00:01
Hello, and in this lecture, in this lesson here, we're going to discuss the center of mass.
00:06
So we have two particles.
00:09
We have v1, which we have the first particle with moves with velocity 1 in the positive x direction, and we have v2, which moves in the negative x direction.
00:21
So this is our first particle, and this is our second particle.
00:25
So we're asked to find the velocity of the center.
00:30
We're told that the velocity of the center of mass of these two particles is zero.
00:35
So first of all, let's explain what we mean by center of mass.
00:40
So we can think of this as the point in space where we can treat the two particles as one.
01:02
So it's going to be some sort of average of the position of the two particles.
01:09
And mathematically, we define this as the mass of the first particle times the position of the first particle plus the mass of the second particle times the position of the second particle divided by m1 plus m2, the sum of the masses.
01:28
So we now know what we mean by the centre of mass.
01:33
However, we want the velocity of the centre of mass.
01:36
So how would we go about this? well, in general, velocity is equal to the derivative of position with respect to time.
01:46
So let's try that.
01:47
Let's say the velocity of the centre of mass is equal to the derivative of the centre of mass, the position of the centre of mass with respect to time.
01:57
So that is equal to, by subbing in what we have r, is equal to m1 times the position of the first particle plus m2 times the position of the second particle divided by the sum of their masses.
02:14
Now, for example, let's say these particles are balls and we kick the ball.
02:21
We don't expect the mass of the ball to change as it's moving.
02:24
So therefore, we have the derivatives with respect to time of the masses are going to be equal to zero.
02:32
So the only thing that's going to be changing is the actual position of the ball when we kick it or the particles as they're moving...