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)

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)


Example Problem #2

Using the same method as above, first, we need to measure or determine the variables required by the equation. For this example problem, these are provided as follows: 

mass (kg) = 9

linear velocity (m/s) = 8

moment of inertia (kg-m^2) = 7

angular velocity (rad/s) = 9

Enter these given values into the calculator or above yields: TE = 1/2*9*8^2+1/2*7*9^2 = 571.5 (Joules)