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Frames1

# Frames1 - Kinematics Mechanics and Frames of Reference Part...

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Kinematics, Mechanics, and Frames of Reference Part 1 Inertial versus non-Inertial Frames As McCall describes, pages 10-13, Inertial Frames are those in which Newton’s first law is valid. That is, if no force acts on an object, then its velocity – measured with respect to an inertial frame – does not change. Stated otherwise, the difference between any two Inertial Frames is that they have a constant relative velocity the one with the other. Accelerations measured in the two frames will be equal. It is therefore possible to choose a particular Inertial Frame to solve a particular mechanics problem: often we can achieve substantial simplifications by a “good” choice. However, if we are only concerned with “kinematics” – the relationship between displace- ment, velocity and acceleration – and not with “dynamics” – the relationship between force and acceleration – then any frame of reference will do. Although Newton’s first law will not be valid – without modification – in non-Inertial frames, we can still use the standard kinematic equations. Once again, we can achieve substantial simplifications by a “good” choice of frame. So, it is important to practice solving problems in different reference frames. With practice, we can start to see what makes for a good choice . . . Notation In all the examples, we will use two frames of reference, S and S . Usually, S will be the frame that we might ordinarily use – it is attached to planet Earth, for example – but, in principle, S could be the ordinary one. The only reason for choosing one frame rather than the other is convenience. To start, we will look at the situation in one dimension, where an object – any object – at x in frame S is at x in frame S , and at time t = 0 we will always choose that the two frames coincide. This means that x = x when t = 0. See the two diagrams: 1

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