1. Learning Objectives : 1.To know the names of some special case moments.... (Couple/Torque) 2.To understand stable/unstable equilibrium, tilting, & toppling Book Reference : Pages 100 & 101-103

2. Definitions : Couples & Torques “A couple, (sometimes called a torque) is a pair of equal and opposite forces acting on a body but not on the same line” Force F Taking moments about a random point p..... Force F d - x x d p

3. Force F The moment at the end nearest p : Fx (anticlockwise) The moment at the other end : F(d-x) (anticlockwise) Total moment is the sum: = Fx + F(d-x) Multiplying out.... Fx + Fd - Fx Force F d - x x d p

4. So regardless of where you take the moments the total moment is always Fd Couple = Fd (or torque)...... In squiggly Greek letters τ = Fd (The units will be NM) (τ is pronounced tau)

5. Stable & Unstable Equilibrium: An object in Stable Equilibrium will return to the equilibrium position once released Centre of Mass Weight Point of Support Stable because Centre of Mass is directly below the point of support and raises as it is tilted

6. Stable & Unstable Equilibrium: An object in Unstable Equilibrium will not return to the equilibrium position once released Centre of Mass Point of Support Unstable because Centre of Mass is directly above the point of support and lowers as the object is tilted

7. Neutral Equilibrium: An object in Neutral Equilibrium will roll Object will roll, centre of mass neither raised or lowered. Centre of Mass Force

8. Which is which?

9. Unstable stable Neutral

10. Tilting : p

11. b d F W p

12. Taking moments about p... Clockwise : Fd Anticlockwise : Wb/2 At the point of tilting Fd = Wb/2 What force is required to start to tilt a bookcase weighing 800N with a base of 80cm x 80cm if the force is applied at the top of the 1.8M bookcase?