NYJC_EJC Frames of Reference Notes

c 9814 H3 Physics Frames of Reference - Notes Page 1 H3 Topic 1 – Frames Of Reference (Non-Relativistic) Content • Reference frames • Inertial frames • Centre of mass frame Learning Outcomes Candidates should be able to: (a) state that a frame of reference is a set of coordinates that can be used to determine positions and times of events in that frame (b) show an understanding that Newton’s laws of motion are obeyed in all inertial frames of reference (c) recall and apply the Galilean transformation equations to solve problems relating observations in different inertial frames of reference (d) show an understanding that the centre of mass frame (or zero momentum frame) is the inertial frame in which the total linear momentum of the system is zero (e) solve one-dimensional collision problems by considering velocities relative to the centre of mass of the system (i.e. in the zero-momentum frame).

c 9814 H3 Physics Frames of Reference - Notes Page 2 1. The Concept of a Frame of Reference A frame of reference is a specific space or set of coordinates in which an observer makes measurements of physical quantities, such as the position and time of events. Every velocity or speed measurement is inherently relative to a "point of reference" taken to be stationary. For example, a car moving at is measured relative to the road's surface. If measured from a moving truck, that speed would differ. Generally, a coordinate system (often with an origin at the point of reference) is established to facilitate quantitative calculations. 1.1 Inertial Frames of Reference An inertial frame is one in which the point of reference is not undergoing acceleration. In these frames, Newton’s laws of motion are valid; specifically, an object with no net external force remains at rest or moves at a constant velocity. • The Earth is often treated as an approximate inertial frame, despite its small rotational and orbital accelerations. • Any frame moving at a constant velocity relative to an inertial frame is also an inertial frame. • Einstein’s first postulate suggests that all laws of physics remain the same in every inertial frame. 1.2 Non-Inertial Frames of Reference A non-inertial frame is one that is accelerating relative to an inertial frame. In such frames, Newton’s laws are not obeyed. For instance, an accelerating aeroplane is a non-inertial frame because it does not obey Newton's first law relative to a stationary observer.

c 9814 H3 Physics Frames of Reference - Notes Page 3 2. Galilean Transformation Equations 2.1 Coordinate Transformations Consider two inertial frames of reference S and S’ respectively. To keep things simple, we have omitted the z -axis. The reference frame S ’ is moving at a speed of u and the origin of the two reference frames coincide at time t = t’ = 0 such that their separation at a later time t is ut. The