Levers and Gears

I’m going to be explaining manual transmissions to Gamma in a month or two, so this is my homework for that.

The pre-requisite for my class Learn to Drive Stickshift is an understanding of Levers and Gears. You should have already taken the class Simpler Machines.

As we discussed last week, a wheel can be thought of as an group of levers around the axle. Gears make this easier to visualize, just think of the gear teeth as the ends of the levers.

What does a lever do? It allows one to produce varying amounts of distance or force, depending on where the fulcrum is. Want more distance on the other end? Move the fulcrum closer to you. Want more force on the other end? Move the fulcrum farther away.

What do gears do? Same things as gears – they allow one to produce varying amounts of distance or force, depending on where the fulcrum is. The difference that the fulcrum for gears is the gear ratio, or the radius of the drive gear compared to the radius of the output gear.

The other difference is that gears don’t usually deal with distance like a lever, but rather distance over time – better known as speed.

If both gears (one input and one output) are the same size, then that’s like a lever with the fulcrum in the middle. It multiplies neither force nor distance, it just changes direction.

diagram comparing gears to levers, with equal gearing

If the input gear is larger than the output gear, then that’s like a lever with the fulcrum farther from the input. It multiplies force and divides distance or speed. This is a low gear – it provides the oomph (technical term) to get things moving, albeit moving slowly.

diagram comparing gears to levers, setup for a low gearing

If the input gear is smaller than the output gear, then that’s like a lever with the fulcrum closer to the input. It multiplies speed/distance and divides force. This is a high gear – it provides the high speeds but with a lack of oomph. Note that this is called overdrive when the input gear is smaller than the output gear. Overdrive used to be a big deal on cars years back, but that was when transmissions had 3 gears and the highest speed limit was 55 mph. Now transmissions have 8 or 9 speeds and speed limits are 75 or 80, so everything can go fast enough and no one runs out of gears anymore.

diagram comparing gears to levers, setup for a high gearing

Now then, please take your gear, your quiver and your bow, and go out to the field and hunt game for me

Genesis 27:3

Simpler Machines

I’m going to be explaining manual transmissions to Gamma in a month or two, so this is my homework for that.

The pre-requisite for my class Learn to Drive Stickshift is an understanding of Simple Machines.

The classic list of Simple Machines is Lever, Wheel, Pulley, Inclined Plane, Wedge, and Screw.

I disagree with the list, as it could be simplified. I.e. those are not the simplest machines. One of my favorite parts of science was simplifying things by cancelling units. I am going to try to show that here.

First is Screw, the most egregious example, the Screw is not a Simple Machine. It is a Compound Machine.

Take a wheel, make it thicker, and apply an inclined plane to it.

That’s a screw, just an inclined plane-wheel. Since Screw can be reduced to two simple machines, it does not count as a simple machine.

Next is Wedge. While I don’t think this can be reduced, I do think this is just an inclined plane.

If we move an object up an angled surface, we call that surface an inclined plane. But if we take an angled surface and move it into an object, we call it a wedge.

I disagree that wedge gets to be a known as a unique simple machine. I actually don’t care which term we use (it is easier to say “wedge” than “inclined plane”).

Wedge and Inclined Plane do the same thing – use an angled surface to make it easier to separate things. For the wedge, one is generally separating one object into two. For the inclined plane, one is generally separating one object from another. But it’s the same basic concept, and it shouldn’t count twice.

Since we’re on the topic of Inclined Plane, I thought there should be some overlap between Lever and Inclined Plane. I thought about how to combine them, or reduce Lever somehow. But my conclusion was they are both simple machines, and it may help to think of the lever not as a lever but think of it as a fulcrum. Replace Lever in the list with Fulcrum and it is more obvious that it’s not sharing anything with Inclined Plane.

Next is Pulley. It should come as no surprise to you that I consider a pulley to be a wheel plus a rope. Since one of its components is a Simple Machine, it can be reduced and is therefore not a Simple Machine.

I am open to the possibility that Rope should be promoted to Simple Machine.

Pulley, on the other hand, is just an application of Wheel. It’s a similar comparison to Wedge and Inclined Plane. Wedge and Inclined Plane are the same machine, just one is moving and one is stationary.

It’s the same with Wheel and Pulley – it’s the same machine, just one moves (a distance, yes they both move in that they rotate) and one is stationary.


That’s the end of my complaining about the classifications of Simple Machines.

For your homework for next week, please come prepared with an explanation of how a wheel can be reduced to an infinite number of very small levers around a central fulcrum.

The four wheels were underneath the borders, and the axles of the wheels were on the stand. And the height of a wheel was a cubit and a half.

1 Kings 7:32

If I Were Governor

This is not an exhaustive list, but just a few things I thought of while driving, for what I would do if I were governor of my state.

