Almost Forgot to Cash In

The Elite Class teachers' office at Jiangcheng No. 6 High School operated differently from the subject-group and grade-group model used by other schools.

Only the top teachers responsible for teaching the Elite Class sat in the spacious office.

This arrangement allowed the teachers to conduct comprehensive performance analyses and collective consultations for the several dozen top students in the class at any time.

Such an absolute concentration of teaching talent and preferential allocation of resources was unimaginable at an ordinary public high school.

That was why Liu Limin had dared to pat his chest and say that No. 6 High School's platform could offer Li Dong a higher ceiling.

When Old Chen led Li Dong into the office, there were no other teachers inside.

He walked to his desk, pulled open a drawer, and began rummaging through it.

"What kind of problem should I find for this kid?"

Old Chen muttered to himself.

"Use calculus to derive an Electromagnetism oscillating circuit? No..."

Old Chen had just pulled out a sheet of paper when he remembered that Li Dong was a freak who could mentally calculate even double integrals and partial derivatives. He decisively shook his head and stuffed the paper back.

When it came to mathematical tools, this kid was practically a monster.

"I need something that can truly test his physical intuition."

At last, he pulled an A4 sheet from a folder.

He nodded as he looked at the question on it.

The problem was not actually that difficult. For students who frequently took part in physics competitions, as long as they had some talent, they could generally grind out an answer in the end.

Of course, that depended on the school.

If it were given at Jiangcheng No. 7 High School... it would absolutely make Jiang Yizhou cry on the spot.

This problem required inspiration. It required the right angle of attack.

If you possessed keen physical intuition and could see through the hidden physical picture in the problem at a glance, you could solve it in seconds.

But if you failed to find that entry point and stubbornly calculated using conventional dynamics...

Then congratulations—even if you filled ten pages with Lagrange Equations, you would ultimately end up trapped in a nonlinear differential equation with no elementary analytical solution, walking straight into a dead end that could not be solved at all.

In the end, your physics teacher would only pat you on the shoulder and earnestly advise you, "Kid, don't take the crooked path of physics."

Old Chen handed the A4 sheet to Li Dong.

"Here, give this a try."

Li Dong took it curiously and lowered his head to look.

[A uniform slender rigid rod of mass m and length 2l initially stands upright on a smooth horizontal table. Due to a slight disturbance, the rod begins to fall. Find the trajectory equation of its instantaneous center of rotation during the process of falling while maintaining contact with the tabletop, and sketch the trajectory.]

After reading the problem, Li Dong raised an eyebrow slightly.

"Huh? This is interesting."

Almost the moment he saw the question, he spotted its trap.

For an ordinary high school student, or even a freshman in college, their first reaction upon seeing this kind of rigid-body motion would definitely be to set up coordinates.

Then they would write the translational equation for the center of mass, followed by the rotational equation about the center of mass, and finally try to forcibly solve the coupled system of differential equations.

But once they actually did that, they would despairingly discover that the relationship between the rod's falling angle θ and time t was a complicated nonlinear function with no elementary analytical solution at all!

Their scratch paper would end up an absolute mess.

So this problem was not testing computational ability at all!

In Li Dong's mind, the illusory rigid rod had already begun falling across the smooth tabletop.

"The tabletop is smooth in the horizontal direction, which means there is no external horizontal force at all!"

"Since there is no horizontal external force, the rod's center of mass must conserve momentum in the horizontal direction! Its initial momentum is zero, so its momentum remains zero throughout the process."

"Therefore, the center of mass cannot undergo any horizontal displacement. It can only fall straight down along a vertical line!"

Li Dong's eyes lit up.

"Isn't this the classic ladder-sliding-against-a-wall model?"

He had found the entry point!

"Teacher Chen really wasn't lying. This problem is pretty fun."

Since it was so fun, Li Dong planned to derive the trajectory of the instantaneous center from three different angles.

Holding his pen, he wrote Solution One and Solution Two on the paper. Just as he was about to write Solution Three...

Click.

The office door was pushed open.

A refined-looking teacher entered carrying a thick stack of test papers, then casually set them on a desk.

Li Dong instinctively looked up.

It was the biology teacher from the previous class!

The moment he saw the biology teacher, Li Dong blanked out for a moment, as though he had forgotten something important.

Fuck!

Mendel!

I still haven't fully figured out the underlying logic behind the "three-line system" of cytoplasmic male sterility that the biology teacher talked about!

Even worse, Mendel, the guy who grew peas, was still waiting eagerly in the Azure Dragon Study Group for my explanation!

Li Dong suddenly realized that he had no time to waste!

Those big shots in the group could log off at any moment.

If Mendel logged off in a while, wouldn't this haul just fucking fly away?!

Compared with a god-tier cash cow, what was the trajectory of this broken rod's instantaneous center worth?

Multiple solutions? A detailed derivation? Elegantly showing off in front of the teacher?

To hell with all of it!

Li Dong immediately began writing on the A4 sheet.

Meanwhile, Old Chen leisurely unscrewed his thermos.

Then he glanced at the time, preparing to time Li Dong.

"If this little guy can see through it within a minute, that counts as some exceptional talent."

"If he can do it within thirty seconds... then this kid's physical intuition is probably enough for him to try making a run at Orsay."

Old Chen had just raised the thermos, ready to leisurely take a sip of hot water.

But before the hot water reached his lips—

"Teacher, I'm done! I have a question about a biology topic for the biology teacher. Please wait for me a moment!"

Old Chen froze. His hand jerked violently, and several drops of tea splashed directly onto the back of his hand.

Then he saw a figure dash past him.

"What the hell just went by?"

He hurriedly set down the cup and raised his head. Li Dong had already run over to the biology teacher.

"He's... done already?"

Old Chen quickly lowered his head and looked at the A4 sheet Li Dong had left on the desk.

The handwriting on the paper was messy.

[Answer: The trajectory of the instantaneous center is a quarter-circle arc with radius l.]

Not a single unnecessary word.

He had directly seen through the essence of the rod's fall from the highest-dimensional perspective of kinematic geometry.

Old Chen was not surprised that Li Dong could solve it.

But that time...

Including the time to read the problem, think, and write it down.

Altogether, it had taken less than a minute?

Then he looked at the words "Solution Two" beside Solution One.

What did that mean?

It meant that the instant this kid saw the problem, he had not only instantly found the simplest geometric approach, but had also simultaneously conceived a second method in his mind!

"Two solutions?"

Old Chen removed his glasses, wiped the lenses with the hem of his shirt, then put them back on.

He looked at Li Dong, who was urgently tugging the biology teacher aside and asking questions, and could not help but smile.

"What a little monster."