Physics C Relative Motion

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Presentation transcript:

Physics C Relative Motion When observers are moving at a constant velocity relative to each other, we have a case of relative motion The moving observers can agree about some things, but not about everything, regarding an object they are both observing Bertrand

Inertial Reference Frames Physics C Inertial Reference Frames Frames of reference which may move relative to each other but in which observers find the same value for the acceleration of a third moving particle. Inertial reference frames are moving at constant velocity relative to each other. It is impossible to identify which one may be at rest. Newton’s Laws hold only in inertial reference frames, and do not hold in reference frames which are accelerating. Bertrand

Example: a person on a skateboard throws a ball while a stationary person watches. The path of the ball will look very different to these two people. Physics C Bertrand

A particle A is described by two observers: Physics C A particle A is described by two observers: One observer is in frame S which is fixed relative to the Earth Another observer is in frame S’ is moving to the right (relative to S and therefore the Earth) at vo Relative to observer S’, S moves to the left at –vo The position of the particle relative to frame S is r The position of the particle relative to frame S’ is r’ r and r’ are related by: r = r’ +vot or r’ = r - vot Bertrand

This is Galileo’s Law of Transformation of Velocities Taking equation: r’ = r - vot Differentiating with respect to time: dr’/dt = dr/dt - vo v’ = v - vo dv’/dt = dv/dt - 0 a’=a This is Galileo’s Law of Transformation of Velocities If observers are moving but not accelerating relative to each other, they agree on a third object’s acceleration, but not its velocity!

Physics C Sample problem: A boat heading due north crosses a river at 10 km/hr relative to the water. The water in the river moves at 5 km/hr due east relative to Earth. a. Find the velocity of the boat relative to an observer standing on the bank. b. If this boat has the same speed of 10 km/hr and needs to head due north in the same river, in which direction should it steer? a. 11.2 km/hr at 26.6° E of N b. 30° W of N Bertrand