  • Make all the crosswalk timings consistent. Some count to zero then the light changes to yellow. Some hit yellow at 2 or 3 and go to red on zero. Some hit zero and the light stays green for a few more seconds.
  • Get rid of changing the clocks twice a year. This has gotten some more traction lately, but so far it’s all smoke and no fire.
  • Set a maximum height above ground level for headlights. Too many jacked-up pickups with annoying/unsafe headlight placement.
  • While I’m on that thought, maybe require a CDL for vehicles whose hood exceeds a certain height. If you can’t see people standing in front of your vehicle, you get extra training and scrutiny.

It is He who reduces rulers to nothing, Who makes the judges of the earth meaningless.

Isaiah 40:23

One More Trichotomy

I have an update to an old post about the trichotomy of features. This one pertains to the problems with buying a used car.

trichotomy of used cars- choose two keys, an owner's manual, or an intact windshield

Having bought several used cars over the past few years, I have noticed that it’s tough to find one with both an owner’s manual and two keys. And if they do have those, then there’s a large crack in the windshield. Since I avoid buying cars with bad windshields, it’s 50/50 for me on whether I get 2 keys. I get why people might lose a key, but where are they taking the owner’s manual that it gets lost?

You will know that your tent is secure, For you will visit your home and have nothing missing.

Job 5:24

Slapstick Birds

There are some elements of slapstick humor that never grow old. One of those is people running into things. Replace people with animals, and it’s still fun. That was, if I remember correctly, a big portion of America’s Funniest Videos – people and animals running into or falling off things.

A couple months ago, we got our sliding glass doors (AKA patio doors) replaced, because they were drafty and cloudy and needed it. The view to the backyard is much better now, it’s like the glass isn’t even there, it’s so new and clear.

The animals think so too. We occasionally hear a “thump” and by the time we get over to the doors, there is nothing there. So don’t worry, no birds were harmed in the making of this blog post. But the birds did leave some evidence, so we do know that it was a bird.

Exhibit A:

image of bird residue left on a window after running into it

That was kind of faint, so here’s Exhibit B, with different lighting/exposure.

image of bird residue left on a window after running into it

And if you still didn’t see it, this panning shot should help. Exhibit C:

image of bird residue left on a window after running into it, animated to see it easier

It is hidden from the eyes of every living creature, And concealed from the birds of the sky.

Job 28:21

Roads and Rome

You should all be familiar with the phrase “All roads lead to Rome”, and some people have already made signposts joking about that.

Like this:

image of sign posts saying all roads lead to Rome

But I haven’t yet seen anything about what the signposts in Rome would look like. Wouldn’t roads from Rome thus go everywhere, and possible look like this?

image of sign posts saying Roman roads lead to all, or everywhere

but when he was in Rome, he eagerly searched for me and found me

2 Timothy 1:17

Winter Book Thingy 2023

I’ve been able to fit some book reading in during the long dark winter nights, so here are some more reviews.

First up: Aster and the Accidental Magic by Thom Pico and Karensac

image of Aster and the Accidental Magic book by Thom Pico and Karensac

This one was fine. It’s a graphic novel, aimed at the grade-school set. The drawing style took a little getting used to. No other problems here.

Next up: A Boy Called Bat by Elana K. Arnold

image of A Boy Called Bat book by Elana K. Arnold

This book seemed to be mostly an insight into how an autistic boy thinks, trying to promote understanding and compassion for why he does the things he does. And by that measure, I think it succeeds. I don’t know that it’s the most compelling or gripping storyline, but it has its place.

Next up: The Dungeoneers by John David Anderson

image of The Dungeoneers book by John David Anderson

Of these 4 books, this was the most entertaining. But it is also the one targeted to the oldest audience group, junior high+, so that might have something to do with it. A ragtag group of misfits bonds together in a common quest to [prove themselves to others / gain the family they miss or never had / redeem something for some debt / etc.] Standard adventure fare, but in a good way. Nothing objectionable, other than some peril and vague violence (with swords and clubs and such).

Next up: Granted also by John David Anderson

image of Granted book by John David Anderson

Same author, but much different. Different style, different type of book, different audience (although one could argue they’re both in the Fantasy genre). Whereas The Dungeoneers had a storytelling tone, Granted had a conversational tone. And, but for one word, nothing objectionable if you’re okay with the premise of fairies granting wishes. There was one word thrown in to promote acceptance of alternative lifestyles. The author didn’t make it a big point, but it just seemed enough out of place from the rest of the book that it stood out.

That’s it for this review. More book reviews coming up later this year.

Thus says the Lord of hosts: “Dispense true justice and practice kindness and compassion each to his brother”

Zechariah 7:9