Newtonian kinetic energy

Newtonian kinetic energy

Kinetic energy of rigid bodies

In classical mechanics, the kinetic energy of a point object (an object so small that its mass can be assumed to exist at one point), or a non-rotating rigid body, is given by the equation

where m is the mass and v is the speed (or the velocity) of the body. In SI units (used for most modern scientific work), mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules.
For example, one would calculate the kinetic energy of an 80 kg mass (about 180 lbs) traveling at 18 metres per second (about 40 mph, or 65 km/h) as

E_k = (1/2) · 80 · 18² J = 12.96 kJ

Since the kinetic energy increases with the square of the speed, an object doubling its speed has four times as much kinetic energy. For example, a car traveling twice as fast as another requires four times as much distance to stop, assuming a constant braking force.
The kinetic energy of an object is related to its momentum by the equation:

where:

is momentum

is mass of the body

For the translational kinetic energy, that is the kinetic energy associated with rectilinear motion, of a body with constant mass , whose center of mass is moving in a straight line with speed , as seen above is equal to

where:

is the mass of the body

is the speed of the center of mass of the body.

The kinetic energy of any entity depends on the reference frame in which it is measured. However the total energy of an isolated system, i.e. one which energy can neither enter nor leave, does not change in whatever reference frame it is measured. Thus, the chemical energy converted to kinetic energy by a rocket engine is divided differently between the rocket ship and its exhaust stream depending upon the chosen reference frame. This is called the Oberth effect. But the total energy of the system, including kinetic energy, fuel chemical energy, heat, etc., is conserved over time, regardless of the choice of reference frame. Different observers moving with different reference frames disagree on the value of this conserved energy.