Further Centres of Mass

Further Centres of Mass

Rigid Bodies and Equilibrium

• Equilibrium of a rigid body requires that both net force and net moment of the forces are zero.
• A rigid body is in equilibrium if it remains in rest or continues to move with uniform speed in a straight line.

Understanding Moments

• The moment of a force about a point is the force multiplied by the perpendicular distance from the point to the line of action of the force.
• Principle of moments: For a body to be in equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point.

Location of Centre of Mass

• Centre of mass of a body or a system of particles is the point at which the whole mass of the body or system may be assumed to be concentrated.
• For a uniform body (density is constant), the centre of mass is at the geometric centre.
• The coordinates of the centre of mass (X,Y) of a system of particles can be found using the formulas: X = (sum of (mass * x-coordinate))/total mass, Y = (sum of (mass * y-coordinate))/total mass

Use of Integration in Centre of Mass

• Integration can be used to determine the position of the centre of mass of an extended object, by integrating over the continuous distribution of mass.
• The distribution of mass is described by a mass density function, which may vary from point to point.

Centre of Mass of Composites Bodies

• If a body is made up of several simple shapes for which the centre of mass is known, the overall centre of mass of the composite body can be calculated as the weighted average of the centres of mass of the individual shapes.
• The mass of each shape is considered to be concentrated at its centre of mass for this calculation.