Kinetic Energy Formula

Of the all the forms of energy, there are two forms into which all other forms of energy can be classified; kinetic energy and potential energy of a body or a system.

Definition

One of the most elusive concepts to grasp, in physics, is 'Energy'. Energy keeps on taking various forms and everything that happens in this world is a subtle or major energy change. There is a formula for calculating the quantity of energy in every one of its forms.

Roughly put, kinetic energy is the energy an object possesses due its motion relative to a frame of reference. It is defined as the amount of work necessitated to accelerate an object from its state of rest to a particular velocity. It is that extra amount of energy it acquires due to the work done in accelerating it. Being connected to motion, it always has a velocity component in its formula. The word 'kinetic' is aptly chosen for it as it arises from the Greek word 'Kinesis' meaning motion.

There are two forms of mechanics that you will study. One is classical Newtonian mechanics and the other is relativistic mechanics. Relativistic mechanics is the accurate form of mechanics which superseded Newtonian mechanics, which is only useful when the velocities of objects are much less than the speed of light.

Formula For Point Mass Or Rigid Body

The formula for kinetic energy of a point mass or rigid body moving at non-relativistic speeds (speeds very less than speed of light) is the following:

Kinetic Energy (KE) = ½ X M V²

Here 'M' is the mass of the point mass or rigid body and 'V' is the velocity at which it is moving. The unit of energy is 'Joule'. Let me illustrate how to use this formula with an example.

Consider that an object with a mass of 80 kg is moving at a speed of 40 km/s. Then to calculate the energy value of an object using the above formula, you will have to substitute the value of velocity and mass in the above formula. If you substitute these values,

Kinetic Energy of the Object = ½ X 80 Kg X 40 Km/s X 40 Km/s = 64000 Joules

As you can see it is a simple matter of plugging in the values and calculating. The same formula can also be expressed in terms of momentum as:

Kinetic Energy = P² / 2M

where P is the momentum of a body and M is its mass.

Rotational Kinetic Energy

If, rather than linear motion, the object is rotating, then the formula for kinetic energy that I present above is not useful. The formula is as follows:

Rotational Kinetic Energy = ½ X I X ω²

Here I is the 'Moment of Inertia' of the body and ω is the angular velocity. To calculate the kinetic energy of a body you must calculate the moment of inertia of that body and its angular velocity.

Relativistic Kinetic Energy

If you are dealing with relativistic speeds, the kinetic energy formula based on Newtonian mechanics will not be useful. The relativistic formula is as follows:

KE_relativistic = m γ c² - mc²

where γ = 1/(√(1-v²/ c²), 'c' is the velocity of light, 'm' is the mass of the object, v is the velocity of object according to a reference frame and 'c' is velocity of light. To calculate KE, just substitute values in this formula.

One book that might aid your understanding is the first volume of the 'Feynman Lectures on Physics', where the master physicist unplugs and explains physics as it should be.