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**bbjygm** · 03-25-2019, 06:41 PM

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Introduction

Physics is everywhere. You literally cannot take a single step without encountering some physical law. Physics is the study of the universe and how matter, energy, and forces interact through space and time. Many branches of science rely on physics as it is the purest form of science.

The purpose of this article is to teach the basic principles of classical physics to the layperson. I find the best way to experience and learn about science is to relate them to real-world scenarios and carry them out yourself. Therefore, in this article, I will touch on many hockey-relevant subjects of physics and relate them to hockey (disclaimer: I've never played hockey myself, but I'm somewhat versed in physics). This article will use the Khan Academy physics curriculum as a reference for subjects to cover and in what order.

This is not meant to delve deeply into the equations and nuances of physics. This is only meant to provide high-level descriptions of physical concepts in relation to hockey to help readers better understand how these physical concepts work and interact with the world.

Credentials

I took a physics class in high school, intro to physics in college, and the version of physics that requires calculus in college. I graduated with a B.S. in electrical engineering. I have a passion for math and numbers, and physics was a great way to apply that to the real world. Also I can use the internet.

Chapter One: Motion

In order to understand motion, one must understand scalars and vectors. Scalars are just a plain old number used to describe how much of something there is. As an example, let's use speed. For a car on the highway, if your speedometer reads 70 miles/hour, your speed is a scalar of 70 miles/hour. Vectors have a scalar value and a direction, which can be represented by an arrow. Your speedometer reading 70 miles/hour means your vector amplitude (can be represented as length) is 70 miles/hour and your vector direction is pointing forward down the highway. In one-dimensional space, your arrow can point one of 2 directions (up or down the number line), but on the highway your vector points in a direction in 3D space (hopefully forward down your lane). A vector arrow is always straight, representing your current direction at any instantaneous point in time. Even if you're driving around a curve in the highway, your vector arrow points straight ahead as that's the direction you're currently facing. If you immediately stopped steering, you would go the direction of that vector arrow.

Another example is with a hockey puck: if you shoot at one of the top corners of the goal, the puck's speed represents how fast it's going and the direction points towards the corner of the goal. These two bits of information are combined into a vector to describe the puck's motion.

Vectors can also be broken into components. If a puck is hit upwards at an angle, one could represent that resulting velocity arrow with two smaller arrows that add up to the resulting velocity arrow. This is often done in physics to help isolate certain parts of problems. For example, the velocity of the upward-angled puck would most likely be broken into a velocity vector that points up and a velocity vector that points forward (perpendicular to the ground). These would have magnitudes and angles such that, when added, would result in the puck's actual velocity vector. However, now one could use the up arrow to help with gravitational acceleration calculations and use the forward arrow with determining distances in projectile motion.

Rates come up a lot in physics. They describe how things change. Velocity is a rate. It's the change in distance per unit of time. If a puck goes 90 miles/hour, this can be simplified to 132 feet/second. This means every second, the puck will travel 132 feet, as its position changes with time based on the velocity. Acceleration is the rate of change in velocity. If a puck undergoes 132,000 ft/s^2 of acceleration, that means for every second that the puck is accelerated, its velocity changes by 132,000 ft/s. Pucks get accelerated very briefly, so while the acceleration may seem high the puck doesn't reach speeds of thousands of feet/second. For a collision of 0.001 seconds (the puck was being accelerated by the stick for 1 millisecond), this means the puck underwent a change in velocity of 132 ft/s.

Projectile motion is the motion of an object as it travels through the air while being affected by gravity. Gravity provides a constant acceleration towards a collection of mass. On Earth, that means all objects with mass (anything made of matter) will be accelerated downwards towards the Earth (note: this also means objects are very minimally accelerated towards each other, as well, but it's nigh undetectable to the scales we're dealing with. It takes an object as massive as the Earth to make us feel the gravitational pull we do, so an object as relatively small as a person would not affect anything in comparison). When an object is thrown through the air, gravity's acceleration causes the object's vertical component of its velocity to increase downwards at a constant rate. This illustrates that all objects fall with the same rate due to gravity (although air resistance likes to put a kink in that idea wherever it can). The forward velocity of the object will determine how far it goes in the time it has up in the air before gravity brings it down to the ground. Projectile motion isn't seen much in hockey as pucks move pretty fast when being shot at the goal, so projectile motion doesn't have much time to work to move the puck downward towards the ground. Also, the puck can't fall if it's already on the ice scooting along. Projectile motion shows up when the puck gets deflected weird or flicked into the air for a long pass, causing the puck to follow a tall arc while gravity's acceleration works to bring the puck down to Earth.

Chapter Two: Forces and Newton

Newton's laws of motion are:

1. Every object in motion will remain in motion unless an external force acts on it.
2. Force equals mass time acceleration (f = m*a).
3. For every action there is an equal and opposite reaction.

