University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

203

Pages:

5
Author:

Jabin F.

Moment of Inertia (MOI) of a Thin Rod: Different MOIs for different axes: Ix = 0 Iy = ML²/12 Iz = ML²/12 MOI about an axis perpendicular to the rod and passing through one end: Ip = ML²/3 MOI about an axis perpendicular to the rod and passing through the center: Iend = ML²/3 Problem P-43: A plate shaped as a quadrant of an ellipse is lying in the xy-plane. The equation of the ellipse is: b²x² + a²y² = a²b² The problem asks to find the value of Ixy. Solution: For uniform mass density: dm = (M/πab) dxdy Ixy = ∫∫(x*y)dm Substitute dm into the integral and solve for Ixy. Calculation of Ixy: Ixy = ∫∫(x*y)dm Substitute dm = (M/πab) dxdy into the integral. Evaluate the double integral to obtain the final result for Ixy. Problem P-125: Four particles, each of mass m, are placed at the corners of a rectangle of sides (a, 2a). The problem asks to find the value of the angle θ for the principal axis. Solution: Transform the coordinates from (x, y) to (x', y') using rotation: x' = x cosθ + y sinθ y' = -x sinθ + y cosθ For a principal axis, the product of inertia (Ixy') must be zero. Set up the equation for Ixy' and solve for θ.