4 - Centre of Mass and Equilibrium

Centre of Mass

conceptual point where all the mass of a body can be considered concentrated

1. Point mass representing whole mass of a system

2. Single force/resultant of more then 1 force has to pass through CoM for linear movement

3. Point about which a free body will rotate

Point Mass

Mass at 1 point

1. Newton’s laws are applied to point masses

2. Apply Newton’s laws to CoM

CoM

1. Distribution of mass is equal in all direction

2. No response to gravitational field

Centre of Gravity

1. Distribution of weight equal in all directions

2. Depends on gravitational field

3. Conceptual point which has same potential energy of body + through which resultant gravitational forces will pass

Gravity

force acting between masses

1. Always attractive

2. Depends on masses involved in separation

Finding CoG to CoM

1. Geometric Shape - know the distribution of all points

2. Rigid Bodies - balance/knife edge method (CoG above point of support)

3. Equilibrium - balance

Equilibrium

Balanced set of forces and moments resulting in no acceleration of the body

1. System in eqilibrium:

   • sum of body forces = 0

   • sum of moments about point = 0

2. Moment of force about an axis = product of a force and the perpendicular distance from the line of of action of the force to the pivot point

Moment Equation

Moment = Force x Perpendicular distance

Determining CG (Equipment)

1. Statograph - summing moments about 1 axis

2. Reaction Board - summing moments about 2 axis

Moments about foot pivot point

Force

Mass x Acceleration

Weight

Mass x Acceleration due to gravity (9.81)