A “DC motor” is often a term used to describe any “rotary electrical machine that converts direct current electrical energy into mechanical energy.” In the United States, Thomas Davenport is often referenced when discussing the inventor of the first electric motor; however, the truth is various inventors in Europe had already developed motors before his initial creation. Different types of motors often differ in size and power, as do small toy motors from large motors that power your car, pull elevators, and power large industrial mills. All DC motors are composed of two key components: stator and armature. In most motors the stator is the stationary part of the motor - the magnet in our case - and the armature rotates - the copper coil in our case. Furthermore, the stator is the component providing the magnetic field that rotates and consequently causes the armature to rotate.

Figure 1 Discussion:

The relationship observed between the dependent variable angular speed (rotations per minute) and the independent variable voltage (volts) is positively linear. Since the R² value was 0.909 we can trust characterizing the relationship as linear. The equation mathematically modeling the observed relationship of the change in angular speed being proportionally related to the change in voltage current is: Ta = (PZ/2πA) x Φ.Ia (N-m). Although this equation may seem rather completed with its multiplicity of variables, the first part of the equation before the multiplication sign is practically a constant for DC machines of the same size and type. Therefore, the simplified equation works itself out to be Ta = Φ.Ia (N-m). In most cases, Φ which stands in for magnetic flux, a quantitative measurement of a magnetic field essentially representing how strong such a field is, is the same for the same DC motors which hold constant the power they have the capacity to develop. Thus, the only "changing" variables in our initial equation work out to be torque on the left side of the equation and the armature current on the right hand side. As the voltage increases, the flux and magnetic field simultaneously grow in strength and lead to a stronger torque and faster velocity.

As the number of loops increased, the angular speed also increased until the number of loops reached three, after which the angular speed decreased. The trend has a quadratic or parabolic shape. This trend is due to the combination of Lenz’s Law and the increased mass with the increased number of loops. Lenz’s Law can be summarized in the equation ε = −N(ΔΦ/Δt), where ε is the induced emf or the production of an electromotive force across an electrical conductor in a changing magnetic field, N is the number of loops, ΔΦ is the change in magnetic flux, and Δt is the change in time. As seen in this equation, as the number of loops increases, the magnitude of the induced emf increases. The negative sign denotes the direction. However, although the induced emf increases as the number of loops increases, so does the mass. As seen in the equation for the moment of inertia of a hoop about its center, as the mass increases, the moment of inertia increases. The moment of inertia is how hard it is to turn something, so as the mass increases, the motor becomes harder to turn. This increase in moment of inertia eventually overpowers the increase in induced emf and makes increasing the number of loops decrease the angular speed.

Firstly, as observed, there is a negatively linear relationship between the angular speed and the diameter of the armature. Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion or how hard it is to turn the mass. The moment of inertia for a hoop with negligible thickness about its central axis is I = ½MR². As we kept the number of loops the same, we inadvertently ended up increasing the mass of each loop as the diameter increased. Intrinsically, increasing the mass of each trial as the loops increase increases the moment of inertia of each trial, and, thus, makes it harder to turn such an apparatus from rest. The increase in diameter also increased the moment of inertia due to the radius term in the equation. It is apparent how the moment of inertia becomes larger from trial to trial. Additionally, the larger diameter loops created a weaker magnetic field. As seen in the Biot–Savart law, which can be summarized in the equation B = (μ₀NI)/(2R), where B is the magnetic field intensity, μ₀ is the permeability of free space, N is the number of turns, I is the current intensity, and R is the radius, as the radius of the loops or the proximity of the current increases, the strength of the magnetic field decreases, resulting in a slower angular speed. The magnetic field is strongest right around the wire, so as the diameter gets larger and the wire gets farther apart, the magnetic field gets more spread out and weaker, causing the armature to spin slower.

DC motors are beginning to become more and more common in the application of fans. DC motor ceiling fans utilize AC electricity and produce mechanical energy in the form of rotations. The only downside to DC motor fans, at this point, is the cost, but as they become more popular alongside other energy saving utilities the price is sure to drop.

If you are an avid biker, you may be pleased to know that electric bikes often use a compact DC motor that is built into the hub of the back or front wheel or even mounted in the center of the bike and connected to the pedal sprocket. Electric bikes do not require a license if the maximum speed of the bike is under 20 miles per hour. DC motors are very helpful in electric bikes as they can ensure the power levels and torque needed to increase and decrease speed seamlessly.

DC motors are only one type of the many motors utilized in the ever growing industry of electric cars. However, DC motors are unique as a utility for electric cars as they are energy efficient and durable. Many professional manufacturers, many hobbyists and technicians prefer large DC motors because they have a higher starting torque, a particular series wound motor, and variable speeds with voltage input, just as we discovered in Figure 1!

DC motors are often referred to as “toy motors” and are the most popular toy for toy manufacturers and hobbyists. Small DC motors work very well in the setting of, for example, remote control cars and model trains. The wide variety of voltages that can power DC motors make them a perfect candidate for toys that use controllers to utilize different speeds and movement types.