[MUSIC PLAYING] Hey, I'm Diana.

You're watching Physics Girl, and this is video number 3 in the series of riddles that I'm asking to my friend, Kurt Hugo Schneider, who also happens to be a really big music YouTuber.

We left off in the last video with the Broom Riddle.

So here's the setup for that again.

OK, so I'm going to balance this broom on my finger so that my finger is underneath the center of gravity.

For a situation like a normal broom on earth, you could either use center of mass or center of gravity for this riddle.

OK, so I'm going to pretend that we're going to cut the broom right here.

Right where you balance it.

Right where I balance it.

OK.

So now you have two pieces of this broom, this handle part and then the sweepy part.

OK.

Which of these sides is heavier, or are they the same weight?

25 00:00:49,590 --> 00:00:50,090 Well, This side has to be heavier because that side goes out so much further.

I mean, if we just imagine a "broom," which is basically a long stick with one enormously massively heavyweight on this end, then the balancing point would-- this side is always going to-- yeah, the balancing point would be very close to here.

This side is going to be much heavier, but this side-- it still balances because that side's so far over there, so the torques, or whatever you call it, balance out.

This side has got to be heavier.

Amazing.

You killed that, awesome.

Your reasoning was my favorite type of reasoning, which is taking the riddle and you're like, let's take it to the extreme, which is like if this is super, super heavy, which obviously, this part is heavier than the rest of the broom.

That wasn't a given, but if you've ever felt a broom, what you're balancing is the torques.

So what you're balancing is the torques, and because the broom goes so far over this way, you get a long distance, and then a little bit of mass, and then big mass and short distance over here.

But when you're balancing torques, which is distance times force, you're not putting those gravitational forces in those equations at the ends of the broom, but rather, you diagram it so that the forces that are acting on the center of mass of each of the sides.

Still, the distance on the left is longer, so that mass has to be less.

But there is a situation in which the-- let me see if I can get this right-- the longer side of that cut can be more massive.

So think if you can come up with a situation like that.

So more specifically, if you've got a rod with some distribution of mass, can you make it so that when you balance your finger on the center of mass and then cut it there, this longer side is actually more massive?

If you have a guess, leave it in the comments.

Moving on to the next riddle.

You've already answered plenty of riddles, so you might even want pen and paper for this.

OK, pen and paper.

Got it.

OK.

So I give you two 2s, two number 2s.

OK. A 2 and a 2.

A 2 and a 2.

All right.

You can do anything with them with pretty common math symbols.

So for example, 2 to the 2 would be 4.

2 plus 2 would be 4.

2 times square root of 2 would be-- Got it.

So 2 root 2.

So you could even do like 2.2.

Got it.

So I can also do 22.

I can concatenate them.

You can do 22.

OK.

So I want you to try and make the number 5.

Got it.

Using two 2s.

Just two 2s.

Just two 2s.

All right.

The simplest.

These are the everyday mathematical symbols you're allowed to use.

OK.

Totally cheating if I look at one of the 2s in the mirror and call it a 5, right?

Yes, that is cheating.

OK, just making sure.

Yeah, there you are.

Making sure.

So I'm going to put a 2 on top, and then take the square root, and then take the square root, and then take the square root.

And then I'm going to add a dot, dot, dot, dot, dot, so an infinite square root of 2.

Because that approaches 1.

Uh-huh.

And then divide by 0.2 for 5.

So this is really dot, dot, dot.

So this is sort of just an infinite operation here.

You got around my rule.

Yeah, but the dot, dot, dot is not listed here, and that is certainly something-- Kurt, it's against the rules.

But that kind of out-of-the-box thinking should not be squashed.

It should be encouraged, and so I applaud your solution, Kurt.

It's just there is a simpler way.

There's no trick, OK.

I genuinely want to figure it out.

Square root of 1 over 0.2 squared is 5.

OK, I just need to get rid of the 1.

Square root of 0.2 to the negative 2.

Can I use negative?

Can I use negative 2?

That's allowed, right?

You can use negative 2.

OK, is that the solution?

That's it.

That's it?

Yes.

That's it.

Sweet.

Yay.

That was amazing.

There's nothing simpler than that.

That was a tricky one.

I have to say, that was tricky right there.

Math major right here.

I feel like you shouldn't be doing only music.

Really using that math degree.

First time I've used my math degree in nearly 10 years.

OK, now I'm pumped.

This one pumped me up.

That was really good.

153 00:05:05,790 --> 00:05:07,930 Now I'm thinking about this one, though.

I know some of you can't go on with life without knowing what riddle I gave Kurt, so here is the final bonus riddle.

I'll put the answer in the description tomorrow.

I lost Kurt for about 25 minutes because I gave him another riddle.

I did get it.

You did get it.

But there's clearly some clever rotational, or there's some very intuitive way of seeing this.

I feel like I know what you're going to do with the rest of your evening.

I give you a math problem, you're like, no.

Like, hold on.

Like, just a minute.

I'm like, Kurt, can we do it after.

You're like, just a minute.

This was amazing.

Thank you.

Oh no, thank you.

Thank you so much.

This was so much fun.

This was so much fun for me.

Thank you guys for watching.

It was a fun guest.

And happy physicsing.

Yeah.

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