What Are the Velocity Components of the Center of Mass?

In summary, the conversation discusses the problem of finding the x- and y-components of the velocity of the center of mass of two moving objects with different masses. The solution involves using the equation of motion for each object and rearranging the CM equation to find the velocity. The responder also notes that the objects are moving with constant velocity, making the problem easier to solve.
  • #1
wolly6973
15
0
I am having a tough time with this one...
Body A of mass 4 kg is moving in the +x-direction with a speed of 15 m/s. Body B of mass 5 kg is moving in the -y-direction with a speed of 8 m/s. What are the x- and y-components of the velocity of the center of mass of the two bodies?
How do I relate CM and velocity?
 
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  • #2
wolly6973 said:
I am having a tough time with this one...
Body A of mass 4 kg is moving in the +x-direction with a speed of 15 m/s. Body B of mass 5 kg is moving in the -y-direction with a speed of 8 m/s. What are the x- and y-components of the velocity of the center of mass of the two bodies?
How do I relate CM and velocity?
I assume you know how to calculate the center of mass if given the masses and positions of two objects. In this problem the objects are moving with constant velocity, so the positions will be changing with time. Write the equation of motion for each object, and use the position expressions in the CM equation. With a little rearrangement, you will have the equation of motion for the CM
 
Last edited:
  • #3
Thanks for the help. Your explanation made it very easy to comprehend. I appreciate it.
 

FAQ: What Are the Velocity Components of the Center of Mass?

What does the velocity of the center of mass represent?

The velocity of the center of mass is a measure of the overall motion of a system of particles. It represents the average speed and direction of all the particles in the system, taking into account their individual masses and velocities.

How is the velocity of the center of mass calculated?

The velocity of the center of mass can be calculated by taking the sum of the mass of each individual particle multiplied by its velocity, and dividing it by the total mass of the system.

Can the velocity of the center of mass change over time?

Yes, the velocity of the center of mass can change over time. This can happen when there is an external force acting on the system, or when the particles in the system change their individual velocities or positions.

What are some real-life examples of the center of mass and its velocity?

One example is a see-saw, where the center of mass is located at the point where the plank balances. Another example is a pendulum, where the center of mass is located at the point where the mass is suspended. In both cases, the velocity of the center of mass changes as the system moves.

How does the velocity of the center of mass relate to the conservation of momentum?

The velocity of the center of mass is directly related to the conservation of momentum. If there are no external forces acting on a system, the total momentum of the system will remain constant, which means the velocity of the center of mass will also remain constant.

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