By Masud Chaichian, Hugo Perez Rojas, Anca Tureanu

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Additional info for Basic Concepts in Physics: From the Cosmos to Quarks

Example text

5) The scalar product is particularly useful in expressing the work performed by a force on a particle that describes an arbitrary trajectory between two points, P0 and P . At each point of the curve the force forms an angle with the tangent to the curve at the point. , and draw the corresponding chords S1 ; S2 ; S3 as vectors that join the points P0 , P1 , P2 , P3 , etc. Then take the value of the force at an arbitrary point inside each of these segments. , be the values of the force at such points (Fig.

The scalar product is commutative, A B D B A. Moreover, A A D A2 , that is, the modulus squared of a vector is given by the scalar product of the vector with itself. If A and B are perpendicular, then A B D 0. A B/. The unit vectors satisfy the properties i iDj jDk kD1 and i j D j k D k i D 0: 20 1 Gravitation and Newton’s Laws Fig. 14 The scalar product is used, for example, for calculating the work performed by a force. 5) The scalar product is particularly useful in expressing the work performed by a force on a particle that describes an arbitrary trajectory between two points, P0 and P .

M. Lifshitz, Mechanics, 3rd edn. (Butterworth-Heinemann, Oxford, 2000). A classical text on classical mechanics 7. M. Chaichian, I. Merches, A.