The energy of an object's translational and/or rotational motion.
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Motivation for Concept
One way to think of energy is the ability to do harm. Things that are very dangerous possess considerable energy. With that definition in mind, the concept of kinetic energy can be motivated by considering the danger posed by moving objects. When a baseball is thrown by a child, it is not very frightening, though it can break a lamp. When a baseball is thrown by a major league pitcher, they can cause considerable injury. This contrast indicates that the energy of motion will depend on speed. Similarly, although a baseball thrown at 60 mph is dangerous, a car driving 60 mph is deadly. This contrast indicates that the energy of motion will depend upon mass.
Mathematical Definition
Translational Kinetic Energy
The kinetic energy of a point particle is given by:
\begin
[ K = \frac
mv^
]\end
Kinetic Energy of a System
Since energy is a scalar, the kinetic energy of a system of point particles is the sum of the kinetic energies of the constituents:
\begin
[ K^
= \sum_
^
\frac
m_
v_
^
]\end
where N is the number of system constituents.
Kinetic Energy of a Rigid Body
Consider a rigid body that can rotate and translate. We begin by treating the rigid body as a collection of point masses that are translating with the center of mass of the body and also rotating about it. We therefore write the velocity of each point as a sum of rotational and translational parts: