Motion and Vectors

Introduction

Back when the world was kind of stupid people believed that heavier things fell faster than lighter things. If you haven't been told that heavier and lighter objects hit the floor at the same time when dropped (neglecting air resistance), this might be mortally offending to you. I apologize. It is not my intention to offend you. When eight-year-old me figured out that weight doesn't impact how quickly objects hit the floor, and that my impeccable pre-developed prefrontal cortex was incorrect (the NERVE), I was mortally offended too. 

Not to worry! If you didn't know this before, that's wonderful, because now you do. Go tell your friends about your recently developed neural pathways just like eight-year-old Twisha did.

When Galileo Galilei proved that heavier objects fall at the same time as lighter objects in his famous Leaning Tower of Pisa experiment, the spirit of eight-year-old not-yet-alive Twisha Sharma burst into his house and killed him. Just kidding. Maybe. Anyway, she was furious. Never mind the details.

You're probably excited to learn why heavier objects hit the ground at the same time as lighter objects. Well, that's too bad, because I put it in the Newton's Laws of Motion page! HAHAHAHA!! Hear that? It's the sound of me laughing at you.

As I explain Motion and Vectors to you throughout this webpage, please refrain from setting my house on fire (I don't need more fees to pay, I live in California). I hate formulas too, but you need them for this part! Hang tight! (If you REALLY dislike this, just like I did, you AHEM AHEM can check out the waves page. You didn't hear that from me. But at least give it a fair chance first. The world around you works on these rules). Anyway, I'm going to be making a lot of jokes to keep you engaged, because I know teenagers, and math is the quickest way to lose them.

Inertia

You've probably heard physicists spitting out the word "inertia" somewhere in your life. So what does it mean? What does anything mean? Before we start this unit, let's go over some vocabulary so we're not lost.

Inertia is the tendency of an object to resist changes in motion. Help, that is such a textbook answer. Every object has inertia. Basically, when objects are at rest, they'll stay at rest, and when they're moving, they'll keep moving at the same speed and in the same direction unless something forces them to change the way they're moving. That sounds a lot like Newton's first law of motion, because it is Newton's first law of motion! That's why its also called the law of Inertia.

A force is a push or pull on an object. Forces change the way objects move.

Newtons are the unit of measurement of force (ingenious, right? Newton made the laws of motion).

Matter is anything that has mass and takes up space.

Mass is the amount of matter in an object.

Kilograms are the unit of measurement for mass.

Weight is the effect of gravity on mass.

Volume is the amount of space a mass takes up.

Now that that's over with, let's continue with the information.

Net Force and Equilibrium

The combination of the forces acting on an object is called the net force. For example, if there is a ball being pulled by two children on either side of it the net force on the ball would be the difference of the two forces. This is because, since the forces are acting in opposite directions, some of each force will cancel out the other. If the forces are acting in the same direction, the net force will be the sum of the forces on the object. 

When the net force on an object is equal to 0, an object is said to be in equilibrium. The equation for this is:

∑F = 0

There are two types of equilibrium: static equilibrium and dynamic equilibrium. 

• Static equilibrium is when an object is at rest in a state of equilibrium. For example, a box resting on the floor is in static equilibrium.

• Dynamic equilibrium is when an object is moving in a state of equilibrium. For example, an asteroid hurdling through space has a net force of 0: there is nothing pushing or pulling it. This means it is in dynamic equilibrium.

Speed and Velocity

As I was saying earlier, humanity was pretty stupid back in the olden days. We used to describe things as just "slow" or "fast." What a great description. But, to be fair... if snails are so slow, why do we never see them coming? It's always "oh look! A snail!" but never "oh look! A snail is over there, crawling in our direction!" it's a horrifying thought, I know.

Either way, the words "slow" and "fast" are really not that descriptive. We need to give speed an actual formula. We need a way to figure out how fast an object is going. Galileo Galilei himself decided the formula for speed:

Speed = distance/time

Now, that seems pretty reasonable, right? If I decide to leisurely walk two miles in an hour, my speed would be two miles per hour (2 mph). That took a lot of braincells. I think I need some coffee.

Instantaneous speed is the speed of an object at a specific moment in time. For example, if I decide to go on another walk to build those beautiful calves, but I decide to run, I could be traveling at different speeds during different times. When I start off, I might be running at 5 mph, but when I slow down after half an hour, I might be running at 3 mph. It all depends on what I feel like doing at the moment.

Average speed, however, is the average speed an object travels over a period of time. In other words:

Average speed = total distance/total time

Even though my instantaneous speed was different during my dedicated calf-building run, my average speed was simply the amount of miles I ran divided by the amount of time I spent running. Basically, if I ran four miles in an hour, my speed would be four miles per hour. Help, guys, that took so many brain cells, I'm drowning.

I am using miles and hours for my units, but the convenient thing about the speed formula is that you can use any units you please. The standard unit that is used most often is kilometers per hour, but you can use mph (miles per hour), meters per minute, anything you choose. You can also rearrange the formula to figure the time or distance instead of the speed. Time = distance/speed and distance = speed x time. It's not that bad guys.

Velocity is a vector quantity. It is speed and direction. When I was running at a speed of 5 mph, I was just running. But if I decide to run at a velocity of 5 mph East, I am now running in a certain direction - now, I have a purpose. Since velocity is a vector quantity, a change in either speed or direction counts as a change in velocity, which results in acceleration. 

There is a formula to calculate acceleration, so we know how fast an object is changing speeds:

Acceleration = ∆v/∆t

The delta symbol (∆) shown above is a Greek letter that we substitute for the words "change in." So, another way to write this equation would be: acceleration = change in velocity/change in time. By "change in time," we mean the time interval in which the change occurred.

Motion is Relative

The thing about motion is that it's relative to the perspective of each object. For example, from our point of view, we are stationary. However, from the Sun's point of view, we are whirling through space, clearly in motion. A person standing outside the Subway will see the train move. But a person sitting in the train will see the station move. Motion is always relative to your frame of reference. Alright, now to discuss the final topic in this section.