Motor Mysteries

This is the lesson I share with my students in Google Classroom to set the stage for studying Faraday’s Law and induced voltages. 

Today I am going to present you with a series of mysteries about motors.  Take your time with these and make sure you understand the question before worrying about the answer.

1. Why do electric motors run at constant speed?

We know what makes a motor go:  the wire carries current through a magnetic field.  The field exerts a force on the wire..  The force accelerates the motor so the motor speeds up.  But really think about the electric motors you have used.  I’m talking about things like fans, cd players (or record players if you are old school), or even an electric can-opener.  All of these devices begin to move when you close a switch, providing them with a current.  So they definitely all accelerate —  but only at first!  It seems that they have an initial period when they are speeding up but that their speed then levels off at some constant value.  They do NOT continue to accelerate.  And I am asking you: why not?

This is a genuine question and not a trick.  And the answer is not “friction”.  Even a zero-friction motor would behave this way: initial speed-up followed by velocity leveling off to a constant. Why is that?  

If you have a theory to explain this, please go ahead and post it as a comment.  And it’s ok to be wrong!  I’d be interested in seeing your ideas.  But try to use physics-reasoning.  The answer is not “magic” though it will certainly seem magical. Or you can just read on, spoilers ahead.

To investigate this mystery further, we are going to focus on a simple kind of motor.  I call it “the straight line motor”.  You are looking at a U-shaped circuit in a magnetic field.  The bar on the right is a conductor that rests on the rails, completing the circuit.  That bar is able to slide frictionlessly.

We close the switch. The current flows. And a quick application of the right-hand rule shows that we get a magnetic force, pushing the bar to the right.  The bar speeds up, but again, only initially.  The speed levels off to a constant value.  We still don’t know why…

Before we resolve this mystery, I want to mention that this motor I have described is a real thing!  You can see how to make one here:

And there is a related item called a “linear motor”.  It is slightly more complicated but it illustrates the same principles.  You can see a few here:

The Solution to MM#1

Let’s look at that circuit again, this time doing a few calculations:

We see we have a 12-volt battery.  The resistance of the circuit is a constant, let’s say 3 ohms.  We close the switch, expecting a 4-ampere current, which we could use to find the magnetic force (F=ILB) and then the resulting acceleration (a = F/m).  But if you could watch the current meter, you would see something we were not expecting, something important:

The current is only 4 amperes for an instant, right after we close the switch.  After that, the current decreases as the motor speeds up.  

For real motors, there is a start-up current that is the one you would predict based on the battery voltage and circuit resistance.  And then there is the operating current which is much lower.  In fact, if this little motor of ours had no friction at all, the current would drop all the way down to zero!

You might not believe what you are seeing. So as the motor speeds along, you reach out with your hand and block it.  Strangely, the current shoots back up again, back to the start-up value.  You let go, and the motor once again goes through that speeding-up period. And as it does, the current once again drops down to the operating level.  We now have evidence that lets us unravel that first mystery:

As a motor moves faster, the current reduces until there is only enough magnetic force to balance friction (or whatever mechanical force there is opposing the motion).  If there are no opposing forces, the current drops to zero. 

[Note:  This is actually a very fun experiment to do.  You hold the motor in your hand, watching the current meter.  If you block the motor from spinning, the current shoots up.  When you let go, the current goes back down.  It is strangely compelling and more exciting than I’ve drawn it.]

You should take some time to make sure you understand both the original mystery and our solution.  But even if you understand it, it is quite possible that you have another question. In fact, you SHOULD have another.  When you are ready, read on.

2. What makes the current drop when the motor moves faster?

I hope you believe me when I tell you that the current does drop. (And I hope to show you this in class one day.)  But what makes it drop?  We don’t change the battery.  We use the same wires with the same resistance.  And yet the current drops as the motor spins faster, almost as if the motor and battery were in communication.  You can imagine the motor talking to the battery:

OK, I’m just sitting here, so when the switch closes, send me all the current you can.  Ok, now I am starting to spin….you can ease off the current.  I’m going even faster! Less current please…Ok, I’m at my top speed now, feeling good — OH NO, SOMETHING IS BLOCKING ME! Send more current! Give me all you got!  Oh, wait, I’m moving again….you can  ease off the current…ok, I’m good.”

