12.3
Center of Gravity
The center of gravity (COG) of an object is the point where the object's total weight is considered to be concentrated. Knowing the location of the ce…
Center of gravity of a body is an imaginary point at which the body's gravitational force effectively acts.
It helps to predict a moving object's behavior under gravity and design static structures such as buildings and bridges.
To understand it better, consider balancing a basketball on a forefinger. The basketball placed on the forefinger experiences a gravitational force at the center of gravity in the downward direction.
If the center of gravity of the basketball lies on the axis that passes through the finger, the gravitational force is countered by the normal force balancing the basketball on the finger.
If the basketball slightly moves from the equilibrium position, the center of gravity of the basketball shifts outside the axis line of the finger. As a result, the torque due to its weight acts at this point, and the basketball topples.
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Q1: What is the center of gravity and why does it matter?
The center of gravity is an imaginary point where an object's total weight is concentrated and where gravitational force effectively acts. Understanding its location is essential for predicting how moving objects behave under gravity and for designing static structures like buildings and bridges. It determines whether an object remains balanced or topples.
Q2: How does the center of gravity affect whether an object stays balanced?
When an object's center of gravity lies on the axis of support, the normal force balances the gravitational force, maintaining equilibrium. If the object shifts and the center of gravity moves outside this axis, torque develops from the weight acting at that point, causing the object to topple. This principle explains why a basketball balances on a finger only when centered.
Q3: Is the center of gravity the same as the center of mass?
In a uniform gravitational field, the center of gravity and center of mass are identical. However, in non-uniform fields, they can differ. For example, the Moon's center of mass is near its geometric center, but its center of gravity shifts toward Earth due to Earth's stronger gravitational pull. On Earth's surface, these points coincide for practical applications.
Q4: Where is the center of gravity located for symmetrical versus asymmetrical objects?
For symmetrical objects, the center of gravity coincides with the geometric center. For asymmetrical objects, it lies at some distance from the geometric center. In irregularly shaped objects, the center of gravity can even exist outside the physical material itself, depending on mass distribution.
Q5: How is the center of gravity represented in free-body diagrams?
In free-body diagrams, the weight vector is attached to the center of gravity of the body. This representation shows where gravitational force effectively acts on the object. Placing the weight vector at the correct location is crucial for accurately analyzing forces and solving rigid body equilibrium problems.
Q6: Why does an object topple when its center of gravity shifts?
When an object's center of gravity moves outside its support axis, a torque develops from the weight acting at that displaced point. This torque creates a rotational force that causes the object to tip over. The farther the center of gravity shifts from the support axis, the greater the torque and the faster the object topples.
Q7: Can the center of gravity be located outside a physical object?
Yes, for irregularly shaped objects, the center of gravity can lie at a point external to the physical material. This occurs when mass distribution is highly asymmetrical. Despite being outside the object, this point still represents where the object's total weight is effectively concentrated for gravitational calculations.