Problems for Edward F. Redish |
(a) Consider a vector describing an object's position in a two space: . We want to consider the object moving around the origin in a circle, so it's distance from the origin is a constant, even though x(t) and y(t) are functions of time. Let's create a new polar coordinate basis, with the first unit vector along the direction towards the point and the second perpendicular to it as shown in the figure at the right. Express the unit vectors (note that these change as the position of the object changes) in terms of the fixed unit vectors. |
(c) Now consider that the particle is moving in the circle determined by the polar equations
where ω is a constant. Construct the vector velocity by differentiating with respect to time. Do it in two ways: first by differentiating the expression for the vector in terms of of the x-y basis and second by differentiating the expression for the vector in terms of the r-θ basis. Show that the answers you get are the same.
University of Maryland | Physics Department | Physics 374 Home |
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Last revision 4. November, 2004.