Fundamental Units (Edexcel A-Level Mathematics): Revision Notes

1.1.2 Fundamental Units

Fundamental Units in A-Level Mechanics

In A-Level Mechanics, understanding the fundamental units is essential as they are the building blocks for all physical quantities. These units are part of the International System of Units (SI), which provides a standard for measurements used globally in science and engineering.

The Seven Fundamental Units

1. Mass:

• Unit: Kilogramme (kg)
• Description: Mass is a measure of the amount of matter in an object. It's a fundamental property that doesn't change regardless of location.

2. Length:

• Unit: Metre (m)
• Description: Length is the measure of distance. In mechanics, it's used to quantify how far an object has moved or how large an object is.

3. Time:

• Unit: Second (s)
• Description: Time is the ongoing sequence of events. In mechanics, time is essential for calculating speed, velocity, and acceleration.

4. Electric Current:

• Unit: Ampere (A)
• Description: Though more relevant in electromagnetism, current is included as a fundamental unit. It's the rate at which electric charge flows through a conductor.

5. Temperature:

• Unit: Kelvin (K)
• Description: Temperature measures the average kinetic energy of particles in a substance. While not directly involved in basic mechanics, it is crucial in thermodynamics and kinetic theory.

6. Amount of Substance:

• Unit: Mole (mol)
• Description: A mole represents a quantity of substance, specifically the number of atoms or molecules in a given amount of material. It's more relevant in chemistry but included in the list of fundamental units.

7. Luminous Intensity:

• Unit: Candela (cd)
• Description: Luminous intensity is the measure of the perceived power of light. This unit is more relevant in optics and photometry.

Derived Units in Mechanics

In mechanics, many quantities are derived from the fundamental units. Here are some examples:

8. Velocity:

• Unit: Metres per second (m/s)
• Derived From: Length (metres) and Time (seconds)
• Description: Velocity is the rate of change of displacement with time, and it is a vector quantity.

9. Acceleration:

• Unit: Metres per second squared (m/s²)
• Derived From: Velocity (m/s) and Time (seconds)
• Description: Acceleration is the rate of change of velocity with time.

10. Force:

• Unit: Newton (N)
• Derived From: Mass (kilogrammes), Length (metres), and Time (seconds)
• Description: Force is defined as mass times acceleration. One Newton is the force required to accelerate a 1 kg mass by 1 m/s².
• Formula: $F = ma$ (where $F$ is force, $m$ is mass, and $a$ is acceleration).

11. Energy/Work:

• Unit: Joule (J)
• Derived From: Force (Newtons) and Length (metres)
• Description: Energy and work are related concepts; energy is the capacity to do work, and work is done when a force causes displacement.
• Formula: $W = F \times d$ (where $W$ is work, $F$ is force, and $d$ is displacement).

12. Power:

• Unit: Watt (W)
• Derived From: Energy (Joules) and Time (seconds)
• Description: Power is the rate at which work is done or energy is transferred.
• Formula: $P = \frac{W}{t}$ (where $P$ is power, $W$ is work, and $t$ is time).

Importance of Fundamental Units

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