1.7.1States of Matter
Finding the Centre of Mass — Cambridge IGCSE Chemistry 0620 Revision Notes & Topical Questions
5 min read 5 parts Lesson 10 of 30 Unit quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Part 1 of 5The Centre of Mass
The centre of mass is a single point that represents where an object's whole mass can be considered to act.
Centre of mass
- Centre of mass The point in an object at which its whole mass can be considered to be concentrated, for the purposes of balance and motion.
Uniform density
- Uniform density An object with the same density throughout, so that the centre of mass of a symmetrical uniform object lies at its geometric centre.
Lamina
- Lamina A thin, flat object, sometimes called a plane lamina, which is used in experiments to find the centre of mass.
Plumb line
- Plumb line A weighted thread that hangs vertically, used to draw a vertical line from a suspension point across the lamina.
Part 2 of 5Symmetry Method
Symmetry can be used only for regular shapes with enough lines of symmetry.
1
Identify all the lines of symmetry of the shape, because the centre of mass lies on every line of symmetry.
2
Where two or more lines of symmetry cross, that point is the centre of mass of a uniform symmetrical object.
3
A shape with only one line of symmetry gives only one line, so the centre of mass cannot be found by symmetry alone.
4
For such a shape, use the suspension method instead, and state the centre of mass as the point where the lines cross.
Part 3 of 5Suspension Method
Suspension Method
Suspend
- Suspend Hang the lamina from a pivot or pin, and allow it to settle freely under gravity.
Plumb line
- Plumb line Hold a plumb line from the pivot and draw a line along it on the lamina, which must pass through the centre of mass.
Repeat
- Repeat Suspend the lamina from a second and a third point, drawing a line each time.
Intersection
- Intersection The centre of mass is the point where all the lines cross, and small errors produce a small triangle instead.
Part 4 of 5Worked Example
Question
- A student wants to find the centre of mass of a thin L-shaped piece of card.
- Describe a suitable method.
- The L-shape has no line of symmetry, so symmetry cannot be used.
- Make a hole near one corner, suspend the card from a pin through the hole and let it settle.
- Hold a plumb line below the pin, and draw a line along it on the card.
- Repeat from a second hole near another corner, then find where the two lines cross.
Answer
- Use the suspension method, drawing at least two lines with a plumb line;
- the centre of mass is where they cross.
Part 5 of 5Exam Checklist & Tips
1.7.1 – Key Points for the Exam
- Centre of mass The point through which the whole weight of an object can be considered to act.
- Symmetry A shape that can be divided into matching halves by a line of symmetry.
- Lamina A thin, flat object used to model two-dimensional mass distributions.
- Suspension method A method of finding the centre of mass by hanging an object from different points.
- Plumb line A weighted line that shows the vertical direction.
Common Mistakes
- Assuming the centre of mass must lie inside the outline of the object; for a ring, it lies in the hole.
- Using a single line of symmetry to locate a point.
- Drawing the plumb line from somewhere other than the suspension point.
- Suspending the object from only one point, which gives a line but not the centre of mass.
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