Equations of Motion in Cylindrical Coordinates - In-Class Practice Problems
Explore equations of motion in cylindrical coordinates through a series of in-class practice problems. Enhance your understanding of the derivatives chain rule, product rule, and acceleration components in a visually engaging manner.
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Presentation Transcript
13.6 Equation of Motion: Cylindrical Coordinates Equations of Motion in Cylindrical Coordinates The equations of motion can also be written along cylindrical coordinates. F F F F + + = a m In terms of components: = + + u u u u u u ma ma ma r r z z r r z z Or as scalar equations: = = = F F F ma ma ma r r (EQ 13-9) z z ( ( ) = = = + F m r r 2 r ) or 2 F F m r mz r z
In-Class Practice Problem 1 Looks a lot like 13-85, but in SI units. Maybe fewer typos? Any idea what else you would model like this? https://www.youtube.com/watch?v=s5n-2gb8yfM https://www.youtube.com/watch?v=nsa6kq-qqIE
In-Class Practice Problem 1 Here s one typo, but they fixed it on the right
In-Class Practice Problem 2 Another great chain rule practice problem! Very similar motion to your problem 13-93
In-Class Practice Problem 2 The derivatives Chain Rule and Product Rule
In-Class Practice Problem 2 Evaluating the derivatives at theta = 30
In-Class Practice Problem 2 Calculating the acceleration components
In-Class Practice Problem 2 Equations of Motion if r and theta directions
In-Class Practice Problem 3 Another, another great chain rule practice problem! I haven t come up with any real-world example of this device But the motion over a range of ~+/- 45 is reasonable
In-Class Practice Problem 3 Derivatives (easier than the last one)
In-Class Practice Problem 3 Accelerations and EoM
