PAP111/PHYS1A Tutorial Sheet 8 6 th of November 2010 Claus-Dieter Ohl 1 As this week we ask you to work on the graded homework sheet we give this tutorial as study material for the tutorial. The teaching assistant will guide you through the solutions of questions 1. Question 2 should be possible for you to solve on the spot. Full solutions again will be posted online. 1) Volume integration and moment of inertia To calculate the moment of inertia you need to specify the infinitesimal mass element d m . In Cartesian coordinates this is particularly simple, d m =ρ d x d y d z . Depending on the geometry of the object it may be advantageous to use other coordinate systems. Here we’ll introduce two more coordinate system: a) State the mass element in cylindrical coordinates ( r,φ,z ), i.e. with r as radius, z as height, and φ as angle in the z=const plane using the following coordinate transformation: x = r cos φ , y = r sin φ , and z=z. b)
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Polar coordinate system, Coordinate systems, mass element, infinitesimal mass element, PAP111/PHYS1A Claus-Dieter Ohl