Ch 10 · 1.5.6 Centre of Gravity · O Level Physics 5054

Topic 10 of 17 in Motion, Forces and Energy — O Level Physics 5054 — 20 lessons.

Introduction

Why are racing cars built low and wide, and why does a bus with passengers standing on its top deck tip more easily? The answer is the centre of gravity: the point where an object's weight seems to act. Where it is decides whether an object balances, wobbles or topples. (Syllabus section 1.5.6.)

Key ideas

The centre of gravity of an object is the point through which its whole weight appears to act. For a uniform ruler or a uniform rectangle it is at the centre. An object balances if it is supported directly below (or above) its centre of gravity.

🧑‍🏫 Teacher's explanation

Imagine you are trying to balance a long ruler on your finger. There is one specific spot where, if you place your finger, the ruler stays perfectly level. That spot is the centre of gravity. It is the single point where the entire weight of the object seems to be concentrated. If you were to hang the object from that point, it would balance perfectly because the weight is pulling straight down through your support.

📖 Definitions

🔍 Worked example — Easy

A uniform rectangular wooden block has a mass of 0.5 kg. Calculate the weight of the block acting through its centre of gravity. (Use g = 10 m/s^2)

🔍 Worked example — Standard

A plane lamina (a flat sheet) is suspended from a point on its edge. A plumb line is used to mark the vertical line from the suspension point. If the lamina is rotated around the suspension point, the plumb line marks a line on the lamina. Where is the centre of gravity located relative to this line?

🔍 Worked example — Exam-style

A heavy vase is placed on a table. It is tilted by an angle θ. The vertical line from its centre of gravity passes through the edge of its base. Will the vase topple or return to its upright position?

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

(a) Define the term 'centre of gravity'. [1] (b) Explain why increasing the width of the base of an object increases its stability. [2] [3 marks]

Practical notes

This works because a freely hanging object comes to rest with its centre of gravity directly below the point of suspension, so the centre of gravity lies on every line drawn.

Worked example

Example: why a tall lorry tips. A lorry is loaded with a heavy load high up. Explain why it is more likely to topple on a sloping road than when loaded low down.

🔍 Worked example — Easy

A uniform rectangular wooden block has a mass of 2.0 kg. Where is its centre of gravity located?

🔍 Worked example — Standard

A student uses a plumb line to find the centre of gravity of a triangular lamina. They hang the lamina from a pivot at one corner. The plumb line shows the vertical line passes through a point 4.5 cm from the pivot. If the student repeats this from a different corner and the line passes 3.5 cm from that pivot, what is the approximate location of the centre of gravity?

🔍 Worked example — Exam-style

A tall, narrow cylinder of height h = 0.80 m and base width w = 0.20 m is tilted by an angle θ. At what angle θ will the cylinder begin to topple? (Assume the centre of gravity is at the geometric centre, h/2).

⚠️ Common errors

Common mistakes

Practice

Answers: (1) The point through which the whole weight of an object appears to act. (2) Hang it freely from a pin with a plumb line from the same pin; draw the line of the plumb line; repeat from another hole; the centre of gravity is where the lines cross. (3) Make the base wider; make the base heavier so the centre of gravity is lower. (4) A low centre of gravity and a wide base mean it must tilt through a large angle before the line of its weight passes outside its base, so it is less likely to topple.

Ch 10 · 1.5.6 Centre of Gravity · O Level Physics 5054

Introduction

Key ideas

🧑‍🏫 Teacher's explanation

📖 Definitions

🔍 Worked example — Easy

🔍 Worked example — Standard

🔍 Worked example — Exam-style

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Practical notes

Worked example

🔍 Worked example — Easy

🔍 Worked example — Standard

🔍 Worked example — Exam-style

⚠️ Common errors

Common mistakes

Practice

Summary

All chapters in Motion, Forces and Energy