Tag: Classical mechanics

Why the Earth Does Not Technically Revolve Around the Sun

Why the Earth Does Not Technically Revolve Around the Sun

03/31/18

“Does the Earth really revolve around the sun?”

For the past few centuries it was thought to have been common knowledge that the Earth has revolved around the sun. However, when one looks at the physics closely, it turns out that the Earth does not revolve around the sun, but that it instead revolves around a common center of mass. Not only does the Earth revolve around this common center of mass, but also all of the other planets and even the sun! It just goes to show how a little knowledge of physics can upend one’s worldview.

Radius of gyration

Radius of gyration

02/13/17

“What would happen if we were to take the entirety of the object’s mass and concentrate it at a point?”
During one’s study of statics, one will have to work with the mass and moment of inertia for objects. However, could there be any ways in which we could simplify our calculations just a tad bit? Well, let’s think about it. Everything could be much simpler if we were to take the mass of the object and concentrate it at a single point away from the axis so that the resultant moment of inertia would be equivalent to original moment of inertia? This is the fundamental idea behind a concept known as the radius of gyration, and can be found with the equation k=Im, with k being the radius, I being the moment of inertia, and m being the mass.

The physics of a football tackle

The physics of a football tackle

02/05/17

“How do the laws of physics affect football tackles?”

Because of the excitement for the super bowl stateside, a fan recently asked for an article about the science of football.

If you are from the United States, then you have probably seen or heard about a game called “football” where people divided onto two teams will fight each other for control of a prolate spheroid shaped ball using tackles. However, have you ever wondered about how one can make an optimal tackle? Well, it turns out that all you need is a rudimentary knowledge of physics to find out.

Every object in the universe has a property called a center of mass, or the location of the mean position of matter in a body. When a force is applied on an object which does not go through the center of mass, a torque will be induced, causing a rotation on said body. So now let’s put this theoretical framework into practice. The average human male has their center of mass located slightly above the navel. When one football player tackles another in this area, the player will simply be moved in the direction of the tackle. But if the player were to give a tackle below this zone, a torque would be induced that would completely throw off the player! Luckily, professional coaches have taken note of this, and use this scientific knowledge to advise linemen to stay close to ground while running, making it far more prohibitive for a disabling torque to be thrust upon them!

Science always shows up in the most marvelous ways in our everyday life, and it goes to show that a small bit of knowledge of it can go a long way.

Normal stress

Normal stress

10/08/16

“What happens when stress acts upon an area parallel to the axis of an object?”
The concept of stress is one of the premier foundations of all of engineering science. So, what happens when a stress is applied to an area that is parallel to the axis of the object? Well, this type of action is very simple. Since all of the stress acts through the axis of an object, the only deformations will be parallel to the axis as well. This type of stress would cause tensile or compressive deformations (depending on the direction and strength of materials). Scientists and Engineers have termed this phenomena normal stress. You can find the magnitude of normal stress very simply, as the stress is just the force distributed over the area that it is acting upon (we can represent this symbolically with the equation (sigma)=F/A, with being (sigma) the stress, F being the force, and A being the geometric area)

Hooke’s law

Hooke’s law 02/25/16

Have you ever wondered why the force of a spring appears to grow stronger as you pull it out? This physical phenomena can be explained with the simple use of Hooke’s law. Hooke’s law states that the force of a string can be measured with the equation Fspring=k*x, with k being the spring constant and xbeing the change in distance from the resting point. The Spring constant can be found empirically by measuring the force’s change over a distance and finding the slope. we can integrate this equation in respect to x to find the potential energy of the object to obtain Uspring=12*k*x2. As one can infer, the more we stretch it out, the more potential energy is in the system, and consequently the more kinetic energy it will have when it reaches the starting point, allowing it to reach a further displacement once again.

Young’s modulus

Young’s modulus 02/24/16
Have you ever wondered why a solid body deforms when stress is applied to it? This is a consequence of Young’s modulus. To get the big picture, Young’s modulus is a property of mechanical bodies that defines how much the body deforms under stress. Before we begin, we must define the terms stress and strain. Stress is the internal forces that neighboring molecules of an continuous material apply to each other (equation is ()=FA0, Force over original area), while strain is the measure of deformation of a material (=LL0, change in length over original length). Young’s modulus is the measure of the proportion of these factors E=()which results in F*L0A0*L. The higher a bodie’s young modulus is the more resistant it is.

Angular momentum

Angular momentum 02/21/16
During one’s course of study of physics, one may encounter a concept known as angular momentum. Since momentum is defined as the product of the mass and movement of an object, wouldn’t it follow that there would be a special type of momentum for rotational systems, even if there was no translational movement? This quantity is known as Angular momentum. The mathematical formulation for angular momentum is given as L=I, where Iis the moment of inertia of the system and is the rotational velocity. Angular momentum can also be reformulated as L=r x p, where r is the radius, pis the linear momentum and the angular momentum is the cross product between them. Like linear momentum, Angular momentum is always conserved.

The conservation of energy

The conservation of energy 01/29/16
One of the most fundamental laws of physics is the conservation of energy. To put it simply, energy is the capacity of an object to do work. All of the energy in the universe can neither be created nor destroyed. Energy may be transferred from one object to another, and due to the second law of thermodynamics energy becomes more useless as time goes on, but it is never completely destroyed. This means that all of the energy that human civilization is using currently, weather it be electricity or or simple machines, has existed since the primordial ages of the universe.

Newton’s laws

Newton’s laws 01/28/16

For any student of Physics, Newton’s three laws are some of the most paramount and sumptuous facets of the course of study. These laws are the axioms on which the framework of Newtonian mechanics are contingent upon.

We shall embark our journey with the explanation of Newton’s first law, the law of inertia. Newton’s first law dictates that an object at rest stays at rest and an object in motion stays in motion unless there is a net external force. To illustrate, if one were to throw an object suffused in the vacuum of space, then the object will continue in its trajectory unless it is impinged by an external force, such as gravity or if it encounters air resistance. Likewise, an object at rest will remain at rest unless a force is acted upon it.

Newton’s second law states is the law of forces, which states that a force is equal to an object’s change in momentum, pretty much Force is the derivative of momentum, or F=ma (Force is equal to mass * acceleration). This gives us a mathematical description of force, which allows us to further develop any concepts.
Newton’s third and final law states that For every force, there is an equal and opposite force acting upon contact. To give a concrete example, remember anytime you struck your pillow, you felt a force knock back at you? That was Newton’s third law in action, you exerted a force on the pillow and the pillow exerted a force on you.