7.6:
Kinetic Energy – I
The energy that an object possesses by virtue of its motion is known as kinetic energy. If an object is moving with a velocity v, its kinetic energy is defined as one-half of the product of mass and velocity squared.
The velocity squared here is the dot product of the velocity vector with itself. Therefore, kinetic energy is a scalar quantity as it is independent of the direction of motion and depends only on the speed of the object.
The mass and velocity squared can never be negative. Hence, the kinetic energy possessed by an object is always positive and increases rapidly with increasing velocity.
For instance, if two bowling balls with different masses are moving with the same velocity, the second bowling ball, due to its double mass, has twice the kinetic energy.
If the velocity of the lighter ball is doubled, its kinetic energy is increased four times. If either mass or velocity of an object is negligible, its kinetic energy will be zero.
7.6:
Kinetic Energy – I
It’s plausible to suppose that the greater the velocity of a body, the greater effect it could have on other bodies. This does not depend on the direction of the velocity, only its magnitude. At the end of the seventeenth century, a quantity was introduced into mechanics to explain collisions between two perfectly elastic bodies, in which one body makes a head-on collision with an identical body at rest. When they collide, the first body stops, and the second body moves off with the initial velocity of the first body. If you have ever played billiards or croquet, or seen a Newton’s cradle, you will have observed this type of collision. The idea behind this quantity was related to the forces acting on a body and referred to as “the energy of motion.” Later on, during the eighteenth century, the name kinetic energy was given to energy of motion.
With this in mind, we have the classical definition of kinetic energy. Note that when we say “classical”, we mean non-relativistic; that is, at speeds much slower than the speed of light. At speeds comparable to the speed of light, the special theory of relativity requires a different expression for the kinetic energy of a particle.
The units of kinetic energy are mass multiplied by the square of the speed (kg·m²/s²). The units of force are mass multiplied by the acceleration (kg·m/s²) so the units of kinetic energy are also the units of force multiplied by the distance. These are the units of work, or joules.
The kinetic energy of a particle is a single quantity, but the kinetic energy of a system of particles can sometimes be divided into various types, depending on the system and its motion. For example, if all the particles in a system have the same velocity, the system is undergoing translational motion and has translational kinetic energy. If an object is rotating, it could have rotational kinetic energy. If an object is vibrating, it could have vibrational kinetic energy. The kinetic energy of a system, relative to an internal frame of reference, is called internal kinetic energy. The kinetic energy associated with random molecular motion is called thermal energy. These names will be used in later chapters, when appropriate. Regardless of the name, every kind of kinetic energy is the same physical quantity, representing energy associated with motion.
This text is adapted from Openstax, University Physics Volume 1, Section 7.2: Kinetic Energy.