二、計算題
1. A homogeneous thin half circle of radius R with a total mass M is symmetric about the y axis, as shown in Figure 5(a). (a) Find the coordinate of the center of mass (COM), (x_COM, y_COM). (b) Find the rotation inertia when it rotates around the axis passing through its COM (in parallel with the z-axis). (c) If the half circle is rotated in the xy plane with a small angle θ on a frictionless pivot at point P which is on the y axis, as shown in Fig. 5(b), and released. Show that the half circle will execute simple harmonic motion, and find the period T of simple harmonic motion, where the direction of gravitational acceleration g is in −ŷ. (15%)