Kinetic energy
Kinetic energy is the energy that an object has because of its motion. This energy can be converted into other kinds, such as gravitational or electric potential energy. which is the energy that an object has because of its position in a gravitational or electric field.
The SI unit of energy is the joule, while the English unit of energy is the foot-pound.
Kinetic & Potential Energy
Kinetic Energy is the maximum amount of work a moving body can do due to its motion, whereas Potential energy is the maximum amount of work a body can do due to its configuration or position in a field force. Kinetic Energy is valid for all sorts of forces as seen from this derivation.
- [math]\displaystyle{ \mathbf{F} \cdot d \mathbf{x} = \frac{d \mathbf{p}}{dt} \cdot d \mathbf{x} = \frac{d \mathbf{p}}{dt} \cdot \mathbf{v}dt = \mathbf{v} \cdot \frac{d \mathbf{p}}{dt} dt = \mathbf{v} \cdot d \mathbf{p} }[/math]
but Potential Energy is not as can be seen here
[math]\displaystyle{ \mathbf{F} \cdot d \mathbf{x} = - \nabla V \cdot d \mathbf{x} = -\frac{\partial V}{\partial x_i} \cdot dx_i = - dV }[/math]
which clearly suggests that only conservative forces can have potential energy associated with them; see conservation of energy.
Translational kinetic energy
The translational kinetic energy of an object is:
- [math]\displaystyle{ E_\text{translational} = \frac{1}{2} mv^2 }[/math]
where
- [math]\displaystyle{ m }[/math] is the mass (resistance to linear acceleration or deceleration);
- [math]\displaystyle{ v }[/math] is the linear velocity.
Rotational kinetic energy
The rotational kinetic energy of an object is:
- [math]\displaystyle{ E_\text{rotational} = \frac{1}{2} I \omega^2 }[/math]
where
- [math]\displaystyle{ I }[/math] is the moment of inertia (resistance to angular acceleration or deceleration, equal to the product of the mass and the square of its perpendicular distance from the axis of rotation);
- [math]\displaystyle{ \omega \ }[/math] is the angular velocity.
Kinetic Energy Media
Wooden roller coaster txgi
Émilie du Châtelet (1706–1749) was the first to publish the relation for kinetic energy E_\text{kin} \propto m v^2, derived from the experimental observation of objects dropped into clay. (Portrait by Maurice Quentin de La Tour.)
Log of relativistic kinetic energy versus log relativistic momentum, for many objects of vastly different scales. The intersections of the object lines with the bottom axis approaches the rest energy. At low kinetic energy the slope of the object lines reflect Newtonian mechanics. As the lines approach c the slope bends at the lightspeed barrier.
