Point Mass (Particle) Explained

Can a cat be a particle? (preview: a 2021 Chinese exam question)

0:00
Read the question carefully. It's about the cat's velocity. If it asked how posture affects velocity, then posture would matter a lot, so it couldn't be a particle. But now I only study velocity. I only need its displacement in this time, divided by the time. So it can be treated as a particle. Enough talk. Let's begin.

In this lesson, and why physics is lazy

0:22
This is a Basics lesson. Today: the particle. It's the first concept in high school physics. The particle idea boils down to two words: Which two? Being lazy. I'm on the Peking University campus, Suddenly I get a message from Qi Xiaoyu. She's on the Tsinghua campus. She wants me there right away. I'm new in Beijing, I don't know the roads, so I pull out my phone to navigate. How do I get from Weiming Lake at Peking University to Tsinghua? Soon the app shows me a route. Look, here I'm just a dot. On the map, it doesn't draw my photo or my whole body. No little person walks while I navigate. Does that stop me finding the way? No. You've used navigation: a walking person on screen would be inconvenient.

1:29
It blocks the road, or looks creepy. A very successful example of being lazy. By being lazy, navigation gets simpler. A lot of high school physics is laziness. The particle is the classic example. Now, the definition of the particle. For now, it's just a tool for being lazy.

Definition: particle and ideal model

1:54
Definition: shape and size are ignored, a point that has only mass. This is important and often tested. Questions often ask: is a particle a geometric point? No. Why? It has one extra property: mass. We said the particle is for being lazy, but not carelessly. Being lazy has a condition. It can't affect solving the problem. Most physics problems can't ignore mass. Later, with Newton's second law, you'll see mass matters a lot. So to avoid affecting the solution, the particle deliberately keeps its mass. Think: a particle is a point with mass. Compared with a geometric point, the only difference is mass. Why learn it? To be lazy, or nicely put: simplify the problem. Some ask what the particle model shows, that is, which scientific method or mindset it uses.

3:04
Remember the term: idealized model. Treating an object as a particle is the method of building an idealized model. That term is tied to the particle. Hear particle, think idealized model. Of course, it doesn't exist in reality. How to understand it? Imagine the particle as a lazy filter. A real object has edges and corners. But we can add a lazy filter ourselves. Take my sunglasses. When I put them on, the object becomes a particle to me. I filter out its size and shape. Take them off, and it's itself again. So the particle is a lazy filter. Can we use this filter in every situation?

The lazy filter does not always work

3:56
Everyone likes being lazy, right? Fun! But no, not in every case. Here's an example. Qi Xiaoyu sent me two photos and asked which one looks better. Say I turn on the lazy filter and reply: "They're about the same." That shows zero survival instinct. I'd be single forever! I can't say that. I can't be lazy here, or I'm dead. I must fire up all my brain's CPU and use all my attention to play spot the difference. I also invent words that sound different. For the left one: this touch of black. A bit playful, yet still poised. Your style owns this black. Plain outfit, but on you, perfect. As for the right one: Few dare to wear this. Why?

5:05
Worn, it has no special features, but on you, it's different. You two bring out the best in each other. It looks made for you. You need ready-made phrases like these for when your girlfriend asks. So I can't treat her as a particle, right? Other times it's different. For example, these four female stars are my favorites lately First is... Zhao Jinmai, right? Her TV drama Reset is super popular lately. A bus keeps exploding in an endless loop. Chinese dramas are really good now. A truly watchable endless-loop drama. Zhao Jinmai is the female lead. After watching Reset I became her big fan. The second is... our Tan Songyun, right? The third, Liu Haocun, right? The fourth: a recent Winter Olympics star, the amazing Chinese skier Eileen Gu. I like her a lot.

6:09
Suppose I'm sent four photos and asked to comment. Which of these four do you like best? Who's the prettiest? Dare I judge them one by one? Zhao Jinmai: such big eyes, lovely. Tan Songyun has such a sweet look. Dare I say that? Eileen Gu has a very striking look. She's mixed-race. Dare I say that? If I did, I'd get beaten up. So I decisively switch on my lazy filter. All the same. You're the prettiest. Only then can I pass safely. Whether I can use the filter depends on the scene and the problem. I must handle each problem flexibly. A lot of physics is closely tied to the philosophy of life. Try to get a feel for that. Keeping the filter always on costs you a lot of fun. Take this one. What's this? A diver jumping, right? Every time I watch, I laugh.

7:12
Watch for yourselves. I won't say more. But as a particle, you'd miss the fun. So whether an object counts as a particle isn't fixed. Analyze each specific problem. Now the second key point on particles. There are only two. First: definition and concept.

When can an object be a particle?

7:31
Second: when can an object be a particle? One sentence sums it up. If its shape and size have no effect, or little effect, on the problem studied, no effect is fine, little is fine too, then we can treat it as a particle. That may feel far from exam questions, so I summarized common exam scenarios. Sum them up and problems get easier. I split them into two blocks. First: when it can be a particle. Two are common. One: vehicle much smaller than distance A ship works too. For example, a train 1 km long travels 12,000 km and you must find its speed. The train is long, but tiny next to the distance, so treating it as a particle is fine. Two: orbiting (revolution). Earth around the Sun, or the Moon around Earth.

