Center of Mass(Center of Gravity) Two Dimensional Case

TL;DR

Center of mass of a system of point masses in two dimensions is calculated easily by dividing moment by total mass for x and y coordinates.

Transcript

in this video we're being asked to find the center of mass of the following system of Point masses so this is the two-dimensional case in this case it's also called the center of gravity so the center of mass is this ordered pair here where the first component so the x-coordinate is equal to the moment about the y-axis divided by the total mass whi... Read More

Key Insights

• 💆 Center of mass in two dimensions is also known as the center of gravity.
• ❣️ Calculating the center of mass involves dividing the moment by the total mass for x and y coordinates.
• ❣️ The x-coordinate is calculated using the moment about the y-axis, while the y-coordinate is calculated using the moment about the x-axis.
• ✖️ The formula for finding the x-coordinate involves multiplying the masses by their corresponding x-coordinates.
• ✖️ Similarly, the formula for finding the y-coordinate involves multiplying the masses by their corresponding y-coordinates.
• 💆 It is important to remember to divide the calculated values by the total mass of the system.
• 💆 Memorizing the formulas for center of mass calculation involves understanding the relationship between masses and coordinates.

Questions & Answers

Q: What is the center of mass in the two-dimensional case?

The center of mass in the two-dimensional case is where the x-coordinate is the moment about the y-axis divided by the total mass, and the y-coordinate is the moment about the x-axis divided by the total mass.

Q: How do you calculate the x-coordinate of the center of mass?

To calculate the x-coordinate, you multiply the masses by their corresponding x-coordinates and divide by the total mass of the system.

Q: What is the formula for finding the y-coordinate of the center of mass?

The formula for finding the y-coordinate involves multiplying the masses by their corresponding y-coordinates and dividing by the total mass of the system.

Q: How can you easily memorize the formulas for the center of mass calculation?

It is easy to memorize the formulas by remembering to multiply the masses by their corresponding coordinates (x or y) and then dividing by the total mass of the system.

Summary & Key Takeaways

• Center of mass in two dimensions is also called the center of gravity.

• To find the x-coordinate, calculate the moment about the y-axis divided by the total mass.

• To find the y-coordinate, calculate the moment about the x-axis divided by the total mass.