Rigid Bodies in Equilibrium Know the conditions for tilting Understand how to use above to solve questions To be able to solve equilibrium problems where you must choose where to take moments about.

More on moments You’re not limited to taking moments about a pivot / hinge. Can take a moment about any point. Take moments about this end We normally choose a point to get rid of an unknown (perp. distance = 0, moment = 0)

Example Here is a light rod with some forces acting on it. What has to happen for it to remain in equilibrium? Is it possible to work out the forces R1 and R2? 2000N 5000N 1m 6m 3m R1 R2

Example I’m going to take moments about R1 2000N 5000N 1m 6m 3m R1 R2

Example There’s a quick way to find the other force. If in equilibrium, vertical forces are in equilibrium. 2000N 5000N 1m 6m 3m R1 R2

Keywords Light – no mass Uniform – mass is evenly distributed in object. We can take the centre of mass, where the weight acts, to be in the middle of object Non-uniform – mass is not evenly distributed. Centre of mass will have to be found, or is given. Non-uniform – that day you paid £1 to come to school in your pyjamas and everyone just kept saying ‘It’s just a phase.’

Try to balance them all! Pick a set of characters and a scale, and try to balance them all. You have 15 mins to get all the characters on. Bonus points are given for awesomeness.

Tilting When an object is on the point of tilting it will not actually tilt. Considering tilting helps us decide on the important condition. This is that the reaction force at the other support will become zero. You could also consider strings where the tension in one string will become zero.

Example A Uniform beam, of mass 16kg and length 12m, rests horizontally on supports at 2m from its left end and 4m from it’s right end. A child of mass 32kg and an adult of mass 70kg stand on the beam at the left end and right end respectively Find the mass which the adult would need to be carrying for the beam to be just on the point of tilting.

Example 0N R 2m 4m 6m 16g 32g (70+x)g

Example 0N 1176N 2m 4m 6m 16g 32g (70+x)g

Independent Study Exercise B Q3-8 p14 & Exercise C Q1-6 p17 (solutions p 146-147)