Kreisel als Drehzahlmesser (Dynamik, Technische Mechanik)

Example problem dynamics - gyroscope as rev counter - K02 A gyroscope can also be used as a rev counter, namely as follows: A housing 2 is mounted frictionless and rotatable in a frame 1 and connected to it by a torsion spring. A gyroscope 3 mounted in the housing 2 rotates with the relative angular velocity ω_R against this housing. If the frame 1 is now rotated with a constant angular velocity Ω, a constant angle ϕ is established after a transient process and Ω can be determined. Given: Centres of gravity lie at the intersection of the axes of rotation Housing 2: ϕ, main moments of inertia I_Gx, I_Gy, I_Gz, linear torsion spring with constant c_T, completely relaxed for ϕ = 0 Gyro 3: ω_R = const., moments of inertia: I_x, I_y = I_z Calculate the constant angular velocity Ω of frame 1 after the transient phase, assuming that ω_R is much larger than Ω. Source: Aufgabe 4.4.3 (S. 42) aus P. Lugner et al., Technische Mechanik, 1992 Springer-Verlag, Wien 00:00 Intro & example explanation 04:24 Free-body diagram 07:29 Angular momentum 13:00 Time derivative of angular momentum 16:51 Cross product in the angular momentum derivative 18:58 Calculation of the cross product: Epsilon tensor 25:17 External moment: torsion spring 26:13 Theorem of angular momentum 28:25 Simplification: ω_R much larger than Ω 30:16 Concluding remarks ======================================================== Related links: Blog: https://maomech.wordpress.com Twitter:   / maomech   Facebook:   / maomecha   LinkedIn:   / markus-orthaber-b160a418b   ========================================================