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AP Physics 2: Exam Prep26 chapters | 139 lessons

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Instructor:
*Sadije Redzovic*

Sadije has taught high school physics and physical science. She has a bachelorâ€™s in physics and a masterâ€™s in biomedical engineering.

In this lesson, you will learn the importance that the speed of light plays in modern science. This includes the topics of special relativity and mass-energy equivalence

Have you ever considered that space and time are not as you perceive? That a clock can read different times based on its movement relative to you or even be a different size based on its movement relative to you? Intuition may have you think that such contemplations are in the realm of science fiction, but such considerations have actually been proven by experiment and are the basis of many modern technologies.

Let's explore the scientific concept, special relativity, that underpins these counter-intuitive notions together. After exploring special relativity we will also run across, arguably, the most famous science equation ever discovered: E=mc2. This equation is the basis of mass-energy equivalence, which is an additional concept that we will explore. Mass-energy equivalence and special relativity are connected in many ways. This includes the scientist that discovered them and their common dependence on the speed of light.

Before we delve into the concepts of special relativity and mass-energy equivalence, let's take a moment to recognize the importance of these concepts and give recognition to the scientist that discovered them. The concept of mass-energy equivalence transformed humanities understanding of nuclear physics and special relativity caused scientists to rethink the nature of time and space. Many modern discoveries and technological innovations are based on one, or both, of these concepts. Mass-energy equivalence is the basis of nuclear energy and without special relativity the Global Positioning System would not function. Also, particle accelerators, which are used in many fields, rely on both of these concepts. These ideas, and many others, are the work of one of the most famous scientists to have lived. That is, Albert Einstein.

The first topic that we will explore is the speed of light. The speed of light is important because nothing can travel through space faster than the speed of light in a vacuum. This has many implications in science, which makes the speed of light in a vacuum important enough to have its own mathematical symbol, c. The value of this scientific constant is 186,000 miles/sec, or 3 x 108 m/s.

The mathematics of special relativity are somewhat complex, but for now it is important to know that the speed of light plays an integral role in such calculations. It is also important to know that special relativity shows that the equations of classical mechanics fail to work when exploring objects that are moving at speeds nearing c.

One of the main implications of special relativity is that objects moving closer to the speed of light experience time more slowly than objects moving at slower speeds. This is called time dilation. The classical illustration of this is the twins paradox. In this story, one twin stays on Earth while the other twin rides on a rocketship that is travelling near the speed of light. When the twin from the rocketship returns to Earth he or she has aged significantly less than the twin that remained on Earth.

The other main implication of special relativity is that objects moving closer to the speed of light are observed to be shorter than objects moving at slower speeds. This concept is called length contraction. Therefore, if you were measuring the rocketship referred to in the twins paradox, you would measure a larger length when the rocketship is with you on Earth compared to measuring the object while it is travelling at a speed close to c.

Mass-Energy equivalence is also dependent on c and can be summarized in a single equation: E=mc2. In this equation E is energy and m is mass. The concept and mathematics of mass-energy equivalence illustrate, that contrary to the development of mass and energy as separate concepts in classical mechanics, they are actually one and the same.

In everyday life, it seems like everyone and everything experience space and time the same. In actuality experiences of space and time depend on how fast an object is moving. When objects are moving at speeds close to c, the equations of Newtonian physics are invalid and special relativity must be taken into consideration. The two main concepts that can be derived from special relativity are time dilation and length contraction.

Another concept that depends on the constant c is mass-energy equivalence. In mass-energy equivalence, mass and energy are viewed as one and the same, not two separate concepts as they are laid out in classical mechanics. The mass-energy equivalence equation determines how much energy is in a given amount of mass and these values are related by c2.

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AP Physics 2: Exam Prep26 chapters | 139 lessons

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