Question

-Ja A Figure 2: A model of a tennis racket 5. A tennis racket is modeled as a uniform lamina of an areal density ρ [kg m-2] that has a shape of an ellipse with the semi-major axis a and semi-minor axis b and a mass m 4Tbp with attached to it uniform rod of length 2a and mass m. The origin of the Cartesian system of coordinates Oryz is placed at the centre of the ellipse as shown in Figure 2. The lamina lies in the Ory-plane. Find a) the total mass and the center of mass of this rigid body, 3 marks] b) the inertia matrix for the elliptical lamina with respect to its centre of mass with the use of integration, the Perpendicular Axis Theorem and the equation of ellipse 를+ 17 marks] c) the inertia matrix for the uniform rod of length 2a and mass m with respect to its centre of mass with the use of integration 3 marks] d) the principal moments of inertia for the whole body with reference to the point A (using the Parallel Axis Theorem). 17 marks Total: 20 marks]

Answer 1

2a mas s m t ma "rna>) I1) Center 29 Cam be Sod

gdy

maas Gd element เร่ idth da , at distance n mas damit 2° Co M m Com 3 Icom F

iciple moment al Iner to the plane al lamina Tram axis g。ing though 3 m a 3