Unit 4.9 – Centre of Mass

1. For Symmetrical Objects:
   • In objects with uniform density and symmetrical shapes (e.g., spheres, cubes, rods), the centre of mass lies at the geometric centre.
2. For Irregular Objects:
   • For irregularly shaped objects or objects with non-uniform density, the centre of mass may not lie within the object itself. For example, the centre of mass of a boomerang or a ring lies outside the material of the object.
3. Motion of the Centre of Mass:
   • If an external force acts on an object, the centre of mass moves as if all the mass of the object were concentrated at that point.
   • Internal forces (e.g., forces between parts of the same object) do not affect the motion of the centre of mass.
4. Centre of Mass vs. Centre of Gravity:
   • In most cases, the centre of mass and the centre of gravity coincide, especially near the Earth's surface where gravity is uniform.
   • However, in situations where the gravitational field is not uniform (e.g., very large objects like planets), the two points may differ.

Quick Review, Exam Tips, Tricks & Traps

1. The centre of mass is the point where the entire mass of an object is assumed to be concentrated.
2. For symmetrical objects with uniform density, the centre of mass lies at the geometric centre.
3. The motion of the centre of mass depends only on external forces, not internal forces.

1. Always check whether the object is symmetrical or irregular to determine the location of the centre of mass.
2. Use symmetry arguments to quickly identify the centre of mass for regular shapes like spheres, cubes, and rods.
3. Remember that the centre of mass may lie outside the physical boundaries of an object (e.g., a ring or a hollow sphere).

1. Students often confuse the centre of mass with the geometric centre for irregular objects. Always consider the distribution of mass.
2. Misinterpreting the effect of internal forces: Internal forces do not affect the motion of the centre of mass.

1. Look for symmetry in the object to quickly locate the centre of mass.
2. In MCQs, eliminate options where the centre of mass is incorrectly placed for irregular objects.

Additional Content: Applications of the Centre of Mass

• The position of the centre of mass affects the stability of an object.
  • A lower centre of mass makes an object more stable (e.g., cars are designed with a low centre of mass to prevent tipping over).
  • A higher centre of mass makes an object less stable (e.g., tall buildings or leaning towers).

• In sports like high jump or gymnastics, athletes manipulate their body positions to shift their centre of mass for better performance.
• For projectiles, the centre of mass follows a parabolic path regardless of the object's rotation.

• Engineers use the concept of the centre of mass to design stable structures, vehicles, and machinery.
• For example, cranes are designed to keep their centre of mass within a stable base to prevent tipping.

• In celestial mechanics, the centre of mass of a system (e.g., Earth-Moon system) is used to study orbital motion.
• The Sun and planets orbit around their common centre of mass, called the barycentre.