Learning Objectives :Learning Objectives :1.1. To know the names of some special case To know the names of some special case

moments.... (Couple/Torque)moments.... (Couple/Torque)

2.2. To understand stable/unstable To understand stable/unstable equilibrium, tilting, & topplingequilibrium, tilting, & toppling

Book Reference : Pages 100 & 101-103Book Reference : Pages 100 & 101-103

Definitions : Couples & TorquesDefinitions : Couples & Torques““A couple, (sometimes called a torque) is a A couple, (sometimes called a torque) is a pair of equal and opposite forces acting on pair of equal and opposite forces acting on a body but not on the same line”a body but not on the same line”

Force F

Taking moments about a random point p.....

Force F

d - xx

d

p

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 - xx

d

p

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)

Stable & Unstable Equilibrium:Stable & Unstable Equilibrium:

An object in An object in Stable Equilibrium Stable Equilibrium will will return to the equilibrium position once return to the equilibrium position once releasedreleased

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

Stable & Unstable Equilibrium:Stable & Unstable Equilibrium:

An object in An object in Unstable Equilibrium Unstable Equilibrium will will notnot return to the equilibrium position return to the equilibrium position once releasedonce 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

Neutral Equilibrium:Neutral Equilibrium:

An object in An object in Neutral Equilibrium Neutral Equilibrium will will rollroll

Object will roll, centre of mass neither raised or lowered.

Centre of Mass

Force

Which is which?Which is which?

Which is which?Which is which?

Unstable

stable

Neutral

Tilting :Tilting :

p

Tilting :Tilting : b

d

F

W p

Taking moments about p...Taking moments about p...

Clockwise : FdClockwise : Fd

Anticlockwise : Wb/2Anticlockwise : Wb/2

At the point of tilting Fd = Wb/2At the point of tilting Fd = Wb/2

What force is required to start to tilt a What force is required to start to tilt a bookcase weighing 800N with a base of bookcase weighing 800N with a base of 80cm x 80cm if the force is applied at 80cm x 80cm if the force is applied at the top of the 1.8M bookcase?the top of the 1.8M bookcase?