CORE Physics (9223) | Centre of mass

🔬 Study Notes: Centre of Mass (CORE Physics 9223)

Hello future physicists! Welcome to the exciting world of balance and stability. This chapter is super important because it connects the idea of force (gravity) with how things stay upright (or why they fall over!). Understanding the Centre of Mass helps us design stable cars, tall buildings, and even helps athletes improve their performance.
Don't worry if this seems tricky at first—we'll break it down using real-world examples you see every day!

1. Defining the Centre of Mass (CoM)

What is the Centre of Mass (CoM)?

Imagine you are trying to balance a broomstick on one finger. There is only one exact spot where you can place your finger so that the broomstick stays perfectly still. That special point is its Centre of Mass.

The Centre of Mass (CoM) is the specific point where the entire mass of an object appears to be concentrated.

• Key Concept: When we talk about gravity pulling on an object, we treat the entire gravitational force (the object's weight) as acting only through this single point.
• The Analogy: Think of the CoM as the object's personal "balance point." If you support an object at its CoM, it will balance perfectly.

CoM vs. Centre of Gravity (CoG)

At the International GCSE level, the terms Centre of Mass (CoM) and Centre of Gravity (CoG) are usually used interchangeably.
Technically:

• The CoM relates to how the object's mass is distributed.
• The CoG relates to the point where the total gravitational force (weight) acts.

For all calculations and concepts in this course, you can assume CoM = CoG.

Where is the CoM Located?

The location of the CoM depends entirely on the shape and mass distribution of the object.

1. Regular, Uniform Shapes:

• For symmetrical objects (like a uniform ruler, square, or sphere), the CoM is exactly at the geometric centre.
• Example: The CoM of a perfect cube is where all its diagonals cross.

2. Non-Uniform or Irregular Shapes:

• If an object is irregular (or if the mass is heavier on one side), the CoM will shift towards the heavier side.
• Did You Know? The CoM doesn't always have to be inside the object! Think of a doughnut or a horseshoe; the balance point is in the empty space!

2. Finding the Centre of Mass Experimentally

We often need to find the CoM of flat, irregular objects (called laminas) experimentally. We use a simple method based on how gravity works: the Plumb Line Method.

The Plumb Line Method (For Irregular Laminas)

This method relies on the fact that when an object is hanging freely and is at rest, its Centre of Mass must be directly below the point of suspension. Why? Because if the CoM wasn't directly below the pivot, gravity would exert a turning force (a moment) that would cause it to swing until it settles.

Step-by-Step Guide to the Experiment

You will need an irregular flat sheet of cardboard, a pin (to use as a pivot), a stand, and a plumb line (a string with a weight attached).

1. Prepare the Object: Punch at least three small holes (A, B, and C) near the edges of the irregular lamina.
2. First Suspension: Hang the lamina freely from hole A using the pin and stand.
3. Use the Plumb Line: Hang the plumb line from the same pin. When the lamina and plumb line are perfectly still, the plumb line shows you the exact vertical line passing through the CoM.
4. Mark the Line: Carefully draw a vertical line on the lamina exactly along the plumb line (Line 1).
5. Repeat the Process: Move the pin and hang the lamina from a different hole (hole B). Let it settle.
6. Find the Intersection: Draw the new vertical line (Line 2) along the plumb line.
7. The CoM is Found: Repeat with the third hole (C) to draw Line 3 (this is a check, two lines are technically enough). The point where all three lines intersect is the Centre of Mass (CoM).

Avoiding Common Mistakes

• Mistake: Drawing the line before the object has completely stopped swinging.
  Tip: Wait until the plumb line is absolutely still to ensure accuracy.
• Mistake: Drawing the line slightly offset from the plumb line.
  Tip: Use a thin pencil and make sure your eye is level with the lamina when marking the line.

3. Centre of Mass and Stability

This is where the CoM concept truly fits into the "Forces and their effects" section. The position of the Centre of Mass is the single biggest factor determining how stable an object is—that is, how hard it is to knock over or topple.

Stability Explained

An object’s stability is its ability to return to its original position after being slightly disturbed. Stability is maximized by two main factors:

1. A Wide Base Area

• The base area is the area of contact between the object and the surface it rests on.
• The wider the base, the more stable the object.
• Example: A pyramid is much harder to knock over than a thin pole because it has a huge base area.

2. A Low Centre of Mass

• The lower the CoM is, the more stable the object is.
• Example: Racing cars are built extremely low to the ground (low CoM) to prevent rolling, especially when cornering quickly. Double-decker buses have very heavy engines (low CoM) placed near the bottom for safety.

Toppling – When Things Fall Over

An object will topple (fall over) when its weight acts outside its base area.

Step-by-Step Explanation of Toppling:

1. The total weight of the object acts downwards through its Centre of Mass.
2. We imagine a vertical line extending downwards from the CoM. This is the line of action of the weight.
3. As you tilt an object, the CoM moves sideways.
4. As long as the line of action of the weight falls *inside* the base area, gravity creates a moment (a turning force) that pulls the object back upright. This makes the object stable.
5. The moment the line of action of the weight falls *outside* the base area, gravity creates a moment that increases the tilt, and the object topples.

Analogy: Think about carrying a heavy backpack. If you lean forward too much (shifting your CoM outside your feet), you will lose your balance and fall. Your feet are your base area!

Practical Applications of Stability

We rely on stability in many real-world designs:

• Cranes: They have heavy counterweights placed low down to lower the overall CoM, increasing stability even when lifting heavy loads high up.
• Sports: A wrestler adopts a wide stance and crouches down (increasing base area and lowering CoM) to make it harder for an opponent to throw them.
• Leaning Tower of Pisa: This famous tower hasn't fallen because, despite its lean, its CoM is still high enough, and its line of action of weight still falls just inside the large circular base!