Gravitational Fields

Gravitational field strength:
It's the force per unit mass on a small mass placed in the field. It can be represented by the equation g=F/m (F is the gravitational force acting on a small mass m) or g=GM/r²(r² is the distance from the centre of the large mass M).

Is the earths gravitational field radial or uniform?
It's radial because the earths gravitational field strength decreases as the distance from the centre of the earth increases.
                                          
Radial Field.                                                                     Uniform Field.

Newton's Law Of Gravitation: 
Sir Isaac Newton's law of gravitation tells us that there is a gravitational force acting between all matter. This law can be represented to it's general form: F=GMm/r²     (G is the universal gravitational constant, where G=6.67384 × 10-11 m3 kg-1 s-2)



Gravitational Potential:
The gravitational potential at a point in the gravitational field is the work done per unit mass to move a small object from infinity to that point. V=W/m (V "J/kg" is the gravitational potential and W is the work done "J").

Equipotentials are lines of constant potential.

Whats behind GPS and satellite navigation?

The GPS (GLOBAL POSITIONING SYSTEM)  is the key to modern navigation. It is used for commercial, military and civil purposes. It's controlled by the US Government. For this reason Russia has it's own called GLONASS and China as well called COMPASS. Thankfully the Europeans are also developing their own navigation satellite called Galileo. The Galileo would be much more accurate then the other named satellites ( no more then 1 meter away).

What makes the satellites stay in their orbits?
The satellites are in a uniform circular motion where the the gravitational force is equal to the centripetal force acting from the satellite to the earth. This keeps the satellite above the earth at a fixed radius of the orbit.
 This is an example similar to the one stated above.                                                                                                                                                                                                                                                                                                                                                   Here is an article from BBC NEWS about the drawbacks using GPS and other navigational satellites:
http://www.bbc.co.uk/news/science-environment-29758872

SHM- Simple Harmonic Motion:

An object moves in a Simple Harmonic Motion when its acceleration is proportional to the displacement and when they are opposite to each other.

This image above gives us a simple idea of the changes between Velocity and Acceleration.

A more graphical approach would look like this:


The velocity graph is translated by 90 degrees to the right from the displacement graph.
The acceleration graph is reflected from the x-axis.

Momentum And Impulse:

So what is momentum?
Momentum is a vector quantity where it has magnitude and direction. It is represented by a letter P and the equation for working out momentum is P(Ns)=m(kg)*v(m/s). Momentum is all around us from snooker to boxing. Without momentum everything in our universe would be still like a dull rock!

From this image pictured above we can see that Ronnie is about to take a shot. So what can he possibly do to maximise and increase the momentum so that he can bring the cue ball back once potting the red ball? To do that he must hit the cue ball very fast so that the ball can have enough velocity to get the required momentum.

 Impulse is the change in momentum. The equation for impulse is: mass * change in velocity. Impulse is closely linked to Newtons second law (F=ma).
We can derive the equation of Impulse from Newtons second law like this:

Circular Motion:

The Basics:
A body travels in a circular motion when it's distance passes in equal amounts of time along a circular path. In addition to this, the speed of the body remains constant whereas the velocity changes all the time. the reason being is that velocity is a vector where it has magnitude as well as DIRECTION. When velocity changes, we know that the body would then be accelerating.


 As we can see from the image the centripetal force acts toward the centre of the circular path. The equation for centripetal acceleration is mv^2/r.
The speed of a body moving in a circle can be specified either by its speed along the tangent at any instant (linear speed) or by the angular velocity. The unit for angular velocity is rad s^-1
The angular velocity is the time for the particle to travel around once divided by the period. ω = 2 π/T


Circular motion and the Large Hadron Collider:




The Large Hadron Collider (LHC) is the most powerful particle accelerator ever built. Based at the European particle physics laboratory CERN, near Geneva in Switzerland, it is the world’s largest laboratory and is dedicated to the pursuit of fundamental science.


Key Facts:

• It has a 27 km diameter.
• Weighs more than 38,000 tonnes
• 100 metres beneath the Swiss/French border at Geneva.

So what Accelerates the particles and changes it's direction?
The LHC has a strong electric field making it the world’s most powerful particle accelerator and it creates collision energies 7x greater than previous machines. Then there are various types of superconducting magnets (9,300 in total) used to steer and focus the beams of particles as they race around the 27km loop of the LHC collider. There is a resultant force acting on the particles and that is the centripetal force whicg acts towards the centre of the collider (4.3km pictured below).