Center of Mass and Center of Gravity | Physics

Summary

This video explains the concepts of center of mass (COM) and center of gravity (COG), highlighting their significance in physics. The COM is the point where an object's total mass is concentrated, while the COG is where its weight appears to act. Using examples like a heavy box and a washing machine, the video illustrates how to find the COM in homogeneous and irregular objects. It also discusses how the COM and COG behave in uniform and non-uniform gravitational fields, alongside methods for calculating COM using specific formulas. Overall, the video provides a clear and engaging understanding of these fundamental concepts.

Takeaways

• 😀 the center of mass is the point where the total mass of an object is concentrated.
• 😀 the center of gravity is the point where the total weight of an object appears to act.
• 😀 for homogeneous objects, the center of mass coincides with the geometric center.
• 😀 the center of mass may lie inside or outside the object, depending on its shape.
• 😀 the center of mass can change position based on the object's orientation.
• 😀 in a uniform gravitational field, the center of mass and center of gravity are at the same point.
• 😀 to find the center of mass of irregular objects, you can hang them from multiple points and draw plumb lines.
• 😀 the center of mass of a right circular cylinder or cone is on the axis of symmetry.
• 😀 calculating the center of mass involves using the formula that considers the mass and position of each object.
• 😀 understanding the difference between center of mass and center of gravity is crucial for analyzing forces acting on objects.

Q & A

What is the center of mass?

The center of mass is the point at which the total mass of an object is concentrated, acting as the balance point around which the mass is evenly distributed.

How can you find the center of mass for homogeneous objects?

For homogeneous objects, the center of mass is located at the geometric center. For example, the center of mass of a circular object is at its center.

What is the relationship between center of mass and center of gravity in a uniform gravitational field?

In a uniform gravitational field, such as near the Earth's surface, the center of gravity coincides with the center of mass.

Can the center of mass be located outside the physical boundaries of an object?

Yes, the center of mass can be located outside the object, as seen in shapes like a banana, where the center of mass is outside its physical structure.

What method can be used to find the center of mass of irregular objects?

To find the center of mass of irregular objects, you can hang the object from three different points and draw vertical lines; the intersection of these lines gives the center of mass.

What happens to the center of mass when the orientation of an object changes?

The center of mass can change its position based on the orientation of the object; for instance, bending or stretching a limb can alter the center of mass location.

How do you calculate the center of mass for multiple objects?

To calculate the center of mass for multiple objects, you use the formula: x_cm = (m1 * x1 + m2 * x2) / (m1 + m2), where m is the mass and x is the position of each object.

What is the difference between center of mass and center of gravity in non-uniform gravitational fields?

In non-uniform gravitational fields, the center of mass and center of gravity may not coincide and can be at different points, as gravitational pull varies with distance from the source.

Can the center of mass change its location when external forces are applied?

Yes, the center of mass can shift in response to external forces, as seen in dynamic situations like a person jumping or throwing an object.

Why is understanding center of mass important in physics?

Understanding the center of mass is crucial in physics because it influences how objects balance, move, and respond to forces, which is essential in mechanics and engineering.