---
title: "Rotational Kinematics and the Angular Velocity Vector"
description: "Angular displacement, velocity and acceleration are defined by the same derivatives as their linear partners, and angular velocity points along the axis. Every point of a rigid body then has a linear "
canonical: https://lightmysky.com/learn/science/rotational-kinematics-and-the-angular-velocity-vector-mt_2UqK-zViqf
source: https://lightmysky.com/learn/science/rotational-kinematics-and-the-angular-velocity-vector-mt_2UqK-zViqf.md
retrieved: 2026-09-12
---

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# Rotational Kinematics and the Angular Velocity Vector

Angular displacement, velocity and acceleration are defined by the same derivatives as their linear partners, and angular velocity points along the axis. Every point of a rigid body then has a linear speed set by its distance from that axis.

Subject: Science · Area: Forces & Motion · Ages 20 to 21
Page: https://lightmysky.com/learn/science/rotational-kinematics-and-the-angular-velocity-vector-mt_2UqK-zViqf

## Ready when they can

- Relates angular and linear speed, tangential acceleration and centripetal acceleration for a point on a rotating body
- Uses the right-hand rule to give an angular velocity its direction
- Solves constant angular acceleration problems with the rotational analogues of the constant-acceleration equations

## Lesson: How spin is measured

Spinning bodies get their own vocabulary: angle replaces position, angular velocity replaces velocity, and angular acceleration replaces acceleration. Angular velocity is a vector along the axis: curl the fingers of your right hand with the spin and your thumb points along it. Flip the spin and the arrow flips too. Rotation maths needs radians, since arc length equals radius times angle only in radians.

Steady spin-up behaves exactly like steady speeding up. With constant angular acceleration, angle and angular velocity follow the familiar constant acceleration equations with rotational symbols: omega equals omega zero plus alpha t, with a matching quadratic for angle. Spin from rest, coast at a fixed rate, brake to a stop: each phase is one equation.

**Example.** Every spinning point also moves in a straight line sense, with radius as the bridge. Linear speed is radius times angular speed, so outer rim points race while hub points crawl: at radius 2 with omega 3, the speed is 6. Two accelerations act: tangential from changing the spin rate, equal to radius times alpha, and centripetal from turning toward the centre, equal to radius times omega squared and always inward.

**Recap.** Angle, omega and alpha mirror linear motion, radians rule the maths, and radius turns spin into speed and two accelerations.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Circular Motion: Angular Speed and Centripetal Force](https://lightmysky.com/learn/science/circular-motion-angular-speed-and-centripetal-force-mt_PW1G6nYStq)
- [Radian Measure and Sectors](https://lightmysky.com/learn/mathematics/radian-measure-and-sectors-mt_SvAYAu6mQ4)

## Opens up

- [Moment of Inertia by Integration and the Parallel-Axis Theorem](https://lightmysky.com/learn/science/moment-of-inertia-by-integration-and-the-parallel-axis-theorem-mt_VFRk1WIzAK)