Enter the mass (kg), the linear velocity (m/s), angular velocity (rad/s), and the moment of inertia (kg-m^2) into the calculator to determine the Total Kinetic Energy. 

Total Kinetic Energy Formula

The following equation is used to calculate the Total Kinetic Energy.

TE = 1/2*m*V^2+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-m^2) 
  • w is the angular velocity (rad/s)

To calculate the total kinetic energy, sum the linear kinetic energy and the rotational kinetic energy together.

How to Calculate Total Kinetic Energy?

The following example problems outline the steps and information needed to calculate the Total Kinetic Energy.

Example Problem #1

  1. First, determine the mass (kg). In this example, the mass (kg) is determined to be 5 .
  2. Next, determine the linear velocity (m/s). For this problem, the linear velocity (m/s) is measured to be 4 .
  3. Next, determine the moment of inertia (kg-m^2). In this case, the moment of inertia (kg-m^2) is found to be 5.
  4. Next, determine the angular velocity. In this case, the angular velocity is 7 rad/s.
  5. Finally, calculate the Total Kinetic Energy using the formula above: 

TE = 1/2*m*V^2+1/2*I*w^2

Inserting the values from above and solving the equation yields: 

TE = 1/2*5*4^2+1/2*5*7^2 = 162.5 (Joules)

FAQ

What is the difference between translational and rotational kinetic energy?

Translational kinetic energy is the energy possessed by an object in motion due to its linear velocity, calculated as 1/2*m*V^2, where m is the mass and V is the linear velocity. Rotational kinetic energy, on the other hand, is the energy an object has due to its rotation, calculated as 1/2*I*w^2, where I is the moment of inertia and w is the angular velocity. Total kinetic energy combines both these forms.

How do you determine the moment of inertia for an object?

The moment of inertia is a measure of an object’s resistance to changes to its rotation. It is determined by the object’s mass distribution relative to the axis of rotation. The calculation can vary significantly depending on the object’s shape and the axis about which it rotates, often requiring integration over the object’s volume or area.

Can the total kinetic energy of a system change over time?

Yes, the total kinetic energy of a system can change over time if there is net work done on or by the system. This can occur through forces applied to the system causing acceleration (changing translational kinetic energy) or through torques applied to the system causing angular acceleration (changing rotational kinetic energy). Conservation of energy principles apply, so any change in kinetic energy would be balanced by changes in other forms of energy within the system.