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Total Kinetic Energy Calculator

Formula

The formula to calculate the Total Kinetic Energy (TE) is:

$TE = \frac{1}{2} m V^2 + \frac{1}{2} I w^2$

Where:

$TE$ is the total kinetic energy (Joules).
$m$ is the mass (kg).
$V$ is the linear velocity (m/s).
$I$ is the moment of inertia (kg-m²).
$w$ is the angular velocity (rad/s).

What is Total Kinetic Energy?

Total kinetic energy is the sum of the linear kinetic energy and the rotational kinetic energy of an object. It accounts for both the motion of the object as a whole and the rotation of the object around its center of mass.

Example Calculation

Consider an example where:

Mass (m): 10 kg
Linear Velocity (V): 5 m/s
Moment of Inertia (I): 2 kg-m²
Angular Velocity (w): 3 rad/s

Using the formula to calculate the Total Kinetic Energy:

$TE = \frac{1}{2} \cdot 10 \cdot 5^2 + \frac{1}{2} \cdot 2 \cdot 3^2 = 125 + 9 = 134 \text{ Joules}$

This means that the total kinetic energy for this example is 134 Joules.