These laws came from Newton's observations and experiments. They can be verified with your own experiments if you have the desire to conduct them or at least just look them up.

According to the second law, a force is mass times acceleration. A force is like a push on an object. If you want to push something harder (apply a larger force), you either need to use more mass for the push or accelerate faster. Gravity's acceleration is actually due to a force. A constant acceleration due to gravity means that the heavier an object is, the harder it's going to push down towards the Earth (pretty intuitive, huh?). Speed being equal, a heavier hockey player can hit someone with more force than a lighter one as they have more mass to apply a force to someone.

The first law states that objects will not change velocity unless an external force acts upon it. Without friction, air resistance, or gravity (think out in space), an object will just keep moving in whatever direction it's going and however fast it's going until it gets affected by something else through a force. This concept may seem a bit less intuitive because we're used to objects stopping. On Earth, gravity is a constant force that keeps objects on the ground, so we don't float up into space. Friction with the ground and air resistance cause objects to eventually stop no matter how fast they are going. Even ice has friction: you can hit a puck across ice in a vacuum (no air resistance) and the puck will eventually slow down due to friction. So in reality, an object like a skater or puck WOULD keep moving, but there are constantly external forces acting on it so we don't experience the first law too often.

The third law says that every action causes an opposite reaction. Try punching someone: you will apply a force to their body, but their body will also then apply a force back at you, potentially hurting your hand. If you hit a puck at a stationary puck, the stationary puck will take off and the first moving puck will slow down, stop, or go backwards. This is because although the first moving puck applies a force on the stationary puck, the stationary puck also applies a force on the first moving puck, causing an acceleration in the opposite direction. If you hit a puck at a wall, if there was no opposite reaction then it would apply its force to the wall and stop dead in its tracks. However, since Newton's third law prevails, the wall also applies a force back to the puck, which then accelerates briefly in the opposite direction of the wall and zooms away. This concept is instrumental in studying collisions, as you can see.

Chapter Three: Circular Motion

Based on Newton's first law, all objects need an external force in order to change its velocity vector. This includes turning. In order for an object to change directions, a force must be applied to it. For example, for a hockey player to turn, the only thing they have to turn with is by using the ice. The player's skate tilts, which digs the blade into the ice at an angle. The ice pushes on the skate, causing an acceleration to the side, changing the direction of the skater.

Circular motion comes into play when the sideways force that is applied to the object keeps "following" it, getting applied to the object as it turns. This constant force keeps the object turning at the same rate, which makes it go in a circle. For the hockey player, the ice is always pushing to the side when they lean, so as long as they keep leaning the skate will have a force applied to it sideways to keep the player turning. This force applied to the object to keep it turning is called centripetal force. Centripetal force is sometimes unintuitive. Imagine hanging on to a rope and being swung around in a circle. As the object being swung around, you'd probably think that there's a force being applied to you outward as you cling on for dear life because you feel like you're about to be launched away. In actuality, the rope is applying a force at your hand inward towards the point you're swing about that changes your direction. Your grip is causing an internal force on the rope that pulls it outward. If the rope can't handle those forces, it snaps, but that's besides the point. The real point is that the rope applies an inward force to change your direction called centripetal force. The "phantom" force that you think is pulling you outward is called centrifugal force. It's not a real force in the system, but it can feel like it from the perception of the object and is sometimes still referenced today.

The principle of circular motion also applies to gravity and orbits. If you're trying to orbit the Earth, you're fighting gravity. Gravity acts as the force that turns your velocity vector back towards the ground (center of the Earth). Your objective is to go fast enough forward that as the gravity force vector pulls you sideways and turns you, you keep moving far enough forward that your velocity still doesn't point at the Earth. This is why some people describe orbiting as falling but missing the Earth. In the rope or skate problems, you have a set circular path to follow and the force applied to you changes, determining your velocity as you circle. In an orbiting problem, the force applied by gravity doesn't change, so you have to set your velocity according to your path's radius so you make a circle around the Earth without the path passing through the Earth's atmosphere.

Chapter Four: Work and Energy

Work is defined as the measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement (source). What this means is that an object must have a force applied to it over a net non-zero distance (must be displaced). Even simpler, you gotta move something somewhere else to have done work.

Energy is defined as the capacity to do work. We're mostly dealing with mechanics in this article, so energy transfer does work, which moves an object from one spot to another. In a hockey pass or shot, energy is transferred from the player to the stick to move it by applying a force and displacing it. Energy is then transferred from the stick to the puck by applying a force and displacing it. All this energy transfer is due to work being done on the stick and puck.

Energy can be stored as well. Potential energy has several different forms, but it usually refers to the energy stored in a system that has the potential to be used. For gravity, lifting something up uses energy, which is stored in the object. This energy can be released as kinetic energy if it falls down. For springs, energy can be stored by compressing or extending the spring which is stored as potential energy that can be used to extend or compress the spring back to its original position. There are other forms of potential energy, such as chemical and electrical, but they all basically mean the energy stored up in a system that's not doing anything and is ready to be released.

