Using gravitation and diffusion as examples, the programme examines the link, the gradient operator, between vector and scalar fields.
|Module code and title:
|MS283, An introduction to calculus
|First transmission date:
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|A. D.(A. Daniel) Lunn; Anne Walton
|BBC Open University
|Ball bearing; Curl; Fields; Gelatine; Haley's Comet; Kahautek; Scalar; Vectors
|Still photographs of the comet Kahautek. Daniel Lunn introduces the programme. He goes on to examine a diagram of the orbit of Haley's Comet and points out the gravitational forces at work here. Anne Walton simulates the vector field (orbit) of Haley's Comet on an air table. A puck moves over the table on a pulley arrangement. By measuring the distance and force, she is able to arrive at an inverse square force law. Daniel Lunn examines several blocks of gelatine which have been impregnated with blobs of dye at different times. The diffusion of the dye through the gelatin in a direction radially away from the blob is clearly seen. Lunn points out the scalar and vector field properties of this phenomenon. Anne Walton, writing and drawing on a board, works out an algebraic expression for the derivative of maximum magnitude, that is, the vector field associated with a scalar field. Walton carries on with her calculations to arrive at the link between the vector and scalar field the gradient operator. Daniel Lunn and Anne Walton then work out a scalar field whose gradient gives the vector field for the Haley's Comet simulation. Daniel Lunn tests the above results on a physical model. He rolls a ball bearing down a surface which simulates the scalar field. The theoretical predictions for the path of the bearing are confirmed.
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