State the role of inertia in the operation of an electric motor.
An electric motor is a device that takes electrical energy and converts it to mechanical energy. To get a sense for how this happens, as well as the role of inertia in the process, let’s draw a sketch of an electric motor. The main parts in an electric motor are these.
First, there’s a coil of wire, which sits in between the poles of a permanent magnet. This wire is connected by a split metal ring, called a commutator, to a circuit which has a power supply as well as some resistance. It’s this power supply that contributes electrical energy to this system. This voltage source induces the flow of current through the circuit. That current moves through the commutator ring to the coil of wire, where it moves around the wire and then back through the other side of the split ring to complete the circuit.
Of course, while all this is going on, while current is flowing through the coil, the coil is in the presence of a magnetic field that points from the north pole of the magnet to the south pole. That means that we have moving electric charge in the presence of a magnetic field. And under these conditions, those charges experience a magnetic force.
When it comes to our four-sided coil of wire, that magnetic force is experienced on two of the four sides, the left side and the right side. And to show that force more clearly on the right side of our coil, let’s draw that side in using a dashed line. Now based on the direction we see current flowing in this coil, we know on the left side of the coil it’s moving in that direction. And on the right side, it’s moving in the opposite direction. Let’s say that this current direction is the direction of conventional current flow, the flow of positive charge.
In that case, using a right-hand rule to solve for the direction of the magnetic force on this charge, on the left side of the coil, there’s a magnetic force that acts downward. While on the right side of the coil, there’s a magnetic force that acts upward. The forces are in opposite directions because the charge is flowing in opposite directions on these two sides.
If we consider these forces in relation to the axis that runs through the center of our coil, we can see that they help to exert a torque about that axis. To see this more clearly, let’s look at our motor from the perspective of looking along that axis of rotation. From that perspective, the coil would look like this to us, with the magnetic forces pointing up on the right side, down on left side, and with the same magnitude in each direction.
Since the axis of rotation for the coil runs through the center of the coil, right about there, we can see that these torques will help to start the coil rotating. That rotation, by the way, is just how it is that electrical energy from our power supply gets converted to mechanical energy of rotation.
Anyway, so let’s say that this coil rotates 45 degrees. Now what do we have going on? Well, since the current still flows the same direction through the coil of wire, that means the magnetic forces on the right and left side are still in the same directions, up and down. But notice what’s happened to the perpendicular distance of the line of action of those forces from the center of rotation of our coil. That distance has decreased. All that to say that while the magnitude of the magnetic force acting on the right and left arm of our coil is still the same, the torque that those forces exert is less than it was before. And again, that’s because this distance is smaller than it was when our coil was arranged in a horizontal plane.
But even though the torque is smaller than it was before, it still has an effect on the rotation of the coil. And the coil continues to turn. But what happens when the coil is in a vertical plane, that is, when it’s rotated 90 degrees from its original orientation?
Well, now we get to an interesting scenario. Assuming that the current in our coil hasn’t changed direction, which it’s just about to thanks to the split ring of the commutator. But assuming it hasn’t, then the magnetic force on what is now our top arm of our coil, which used to be the right, will still point up. And the magnetic force on the bottom arm, which used to be the left arm, will still point down. And by the way, the point we’re about to see wouldn’t change even if the current had switched direction by this point. All that would mean is that the force on our top arm is down and the force on our bottom arm is up.
In this case, it’s actually not the force direction that’s important, but rather the fact that the forces are perfectly in line with the axis of rotation of our coil. In other words, the torque that they supply for the coil is zero. Now this is a problem, isn’t it? I mean, after all, we’re working with an electric motor whose job it is to convert electrical energy to mechanical energy. If our coil stops rotating, then we’re not producing any mechanical energy.
This, it turns out, is where the role of inertia comes into play with an electric motor. Think back to the orientation of the coil when we first started. When it was in a horizontal plane, it looked something like this in the end-on view. And we saw that, thanks to the torque exerted on the coil, it began to rotate in an anticlockwise direction from this perspective.
As the coil rotated, we know that it picked up momentum in this angular direction. This means that, by the time that the coil did reach its vertical orientation where the torque on it is zero, it had already built up so much inertia that it was gonna continue to rotate even though there is no torque acting on it for that instant in time when it was vertically aligned. And notice that, as soon as the coil crossed through that vertical plane, where for that one instant the torque on it was zero, the magnetic forces on the two arms would now switch direction from what they were before.
So now the force on what used to be the right arm and is now the left arm is down. And the force on what used to be the left arm and is now the right arm is up. And these force directions we can see help to encourage the continued anticlockwise rotation of our coil. So really, it was just at that one tough spot where the coil was vertically aligned that the torque on it is zero. And at that instant, what brought us through was the fact that the coil had built up enough inertia so that it would keep rotating anyway.
Here’s how we can write this out in words. We can say that the role of inertia in operating an electric motor is that it keeps the coil rotating when the torque ceases at the position of being perpendicular to the magnetic flux lines. That’s how inertia assists in the operation of this motor.