Newton's Laws of Motion

Yes! I managed to write this page with ZERO, count 'em, ZERO crazy weird equations! Although I feel like those will rear their ugly heads in Projectile Motion... shudder. Anyway... enjoy!

Newton's First Law of Motion

Newton's first law states: 

A body at rest will remain at rest and a body in motion will remain in motion unless acted upon by an external force.

This law is also called the law of inertia, because it is describing the property of inertia that objects have. Inertia is the tendency of objects to resist changes in motion. The more mass an object has, the more inertia it has. This is the reason we are jerked forward when a car suddenly brakes. Our bodies were traveling at the speed of the moving car, and despite the fact that the car quickly slowed down, our inertia keeps us moving forward - hence the reason we fly forward.

This is also shown when a plane suddenly accelerates. We humans are pushed into the back of our seats because our bodies were moving at slower speeds before the plane sped up. Our inertia, our resistance to changes in motion is what pushes us against the speeding plane.

Earth is constantly moving at very high speeds through space. Since we live on the Earth, our bodies are moving at the same speed with it, and so is everything we touch and see. If you stand next to a wall and jump, the wall does not run into you because both you and the wall are traveling at the same speed - the speed of Earth relative to the Sun. We always keep up with the Earth when we jump - clearly inertia at work.

Newton's Second Law of Motion

Newton's second law states: 

The force acting on an object is equal to the mass of that object times its acceleration.

In other words, force = mass x acceleration or F = ma. This law is also known as the law of acceleration.

For instance, let's say you're moving and pushing some boxes around to your sister's room. But, your sister sucks at packing, and some boxes are far heavier than others. If you push a box that has a lot of mass with the same constant force, you will get a smaller acceleration. But if you push a box that only has a little mass with the same force, you will get a much larger acceleration. I have no idea how you have the patience for this. Why would you volunteer to help your sister unpack? I would've called her a bozo and left by now.

Anyway, do you remember that promise I made in the Motion and Vectors page where I said I would explain free fall? I'm about to explain it, so hang tight. Ha, get it?

Acceleration due to gravity is represented by the variable g and g = 9.8 m/s^2. When an object's acceleration is equal to g, and there is no air resistance, we say the object is in free fall. 

If we are speaking in the context of Twisha and coffee, and Twisha is falling towards a planet made of coffee, Twisha will happily accelerate at a constant rate of 9.8 m/s^2 towards the love of her life until she craches into it and cries with happiness.

But wait - Twisha's beloved coffee planet has an atmosphere! No! Air resistance is certainly not negligible when one is discussing the process of falling. When there is air resistence, the acceleration decreases. In fact, the downward net force is now equal to the weight minus the air resistance. In other words, down net force = weight - air resistance. But air resistence depends on the speed and area of an object. As the speed or area increases, so does the effect of air resistance. Poor Twisha. She just wanted her coffee. Now's she's burning up in the atmosphere.

Not only is poor Twisha suffering, she can no longer constantly accelerate towards her coffee planet. At one point, the equation we just discovered will amount to zero -  the air resistance against her will be equal to her weight. They will completely cancel each other out, and she will no longer gain speed - she will fall towards her planet at a constant velocity. At this point, she will have reached terminal velocity (terminal speed if you are ignoring direction. But Twisha sure isn't. She's making sure to aim towards her coffee planet).

Connecting the first law to the second, we now have our reason as to why heavier objects do not fall faster than lighter ones. The pull of gravity is stronger on an object with more mass, as we discovered with the second law. But, objects with more mass also have more inertia. Both these things cancel each other out, producing the same acceleration on both objects.

You might argue that feathers fall super slowly compared on hammers. But that is only because of air resistance. Feathers reach their terminal velocity much faster than hammers do, because of their small mass. Because of this, hammers hit the ground much faster. If you dropped a feather and a hammer at the same time on the Moon, both objects would hit the ground at the same time.

Newton's Third Law of Motion

Ah, this is the popular law. I'm pretty sure this is used in 80% of corny physics pick up lines. Despite the amount of puns made with this law, Newton's third law actually states (say it with me):

For every action, there is an equal and opposite reaction.

This law is also called the law of action/reaction. 

I'll explain these laws with a couple examples. When you punch a wall (not sure why you want to punch a wall. Y'all are some sketchy middle schoolers), the wall punches you back. Well, not exactly. More accurately, the wall pushes back against your punch with an equal and opposite force. That's why your hand hurts and recoils when you punch a wall - because you technically just punched yourself. That's not the way most physicists see it, but it's true.

Another popular example is with a rocket. The rocket pushes on the gas it releases, and in turn, the gas pushes back on the rocket. This propels the rocket off the face of the Earth.

My last example has to do with forces, because this law applies to forces as well. When you drop a ball, Earth's gravity pulls the ball towards its surface. The ball, in turn, also pulls Earth towards its surface. Earth's mass is just so large relative to the ball that the movement is negligible.

Let's say that you are kicking a punching bag (first the wall, now the bag? Y'all need to get your lives together and set your priorities straight). Your weak middle school foot rebounds far more than the bag. But why? According to the third law, you both should've been hit with the same reaction force. 

If you had this question, you were clearly not paying attention to the second law. The bag has more mass than your foot does, and thus experiences less acceleration. You just learned this. Come on.

"I WAS PAYING ATTENTION," you protest, "you're the one who's not paying attention! Clearly this law is just a meme. If action and reaction forces are equal and opposite, why don't they cancel each other out, JUST LIKE YOU WROTE IN THE PREVIOUS PAGE, HUH, TWISHA?!?" *does the Rock eyebrow lift*

Well, you, my dear friend, should shut up. (I send love).

Action/reaction forces don't cancel each other out if you look at the whole system. When you push your car, the horizontal force needed is provided by your feet pushing against the floor. In this way, looking at the entire situation, you can see that you can still move things around without being canceled out by the reaction force. You can't push your car from your dashboard because you're not providing an external force. You're part of the system, and the forces you provide are canceled out.

Welp, this article proved to not be as long as I thought it would be. If you thought that was bad, kys (keep yourself safe). I have to write about projectile motion next. Grrr so many formulas. I'm gonna be so cooked after this... but it's okay, I like writing these. Either way, I'm gonna go watch TV. Good night!