# Circular motion

The topic of circular motion forms the basis of the orbits of stars, planets and satellites. The concepts allow us to model many physical scenarios from cars on roundabouts or racetracks, to modelling an aeroplane banking during a turn:

- radian measure of angle and angular velocity

Mathematically students have to understand the relationship between radial and linear motion, and the key to this relationship is the radian measure. This is quite a mathematically simple measure, but students may never have considered in detail the fundamental aspect of an angle measured in radians and what it represents. For them to fully grasp circular motion it is important that they are comfortable with this method of representing angles:

- application of F = ma = mv
^{2}/r = mrω^{2}to motion in a circle at constant speed

Angular velocity for motion at a constant speed leads on from the understanding of the radian. The idea that acceleration can lead to a change in direction is something that the students will be familar with, but may never have actually had to consider in detail. In this topic, this concept is key. We consider objects moving at a constant speed, but constantly changing velocity, which implies an acceleration. Students have to understand that for circular motion, this acceleration is directed toward the centre of the circle.

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### Tau vs pi

This video contains a good overview of why we use pi in terms of a new constant (tau = 2 pi) - and what one radian is in terms of the circle. This is a good revision video for how circles are defined and could be used to help students to understand circular motion.

Make sure students understand (though it is explained in the video) that tau is no more than a teaching aid for them and they should calculate angles using 2 x pi in physics.

### Radians definition

This simple animation is a very effective demonstration of how radian angles are defined and why there are 2 x pi radians in a circle. This also shows why the circumference is 2 x pi x radius and that all the rest of the calculations stem from this logic.

Students should recall from GCSE mathematics that to go from degrees to radians they need to multiply by (pi / 180).

### PhET Rotational Lab *suitable for home teaching*

An interactive simulation that helps the user visualise rotational motion through the motion of a ladybird on a turntable. Rotate the merry-go-round to change its angle, or choose a constant angular velocity or angular acceleration. Explore how circular motion relates to the bird's x,y position, velocity, and acceleration using vectors or graphs.

### Episode 224: Describing Circular Motion

The whirling bucket of water and the coin on a coat hanger are brilliant demonstrations for getting students to think about the direction of forces involved in circular motion.

The ideas for developing the concept of centripetal force are useful and there are some excellent ideas for questioning students to check their understanding.

### Simple Accelerometer

Short film showing a floating cork accelerometer in use and how to use one to show the direction of acceleration in circular motion.

### Episode 225: Quantitative Circular Motion *suitable for home teaching*

This set of questions and explanations of the equations required for this topic is very useful and would complement exam questions on the topic.

There are also a couple of experiments designed to confirm the equation. The experimental error on the whirling bung is useful to get the students thinking about how to make reliable measurements.

### Circular Motion

This video is useful for teachers to get ideas for demonstrations**,** for example the salad spinner around 20 minutes in, as well as for students to access the various ideas that circular motion gives rise to. Videos such as this can be promoted to more capable students to use as revision but please make sure that they understand that the lectures are designed for undergraduates.