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Unformatted text preview: 1 Newtonian Dynamics 1.1 Review of Newton’s Laws REFERENCES: Arya Chapter 1,2. Newton’s laws: 1. Δ v = 0 in an inertial reference frame. 2. ∑ F = d p dt 3. F ij =- F ji Recall Newton’s second law: F = d p dt (1) when subject to a constant mass F = m d 2 r dt 2 = m a (2) Mass can be determined by applying a force (in an inertial reference frame), or by weigh- ing. This suggests that mass can be defined in two ways: 1. Inertial Mass : The mass determining the acceleration of a body under the action of a given force. 2. Gravitational Mass : That mass determining the gravitational forces between a body and other bodies: F = Gmm r 2 (3) The principle of equivalence is the assertion that Inertial mass and Gravitational Mass are EXACTLY the same. Experimentally, inertial and gravitational mass are known to be the same to within a few parts in 10 12 . The principle of equivalence has two consequences, which are important in the formulation of General Relativity: 1. Light bends in a gravitational field 2. Light traveling down a gravitational field suffers a blueshift 1.2 Frames of reference REFERENCE: Arya, Chapter 16 Newton’s laws have meaning only in an inertial frame of reference. If they are valid in one referece frame, then they are also valid in any reference frame in uniform motion (not...
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This note was uploaded on 09/20/2010 for the course AMATH 261 taught by Professor Rogermelko during the Spring '10 term at Waterloo.
- Spring '10