# Kinetic Energy Formula

Knowing the kinetic energy formulas, you can compute the energy of a system in motion. In here, we provide and explain the rotational and relativistic formulas as well.

Omkar Phatak

Last Updated: Dec 18, 2017

*Potential Energy*

*,*while the energy it possesses when in motion, is termed as

*Kinetic Energy.*

Definition

One of the most elusive concepts to grasp in physics is

*Energy*. It takes various forms and everything that happens in this world is a subtle or major energy change. There is a formula for calculating it in every one of its forms.**Roughly put, kinetic energy is possessed by an object due its motion, relative to a frame of reference. It is the amount of work necessitated, to accelerate an object from its state of rest to a particular velocity.**It is the 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, as it arises from the Greek word

*Kinesis*, meaning motion.

Formula For Point Mass Or a Rigid Body

*speeds very less than speed of light*) is the following:

Kinetic Energy (KE) = ½ M V2

Here, 'M' is the mass of the point mass (

Since linear velocity of the object is

*in Kg*) or rigid body and 'V' is the velocity (*m/sec*) at which it is moving. The unit of energy is 'Joule'.Since linear velocity of the object is

*squared*in the formula and mass appears as a linear term, its kinetic energy increases rapidly with rising velocity and increase in mass. More massive and speedier an object, more is the energy packed in.Consider that an object with a mass of 80 kg is moving at a speed of 40 km/s. 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 m/s x 40 m/s = 64000 Joules

Kinetic Energy = P2/2M

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

Rotational Kinetic Energy

Rotational Kinetic Energy = ½ I ω2

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

Relativistic Kinetic Energy

KErelativistic = mc2(γ - 1)

Where γ = 1/(√(1-v

^{2}/ c^{2}), '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.*Feynman Lectures on Physics*, where the master physicist unplugs the subject and reveals its beauty.