Lesson: Center of Mass of Particles Mathematics

In this lesson, we will learn how to find the position of the center of gravity (or center of mass) of a set of particles arranged in a two-dimensional plane.

Lesson Plan

Objectives

Students will be able to

find the center of mass of a set of particles on a line or in a two-dimensional plane.

Prerequisites

Students should already be familiar with

moments and related calculations.

Exclusions

Students will not cover

center of mass of laminas, nonlight rods, or solids.

Lesson Video

Lesson Explainer

Sample Question Videos

03:07
03:27
13:32

Lesson Worksheet

Q1:

The figure shows three weights arranged in an equilateral triangle of side length 12 cm. Find the coordinates of the centre of gravity of the system.

Q2:

Consider a rhombus in which such that point is located in the first quadrant of a Cartesian plane, is at the origin, and point is on the -axis. Masses of 4 g, 3 g, 6 g, and 10 g are attached at vertices , , , and respectively. Find the coordinates of the center of gravity of the system.

Q3:

The equilateral triangle in the figure has a side length of 36 cm. Point is the intersection of its medians (its centroid) and is the midpoint of . Masses of magnitudes 15 g, 27 g, 40 g, 12 g, and 50 g are fixed at the points , , , , and respectively. Determine the coordinates of the center of gravity of the system.