8:37
Earth and the Moon aren't small. They're huge celestial bodies. But when orbiting the Sun or Earth, treating them as particles barely affects the result so they can be particles. Cases where it can't be a particle. First: the scene tells you that body movement or posture matters. For example, can a bird land on a tree, or a diver's posture. If posture matters, it can never be a particle. That's the first common case. Second: when we study rotation. Like Earth's rotation or a spinning top, or a rotating water ball. Those can't be particles either. Summarize these well. That wraps up the key idea of the particle. Now an example: check what you've learned.

Example 1: which scientific method?

9:38
Example 1: introducing the particle uses which scientific method? Before this problem, let me share the right way to study physics. My one trick: summarizing problems. I did nothing else, just pushed it to the extreme. I took many detours. But you, watching right now, will skip most of them. Why? This series picks the most classic typical problems for each module and type. Just summarize every problem I teach in one notebook. When I ask you to summarize under a problem, whatever I say, you write. That's the most important content. Before every midterm and final, review just this and you're set. When reviewing, doing problems is the most effective way. No need for concept explanations or the textbook. Just do problems. Of course, provided you wrote down the summaries I asked for.

10:43
Now, this problem. If you haven't taken my class, options A, B, C and D may all look right. Can an object be a particle? A: is it summed up from many observations and experiments? A seems right. B, building an idealized model, sounds right. C: analogy. Likening a real object to a point is an analogy. D: logical reasoning. Deciding either way is reasoning. D seems right. Which? You'd hesitate. But I stressed it earlier, right? I stressed a term. See 'physical meaning': it's an idealized model. In Chinese exams, if a question mentions scientific methods or scientific thinking, the particle is tied to idealized model. Note this down: Particle and idealized model are bound together.

11:44
On later questions like this, you'll choose instantly. The answer is B. Be sure to write it down here: Particle and idealized model go together, with two exclamation marks. That's Example 1.

Example 2: five true/false statements

11:58
Example 2: true or false? Mark each with a check or a cross. 1. Any object with very small mass and volume can be seen as a particle. Wrong. Whether we treat it as a particle depends not on the object, but on the problem we study. The problem is key, not the object. A counterexample: a scientist studies an atom's rotation. Is an atom small enough? Small mass and volume: it fits. Treat it as a particle? No. As I said, anything involving rotation can't be a particle, because a point can't rotate. A point has no rotating property, so it's not a particle. Let me stress it again. To sum up: whether it can be a particle depends on the problem, not on the object. 2. If an object's shape and size have no or little effect on the problem, it can be treated as a particle. True. 3. A particle has no size, so it equals a geometric point.

13:02
That's wrong. I stressed earlier the difference between a particle and a geometric point: often tested. There is only one difference: mass. If you missed it before, note it down here. Particle versus geometric point: the only difference is mass. The core is just: it has mass. 4. A particle is just a very small ball. Wrong. However small a ball is, it's not a point. Why? Any ball, however small, has a diameter and a radius. But a point has no diameter and no radius. So a point is not a ball. Note that. A ball, however small, is never a point. 5. A particle is an idealized model that doesn't exist. That part is true. So introducing the concept is meaningless. Of course it has meaning. What meaning? Being lazy, right? So statement 5 is wrong too. In Chinese physics multiple-choice or true/false questions, "Introducing X is pointless" is wrong. Why learn it if pointless?

14:05
You learn it, so it matters. So: wrong, right, wrong, wrong, wrong.

Example 3: 2021 Gaokao (China's college entrance exam): cat, water drop, bird, horse

14:09
Let's do one more. From the 2021 gaokao, China's college exam. Don't underestimate the particle. Some gaokao questions test only particles. But this one isn't easy. Let's look. Four high-speed camera photos. Which statement is correct? A. Studying the cat's walking velocity: the cat can be a particle. This picture is very misleading. Many students say posture clearly matters, so it can't be one. Read the question carefully. It says it studies velocity. If it asked how posture affects velocity, then posture would matter a lot, so it couldn't be a particle. But now I only study velocity. I only need its displacement in this time, divided by the time. So it can be treated as a particle. A is correct. Once more: if option A were changed to studying how posture affects velocity, it couldn't be a particle. B. Studying the water drop, why it has its shape: the rotating ball can be a particle.

15:18
We summarized: anything involving rotation can't be a particle. So B is wrong. C. Studying the flying bird and whether it can land on a stump: the bird can be a particle. Think: whether a bird can land, its posture surely matters. For example, how wide its wings spread, how far its claws close, before it can hold on, and when it can't. Posture definitely matters. So C is also wrong. D. Studying whether the rider and horse can clear the obstacle: the horse can be a particle. This is wrong too. If its front legs lift a bit higher, it clears the obstacle. Too low, and it doesn't. So the horse's front and back legs, and its body's tilt angle, all affect whether it clears the obstacle. So D also involves posture, so it can't be a particle. This question tests when something can, and can't, be a particle. Back to my summary.

16:20
Look at the ones that can't be particles: either posture matters or it rotates. Either way, it can't. In this question, B is about rotation, so it can't be a particle. C and D involve posture, so they can't be. So be sure to write down the summaries. That's it for the particle. Everything you need to know you now know thoroughly.

Summary

16:44
This page is everything in this lesson. Take a screenshot. Congratulations, you've mastered the particle.