In this tutorial we begin to explore ideas of velocity and acceleration. We do exciting things like throw things off cliffs (far safer on paper than in real life) and see how high a ball will fly in the air.

You understand velocity and acceleration well in one-dimension. Now we can explore scenarios that are even more fun. With a little bit of trigonometry (you might want to review your basic trig, especially what sin and cos are), we can think about whether a baseball can clear the “green monster” at Fenway Park.

This is the meat of much of classical physics. We think about what a force is and how Newton changed the world’s (and possibly your) view of how reality works.

“Energy” is a word that’s used a lot. Here, you’ll learn about how it’s one of the most useful concepts in physics. Along the way, we’ll talk about work, kinetic energy, potential energy, conservation of energy, and mechanical advantage.

Momentum ties velocity and mass into one quantity. It might not be obvious why this is useful, but momentum has this cool property where the total amount of it never changes. This is called the conservation of momentum, and we can use it to analyze collisions and other interactions. Bam!

Everything you’ve learned about motion, forces, energy, and momentum can be reused to analyze rotating objects. There are some differences, though. Here, you’ll learn about rotational motion, moments, torque, and angular momentum.

Gravity is the force of attraction between masses. It’s the thing that pulls you down to earth. Here, you’ll learn precise meanings of the words mass and weight, and you’ll also learn how gravity affects falling near earth and orbits in space.

Pendulums. Slinkies. You when you have to use the bathroom but it is occupied. These all go back and forth over and over and over again. This tutorial explores this type of motion.

Atmospheric pressure is like an invisible friend who is always squeezing you with a big hug. Learn more about pressure, buoyant force, and flowing fluid so you can appreciate the sometimes invisible, but crucial, effect they have on us and the world around us.

Heat can be useful, but it can also be annoying. Understanding heat and the flow of heat allows us to build heat sinks that prevent our computers from overheating, build better engines, and prevent freeway overpasses from cracking.

Electric forces hold together the atoms and molecules in your eyes which allow you to read this sentence. Take a moment and learn about the force that holds our bodies together.

Circuits make computers, digital cameras, and video games possible. Circuits are driving an unprecedented rate of change in how we live. In this topic you’ll learn about the physics behind the electronic devices we use.

The magnetic field of the Earth shields us from harmful radiation from the Sun. Magnetic fields also allow us to diagnose medical problems using an MRI. In this topic you’ll learn about the force and field that makes this possible.

Faraday’s law is how we get electrical power from most power plants and hydroelectric dams. Learn how magnetic flux allows us to turn the mechanical energy of falling water through a dam into electrical energy.

Waves are responsible for basically every form of communication we use. Whether you’re talking out loud, texting on your phone, or waving to someone in a crowd there’s going to be a wave transmitting information. Learn about the basics of waves in this topic, then learn more about light waves in the topics below.

Light can seem mysterious. What is light made out of? What causes color? How do 3D movies work? Learn about some of the mysterious properties of light in these tutorials.

Geometric optics

Light waves can be bent and reflected to form new and sometimes altered images. Understanding how light rays can be manipulated allows us to create better contact lenses, fiber optic cables, and high powered telescopes.

Think you know about time and space? Think again. Einstein basically did a pile driver on all our brains when he came up with his theory of special relativity. Note: This topic is under construction. More videos and materials will be added soon.

How can you prove that dS in φ =E.dS is dS Cos θ if the area is tilted at an angle ? I need the mathematical Steps.

Ans;

Dear Zeenath, Electric Flux is defined as the total no of field lines passing normal to the surface. So while calculating, we need to consider the area of the surface normal to the field lines only. That is why we take the dot product of E and ds, where ds is the area vector (not just the area: Area vector is a vector whose magnitude is equal to the area and dirtected normal to the surface.) Then by definition of dot product, dφ =E.dS = EdS cos θ which gives the component of E and the component of area vector in the direction of E (When area vector is in the direction of E, the actual component of area is perpendicular to E) Hope the matter is clear. Mathew Abraham

Understanding the unnaturally small size of the cosmological constant poses one of severest challenges for a theory of gravity. At late times and for large distances, the apparent size of the cosmological constant is constrained to be extremely small in terms of the natural scale for gravity, the Planck mass. In contrast, no observations bound the value of the cosmological constant during the earliest stages of the universe, when corrections to the Einstein-Hilbert action were non-negligible, and its presence can lead to a richer family of metrics. Among the solutions for a more general gravitational action, the presence of a positive cosmological constant does not inevitably lead to a de Sitter expansion. Such solutions must still yield or evolve into a low energy theory in which the effective cosmological constant is small to be phenomenologically acceptable. If the characteristic scales on which these metrics vary are of extremely high energy or short distance, then it may be possible to integrate out such features to arrive at a slowly varying e®ective theory. To determine whether an action for gravity, generalized beyond an Einstein-Hilbert term, admits these features | natural coefficients for the terms in the action and a rapid variation | we must ¯rst solve the highly non-linear field equations. This task is difficult even when only the next curvature corrections are added. In 3 + 1 dimensions, Horowitzand Wald and later Starobinsky [3] discovered oscillating solutions for actions that included quadratic curvature terms but no cosmological constant. Numerical solutions were found in 4 + 1 dimensions in the presence of a cosmological constant and a scalar field, along with the quadratic curvature terms. In this latter scenario, metrics exist that depend periodically on the extra spatial coordinate so that choosing the size of the extra dimension to be the period produces a compact extra dimension without any fine-tunings or singularities. The parameters in the action ¯x the size of the extra dimension uniquely. However, without an analytical approach it becomes di±cult to generalize these solutions to include an evolution in time. Without this freedom, it is di±cult to understand how a universe starting from a more general state can find itself in one of these configurations.