NLM - Center of Mass

Center of Mass

The center of mass of an object is the unique point that can be used to describe the system's response to forces or to torque. We will learn about torque in a future module. For now, we will only concern ourselves with the force acting on the object. The center of mass is the average position of the mass. It can be taken by multiplying each mass in the system by its position then dividing by the total mass. If the object is a single object of uniform mass, then the center of mass is equal to one over the mass times the integral of rdm, where r is the position vector of the mass. Please watch the following presentation that will discuss the center of mass of systems and of uniform objects. 

Center of Mass Practice

Now we will do some practice problems to determine the center of mass of a system and of a uniform object. Please watch the following presentation of some example problems.

Center of Mass Self-Assessment

Now it's your turn. Complete the following Center of Mass problems to verify that you understand how to apply the concept to different situations. These will also give you additional practice with the concept of Center of Mass.

  1. A uniform piece of wood is cut into the following shape. What is the x and y components of its center of mass?

An axis with the 5, 10 and 15cm gridlines on the x-and y. The bottom left square and the middle bottom two squares are colored white while the others are black

SOLUTION Links to an external site.

  1. What is the center of mass of a uniform semicircle of mass M, height L and width 2L as indicated below?

semi-circle shape

SOLUTION Links to an external site.

Center of Mass Practice Problems

Download Center of Mass Practice Problems. Links to an external site.

Download solutions Links to an external site. for the practice problems. 

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