Equations of Motion in Normal and Tangential Coordinates
Equations of motion can be expressed using normal, tangential, and binormal directions. Learn how to apply these concepts and solve practice problems in this comprehensive guide. Explore the n-t coordinate system and understand the right-hand rule for coordinating axes. Dive into solving problems involving speed and normal force using scalar equations.
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Presentation Transcript
13.5 Equation of Motion: Normal and Tangential Coordinates Equations of Motion: Normal and Tangential Coordinates Equations of motion may be written in terms of normal, tangential, and binormal directions. F F u = a m In terms of components: + + = + u u a a F F m m t t n n b b t n In terms of scalar equations: = = = F F F ma ma t t (EQ 13-8) n n 0 b = F mv t t v 2 = or F m n = 0 F b
In-Class Practice Problem 1 Did anyone else notice there is an awful lot of he in this problem? How to find speed? How to find normal force?
In-Class Practice Problem 1 Kinetic Diagram FBD Newton Normal Force
In-Class Practice Problem 1 In stupid units this is about: 560 mph and 1390 lbf In stoopider units this is about 4.4 Miata top speed, and 0.65 Miata weight
Mind Blown n-t Coordinate System Right Hand Rule The normal, tangential, and binormal axis only obey the right-hand rule if we put them in the order: ut x un = ub So we should really be calling it the tangential, normal, binormal coordinate system. But we don t, and we won t, because we still use units like [ft] and [Miata]
In-Class Practice Problem 2 Does anyone see this problem and think: That s a bad idea! ? Why might this be a bad idea? Even though it s a bad idea, how do you solve this problem?
In-Class Practice Problem 2 b t n an
In-Class Practice Problem 2 sin( ) cos( )
