Question

5.) The picture of the trapezoid below is not drawn to scale. PART-B moment of inertia of a thin, uniform, flat, isosceles trapezoidal plate of mass mis ma 14 for station about the axis AB, where a is the perpendicular distance between the sides AB and CD. The side AB is of length 6a and the side CD is of length 2a. With A as the origin, the x-axis along AB and the y-axis perpendicular to AB, the centre of mass of the trapezoid is located at co- ordinates (3a, 5a/12). Using the information given, find the moment of inertia of the trapezoid for rotation about CD. [10 points]

Answer 1

Parallel axis theorem

laris = ICM + mda

where $I_{axis}$ is moment of axis about any parallel axis which is parallel to axis passing through center of mall, $I_{CoM}$ is moment of axis about axis passing through center of mass, and d is perpendicular distance between any axis and axis passing through the center of mass.

So,

ma? = Icon + mp3,

ma? 2592 -= ICOM +m 144

Icons = ma? - m 250 144

11ma? ICOM = 144

Again between CoM and CD

Icd = 11ma m 7a +mG

60ma' ICD = 144

15ma? IcD = 36

5та? Іср = 12