Angular speed and acceleration – Further Maths ExamSolutions Maths Edexcel Revision

Understanding Angular Speed and Acceleration

Angular Speed is defined as the rate of change of angular displacement. It tells us how quickly an object moves around a circle.
Angular Speed is measured in radians per second.
Remember the relation between linear speed (v) and angular speed (ω): v = r*ω where r is the radius of the circular path.

The standard unit for angular speed is radians per second, however, it can also be represented in revolutions per minute (rpm).
Let’s unravel the mathematical representation:
- Mathematically, angular speed = θ/t where θ is the angle swept by the object in time t.
- The relation v = ω*r is derived from the definition of radian measure - where ω is angular speed, v is the linear speed, and r is radius. This equation tells us that for a fixed angular speed, the linear speed increases with increase in radius.

To convert angular speed given in revolutions per minute (rpm) to radians per second, multiply by 2π/60.
To convert from radians per second to revolutions per minute, multiply by the reciprocal, 60/2π.

Angular Acceleration is defined as the rate of change of angular speed. It tells us how quickly the angular speed of an object is changing.
It is denoted by α (alpha).
The units of angular acceleration are radians per second per second (radians per second squared).

Mathematically, angular acceleration = change in angular speed / time.
The relation between angular acceleration (α), angular velocity (ω), and time (t) is given by ω = ω0 + α*t, where ω0 is the initial angular velocity.
The relation between angle covered (θ), initial angular velocity (ω0), angular acceleration (α), and time (t) is given by θ = ω0t + 0.5α*t².