A spring is one way to store energy in an object. The larger the displacement of the spring, the more force is required to get it there. Hockey sticks can be springy during slap shots, storing energy from the swing after hitting the ground as potential energy. Then, the springiness of the stick can release its potential energy faster than it was stored (based on the mechanics of the materials), applying more speed to the puck than without the springiness.

This also leads us to the topic of mechanical advantage. Mechanical advantage is defined as the output force of a machine divided by its input force required. How much a machine transforms the input force or the distance over which that force is applied is its mechanical advantage. For an example, an inclined plane (a ramp) allows someone to push an object up it with less force than is required to lift the object outright, but the tradeoff is that the force must be applied over a longer distance. This means the mechanical advantage is greater than 1 since the output force of the machine (how much is required to lift it) is larger than the input force to the machine (how much is required to push it up the ramp). This is advantageous for humans as we have upper limits to our strength, so we do the work over a longer distance. Another machine to look at is the hockey stick. When the player moves the stick, they are required to move to move the stick a small amount with greater force to get the stick to move a larger amount with less force. However, the tradeoff is that the stick travels a longer distance than the hand. This means the mechanical advantage is less than 1. This isn't bad, though, as this helps apply a faster speed to the puck than if the player just used their arm/hand. Mechanical advantage is only concerned with forces, not velocities.

Chapter Five: Momentum

Momentum is the velocity of an object times its mass. Its a measurement of moving mass and is represented as a vector. It is useful for investigating collisions. An impulse is a change in momentum, and is equivalent to a force applied over time. Impulses are useful because they can help relate problems back to momentum for collisions.

A collision involves a transfer of momentum from one object to another. In elastic collisions, no energy is wasted in the collision itself. In inelastic collisions, (kinetic) energy is lost in the collision, usually in the deformation of the objects, heat, and sound. Elastic collisions never happen in real life, but they can be close enough to approximate actual collision phenomena that they can be used for lots of problems with adequate solutions. Elastic collisions also have the added constraint that kinetic energy (energy stored in a moving object) is conserved as well as momentum, which allows for less unknowns to a problem. For hockey purposes, the most you need to intuit from these concepts is that heavy objects aren't as affected by light objects in collisions. A light player doesn't have as much affect on a heavy player than the heavy player has on the light player. A player has almost no impact to their momentum in a collision with the puck (e.g. shooting), while the player has a much higher impact on the puck.

Center of mass is pretty intuitive based on the name. It's the average position of all parts of a system based on mass. It is the point on which a uniform force on the object acts. Say a hockey player is skating next to the player benches and another player comes in for a hit. If they smash up against the player uniformly, the hit player will act as if the force was applied to its center of mass. If he was a male, his center of mass would be higher up in the torso and would most likely flip over the wall. Females have a lower center of mass and have a lesser chance of flipping over the low walls.

Conclusion

Physic is in everything we do and every way we interact with the world. Relating physical concepts with real-world examples can help bridge the understanding gap and even enlighten people who already know the details of physics with more examples of that concept's uses.

Please excuse me if I got a bit incoherent at the end, this was a long article and I was getting tired. If anyone has questions, please let me know and I'll try and answer them. I'm thinking of doing more in-depth articles for each subject and/or possibly writing an article on non-mechanical subjects with analogies to hockey, such as fluids and electricity.

***luke*** · 03-25-2019, 06:46 PM

Hey I did that last semester

TnlAstatine · 03-25-2019, 06:50 PM

For every action there is an equal and opposite reaction
CRUNCH was the action
Ouch was the reaction
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E A SPORTS its in the game.

SlashACM · 03-25-2019, 06:51 PM

Why

Jepox · 03-25-2019, 07:08 PM

Where were you last semester when I needed you most

***luke*** · 03-25-2019, 07:12 PM

03-25-2019, 07:08 PMJepox Wrote: Where were you last semester when I needed you most

Chegg and wyn tutor on YouTube. Helps the pain

*slothfacekilla* · 03-25-2019, 07:18 PM

GCool · 03-25-2019, 09:04 PM

Well done! I'd be interested in fluids - I missed those in my curriculum. Haha

**bbjygm** · 03-26-2019, 02:03 AM

03-25-2019, 09:04 PMGCool Wrote: Well done! I'd be interested in fluids - I missed those in my curriculum. Haha

Alright, thanks for the input. I took fluid dynamics at some point, I'll have to brush up on it and make another overview for the rest of classical physics. And maybe then do more in-depth entries. Glad you enjoyed!

Baelor Swift · 03-26-2019, 06:43 AM

Might be one of the more creative shitposts I've seen

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