Lesson: Center of Mass

In this lesson, we will learn how to calculate the location of the center of mass of a system of objects with various masses and positions relative to each other.

Video

12:58

Sample Question Videos

  • 06:42

Worksheet: 12 Questions • 1 Video

Q1:

Two particles of masses 2.0 kg and 4.0 kg move in uniform circles with radii of 5.0 cm and 𝑅 cm respectively. The π‘₯ -coordinate of the particle moving in the 5.0 cm radius circle is given by π‘₯ ( 𝑑 ) = 5 . 0 ( 2 𝑑 ) c o s and the 𝑦 -coordinate is given by 𝑦 ( 𝑑 ) = 5 . 0 ( 2 𝑑 ) s i n . The π‘₯ -coordinate of the centre of mass of the particles is given by π‘₯ ( 𝑑 ) = 6 . 0 ( 2 𝑑 ) c m c o s and the 𝑦 -coordinate of the centre of mass of the particles is given by 𝑦 ( 𝑑 ) = 6 . 0 ( 2 𝑑 ) c m s i n . Find 𝑅 .

Q2:

A cubic volume of side length π‘Ž = 1.0 m is cut out of a solid cube of side length 𝑏 = 3.0 m, as shown in the diagram. What are the π‘₯ - and 𝑦 -coordinates of the center of mass of the cube? Assume that the solid cube is of uniform density.

Q3:

A system comprised of a sphere and a cylinder can be arranged in different ways, as shown in the diagram. The cylinder has a length 𝑙 = 1 5 cm and a radius π‘Ÿ = 3 . 5 1 cm. The sphere has a radius π‘Ÿ = 4 . 0 2 cm. The cylinder and the sphere have the same density. In arrangement 𝐴 , the axis of the cylinder along its length passes through the centre of the sphere. In arrangement 𝐡 , the axis of the cylinder along the vertically directed radius of its circular face, horizontally half-way along the cylinder’s length, passes through the centre of the sphere.