9.2:
Center of Mass
The center of mass is the point in a body where the entire mass is assumed to be concentrated. A force applied to it causes the body to accelerate without developing torque.
A body's weight can be represented by an equivalent force acting at its center of mass.
If it is composed of an infinite number of particles, then each particle will have a gravitational force acting on it.
Recall the coordinates of the center of gravity of any body.
Substituting for W and dW gives the location of the center of mass. If the body's density is not constant, the equation gets further simplified.
The center of mass coincides with the center of gravity if the gravitational acceleration is constant.
Knowing the center of mass is important when designing a car, as it is essential to ensure its center of mass is low to the ground for stability.
9.2:
Center of Mass
The center of mass is the point at which the total mass of an object can be said to be concentrated. It is a fundamental principle in mechanics and physics that applies to all objects regardless of their shape or size. The center of gravity is the point at which an object’s weight appears to be concentrated and can be used to balance the object perfectly.
The knowledge of the center of mass can also help us to describe and predict the motion of objects. For example, when a ball is thrown into the air, its center of mass follows a parabolic trajectory determined by the force of gravity acting on it. Knowing the position of the center of mass allows us to predict how an object will move through space. The center of mass and the center of gravity are related but distinct concepts. For example, if an object is spinning rapidly, then this could cause its center of mass to shift away from the center of gravity due to inertia.
In addition, engineers use the center of mass to design stable structures like cars and aircraft that can withstand strong winds while remaining agile in their movements. In robotics, knowing where the center of mass lies helps machines balance on two or three legs without toppling over due to unbalanced forces acting upon them. Finding and understanding the center of mass plays a vital role in many fields ranging from engineering, design, and architecture to sports science and beyond.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics: Statics. Fourteenth Edition, New Jersey: Pearson. Section 9.1, Pp. 466-467.