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Summary ? ? ? ? ? ?  LO: Understand what is meant by the moment of a force.  LO: Solve problems involving moments.