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 = mv2/r = mrω2 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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