Centre of Mass

• Definition: The point at which the entire mass of an object can be considered to be concentrated.
• Acts as though the total mass of the object were located at this point.
• The center of mass of a rigid object is the same as its center of gravity.

Determining Centre of Mass in a Lamina:

Lamina:

• A 2-D shape that is thin and can be considered to be two-dimensional.

Materials:

• Stand
• Strings
• Card
• Pin
• Mass

Procedure:

1. Cut the card into an irregular shape.
2. Allow the card to swing freely from a pin fixed in a retort stand.

Explanation:

• After repeating the procedure, all lines drawn will intersect at a single point on the card, known as the centre of mass or gravity.
• The lines drawn are called plumb lines.

Centre of Mass in Uniform Rods:

• For a uniform rod (e.g., a metre rule), the mass is evenly distributed along its length.
• The centre of mass is located at the midpoint of the rod.
  Centre of Mass=Length of the Rod/2​

Exercise:

1. Draw plumb lines to find the centre of mass in various shapes.
2. Find the torque of a force.
3. Calculate the upward forces F1​ and F2.
4. Find X.
5. State two factors that affect the moment of force.

Experiment:

1. Determine the centre of mass of an irregular-shaped cardboard.
2. Describe an experiment to verify the turning effects of a force.

Force and Torque:

• Torque: The moment or turning effect of a couple.
• Couple: Two equal and parallel forces acting in opposite directions but with different lines of action, causing rotation.
• Example: The quarter-past-three position on a car steering wheel.

This detailed guide covers the fundamental concepts, principles, and applications of moments of forces, including practical examples and experiments.