00:02
So usually in physics, if there is an external force working on a system, you can treat that system as if it is concentrated with all of its mass at the center of mass of the object.
00:19
And you can pretty much ignore the center of mass, motion about the center of mass.
00:27
The motion about the center of mass is important when there.
00:32
There are internal forces like gravity, etc.
00:38
So we're going to kind of take a look at this.
00:42
And the ideas we have two masses joined by a lightweight rod.
00:48
They are in the ratio four to one.
00:52
And our first goal is to figure out where the center of mass is, but it's certainly going to be closer to the larger mass.
01:00
We can solve analytically by taking the product of m1r1, setting it equal to as to r2, and then the two distances have to add up to the full length of the rod 2 .5 meters.
01:24
And let's see, then we can have that r1 is equal to 8 over 2 times r2.
01:36
Or 4 times r2, and 5 times r2 is 2 1ā2 is 2 1ā2, so not surprisingly r2 is a half a meter, and r1 is 4 times larger, 2 meters.
01:57
So that's the easy part to figure out.
02:02
But now we're going to take a look at an external force of 15 that's being applied to mass number one.
02:12
And what we're going to do to begin with is we are going to find the torque acting on the system and thereby think about the system as spinning around with an angular acceleration.
02:33
So torque is equal to fr times sine of theta and that's also equal to i times.
02:44
The angular acceleration.
02:47
So there's one force of 15 newton's acting at a distance r1 and the angle is 90 degrees.
02:59
So we don't have to worry about the sign of the angle.
03:03
The moment of inertia, we can treat this as point masses, even though they're shown as large spheres.
03:11
We'll do m -i -r -i -squared.
03:15
The sum over that as the moment of inertia of the system.
03:22
So that would be 2 kilograms times r1 is 2 meters plus 8 kilograms times 0 .5 meters squared.
03:43
And working that out, that is, let's see, 8 plus 10 kilogram meter squared.
03:59
And r1, so we're considering that the force is applied directly to mass 1.
04:04
So we will put in r1 for our radius, and we wind up with the alpha is 15 times 2 over 10 radiance per second squared.
04:23
And working that out, that's 3 rads per second squared.
04:26
And what we can do is if it's spinning around, that means that mass 1, let me just kind of draw this, mass 1 is going to be spinning downwards, and mass 2 will be spinning upwards...