Locating the Centre of mass using a plumb line

In this post, we will see how to find the centre of mass using a plumb line. Suppose we have to find the centre of mass of an irregularly shaped lamina (a thin sheet) of cardboard.

Steps to follow to locate the centre of mass of an irregularly shaped lamina (a thin sheet) of cardboard using a plumb line.

• Make a hole A in the lamina and hang it so that it can swing freely on a nail clamped in a stand. It will come to rest with its centre of mass vertically below A.
• To locate the vertical line through A, tie a plumb line (a thread and a weight) to the nail (Figure 1), and mark its position AB on the lamina. The centre of mass lies somewhere on AB.
• Hang the lamina from another position, C, and mark the plumb line position CD. The centre of mass lies on CD and must be at the point of intersection of AB and CD.
• Check this by hanging the lamina from a third hole.
• Also, try balancing it at its centre of mass on the tip of your forefinger.

Read about Toppling and stability of a body