---
title: "Circular Motion: Angular Speed and Centripetal Force"
description: "An object going round at steady speed is still accelerating, because the direction of its velocity keeps changing. The resultant force points to the centre and has size mv squared over r, which is als"
canonical: https://lightmysky.com/learn/science/circular-motion-angular-speed-and-centripetal-force-mt_PW1G6nYStq
source: https://lightmysky.com/learn/science/circular-motion-angular-speed-and-centripetal-force-mt_PW1G6nYStq.md
retrieved: 2026-09-12
---

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# Circular Motion: Angular Speed and Centripetal Force

An object going round at steady speed is still accelerating, because the direction of its velocity keeps changing. The resultant force points to the centre and has size mv squared over r, which is also m omega squared r.

Subject: Science · Area: Forces & Motion · Ages 17 to 18
Page: https://lightmysky.com/learn/science/circular-motion-angular-speed-and-centripetal-force-mt_PW1G6nYStq

## Ready when they can

- Converts between period, frequency, linear speed and angular speed in radians per second
- Names the real force acting as the centripetal one in a given setup instead of adding a new force
- Finds the greatest speed for a whirled mass before the string reaches its breaking tension

## Lesson: Round and round, pulled inward

Rotation uses the radian: arc length over radius, with 2 pi per full turn. Angular speed is angle per second, tied to frequency by omega equals 2 pi f and to period by 2 pi over T. Every point on a disc shares one omega, but rim points move faster since v equals omega r.

Centripetal force is not a new force but a job title. On a whirled ball it is string tension, on a cornering car it is tyre friction, on the Moon it is gravity. Inertia tries to carry things straight while the real force hauls them round. There is no outward force in this picture.

Demand grows as m v squared over r. Spin a 0.5 kg ball on a 1 m string that snaps at 50 N. Setting 0.5 times v squared over 1 equal to 50 gives v equals 10 metres per second. Past that demand the string snaps or the car slides.

**Recap.** Link angle, speed, and time in radians, name the real inward force, and check the demand before it snaps.

## Practice

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

## Needs first

- [Newton's Second Law with Numbers](https://lightmysky.com/learn/science/newtons-second-law-with-numbers-mt_Nn2MVJL7bO)
- [Stress, Strain and the Young Modulus](https://lightmysky.com/learn/science/stress-strain-and-the-young-modulus-mt_uWdqhWGT7Y)

## Opens up

- [Rotational Kinematics and the Angular Velocity Vector](https://lightmysky.com/learn/science/rotational-kinematics-and-the-angular-velocity-vector-mt_2UqK-zViqf)
- [Charged Particles Moving in a Magnetic Field](https://lightmysky.com/learn/science/charged-particles-moving-in-a-magnetic-field-mt_evuhZ6cSfI)
- [Simple Harmonic Motion: the Defining Relation and Its Graphs](https://lightmysky.com/learn/science/simple-harmonic-motion-the-defining-relation-and-its-graphs-mt_NTDayHkdfh)
- [Orbits: Period, Speed and Kepler's Third Law](https://lightmysky.com/learn/science/orbits-period-speed-and-keplers-third-law-mt_PLKLykGF8Z)