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Today's video is a follow up from our previous video where we used LEGO and lego motors to explain the concepts of horsepower and torque.

In today's episode we're going to add gears into the equation to see how they can be used to manipulate torque and speed.

So here again we have our two motors. The large motor generates 0.14 newton meters of torque and the smaller motor generates 0.03 newton meters of torque. Last time we have seen that the small motor couldn't generate the torque needed to move this heavy arm. Now we're going to use gears to enable the small motor to move the heavy arm.

Instead of trying to move the heavy arm directly with the small motor, we're going to connect a gear to the motor's shaft and we're going to attach another gear to the heavy arm.

We're going to call the gear on our motor the driver gear. Because this is the gear where the force input is and this the gear that does the work. This gear has 8 teeth We'll call the gear on the heavy arm the driven gear, this gear receives the force input and has work done on it. This gear has 40 teeth.

How do we obtain the ratio between the two gears? We simply divide the number of teeth on the driven gear by the number of teeth of the driver gear. And the result is 5, this is our gear ratio.

So what does the gear ratio tell us? It tells us how much we have increased the torque using this gear arrangement. Our initial torque on the small motor was 0.03 Nm. To figure out the new torque output value at the large gear we simply multiply the initial torque with our gear ratio. So 0.03 Nm x 5 gives us 0.15 Nm. This means that with the help of gears the small motor is now outputting more torque than the large motor.

So why does this gear arrangement increase the torque coming from the motor? The answer is pretty simple...it's because the large gear is larger than the small gear. To fit a larger number of teeth onto a gear you must increase it's radius. By increasing the radius you're increasing the physical distance between the force input and the force output. In other words by increasing the radious you're increasing the leverage provided by the gear. The gear acts like a lever, and as you probably know or have experienced yourself the larger the lever the larger the force output.

The torque increase coming from larger gears comes at a price and the price is rotation speed.
Our small lego motor has an initial torque of 0.03 Nm that we have increased to 0.15 Nm using a gear ratio of 5. But our gear ratio of 5 also reduces speed.
Our small lego motor is capable of doing 275 full rotation in one minute. It spins at 275 rpm. It's significantly faster than our large lego motor which does 146 rpm. But as you can see after we install our gears to increase the torque the small lego motor actually becomes slower than the large motor. How much slower? We can again easily calculate that using our gear ratio. We simply divide the inital speed with the gear ratio to get our new output speed. So 275 divided by 5 is 55 rpm. This means that to have more torque than the larger motor the small motor had to it's speed. By becoming five times stronger it also became 5 times slower.

So why does this kind of gear ratio decrease speed? The answer is again simple and again it's the gear size. To fit a larger number of gears we need a larger gear radius. A larger gear radius also means a larger circumference, or the total length along the edge of the gear. The larger the circumference the more distance needs to be covered to make the larger gear achieve one full rotation. Our gear ratio can aslo be expressed as 5:1. It tells us that for every 5 rotations of the driver gear the driven gear makes only one rotation.

All of this explains why gear ratios of a typical car transmission usually look something like this.

The lower gears reduce speed and increase torque. This because we need the most torque to get the vehicle going from a standstill in first gear and we also need torque to help increase acceleration to get the vehicle up to speed. But once we're up to speed the vehicle has a lot of inertia and we don't need as much torque to push it along, what we need is increased rotational speed or an increased number of wheel rotations per minute to allow the vehicle to achieve even higher speeds.

A special thank you to my patrons:
Daniel
Peter Della Flora
Daniel Morgan
William
Richard Caldwell
Pepe
Brian Durning
Brian Alvarez

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