Center of Mass of L-Shaped Lamina
3D visualization of the center of mass calculation for a uniform L-shaped plate
Vertices Coordinates: O(0,0), A(2,0), B(2,1), D(1,1), E(1,2), F(0,2)
Centers of Mass: C₁(0.5,0.5), C₂(1.5,0.5), C₃(0.5,1.5)
Center of Mass Calculation
X = [1(0.5) + 1(1.5) + 1(0.5)] / (1 + 1 + 1) = 2.5/3 = 5/6 m
Y = [1(0.5) + 1(0.5) + 1(1.5)] / (1 + 1 + 1) = 2.5/3 = 5/6 m
Result: Center of mass is at (5/6, 5/6) meters
The L-shaped lamina is divided into 3 squares, each with adjustable mass (default 1 kg each). The center of mass of each square is at its geometric center (C₁, C₂, C₃). The overall center of mass is calculated by taking the weighted average of these positions.
The center of mass of the L-shape lies on the line OD when masses are equal. We could have guessed this without calculations. Can you tell why?