Of course, that’s not really what happens.  But when you do the experiment, it sure seems like that. So what is really happening?

 Here is another explanation,  one that does not require talking motors.  And this one is really ALMOST true…

The Nearly-Correct Solution to MM#2 

Inside every motor is a kind of invisible “Anti-battery”.  It is a voltage source, separate from the actual external battery, and it has some interesting properties:

1. It only provides voltage when the motor is moving. 

2. The faster the motor moves, higher the “anti-battery” voltage.

3. The “anti-battery” always opposes the voltage of the external battery.

It’s like a battery placed the wrong way in a flashlight so that it opposes the other batteries, causing a reduction in the net voltage. That is why I am calling it an “anti-battery”.  (It is also called a “back EMF” but I like “anti-battery” better.)

 But how does this explain the mystery of the dropping current?

Well, when the motor is starting from rest, there’s no anti-battery, no opposition. So the net voltage would be at its highest and you would get the most current. Then, as the motor moves faster, the anti-battery voltage gets higher, so the net voltage gets lower…and the current drops, just as we have seen.  But if you block the motor, the anti-voltage goes away and once again your current shoots back up to the maximum value.  Remember, the anti-battery only has voltage when the motor is actually moving.

I believe the explanation I am offering you would be approved by the physics authorities if I agreed to make two minor changes.  I think they would let me use the name “anti-battery”.  But they would insist on the following:

1.  Delete the word “invisible”.  The anti-battery is absolutely visible if you know where to look.

2.  Delete the word “Inside”.  The anti-battery is not inside the motor.  It’s also not outside the motor. Hmm…

This brings us to the third motor mystery.  

3. Where is this “anti-battery”?

I’m not ready to give this one away just yet.  Let me see if I can jog your memory.

You did a lab this year where you used a generator to store charge on a capacitor.  The plan was to use the stored charge to light a lightbulb.  It worked…but something else also happened during that lab if you were not quick enough on the switch.  Do you remember what that was?

After the lab was finished, I took a generator and connected the wires directly to a battery.  Do you remember what happened?

Then, one of you held a generator that I had connected to a second generator. We each took turns cranking our generators. Do you remember what happened?

Think back to those events and you will not be surprised to hear the solution to this third mystery.

The Solution to MM#3

The “anti-battery” is not some invisible or even visible thing INSIDE the motor.  The anti-battery IS the motor itself,  now acting as a generator.  What you saw in our old lab was that motors and generators are the same physical devices: essentially, just coils of wire, mounted in a magnetic field.  When you provide voltage, the device acts like a motor — it spins. When you make it spin, it acts like a generator — it produces a voltage.

All we are saying now is that even when the device is being used as a motor, it still acts like a generator. As it spins, it generates a voltage.  And that voltage fights the battery voltage, always.  So the spinning motor has lower current.

You may be thinking: wouldn’t it be nice if we could get that generated voltage to assist the battery rather than fight it?  Well, it would be, but the laws of physics prevent that. The induced “anti-voltage” always opposes the battery voltage.  You will be hearing more about this later. 

You may also be thinking: if a spinning motor simultaneously acts like a generator, does that mean that a spinning generator also acts like a motor?  And the answer is yes! It does!  But this time, it’s a magnetically induced force opposing an external force.  That is why those generators got dramatically harder to spin when you closed the switch!  [That is part of the reason we do labs: to give you physical experience and memories of observed phenomena.]

This interplay between motors and generators is fascinating but also challenging to understand.  We will revisit this again later. But first we have one more question to ask:

How does the spinning wire act like a generator in the first place?  

That is the topic we will be exploring for the rest of this unit. Stay tuned…