Translational Kinetic Energy (College Board AP® Physics 1: Algebra-Based)

Translational kinetic energy

What is translational kinetic energy?

• Translational motion is motion in a straight line without rotation

  • Every point on the object moves with the same velocity

• Translational kinetic energy is the energy that an object has due to its translational motion

Calculating translational kinetic energy

• The translational kinetic energy of an object can be calculated using the equation:

• Where:

  • = translational kinetic energy, measured in

  • = mass, measured in

  • = velocity, measured in

• Translational kinetic energy is a scalar quantity with magnitude only

• Therefore, only the magnitude of the velocity needs to be considered

• Translational kinetic energy is:

  • directly proportional to the mass of the moving object

  • directly proportional to the square of the object's velocity

Translational kinetic energy in reference frames

• Observers in different frames of reference can measure values of position and velocity very differently

  • This is covered in more detail in the study guide on Reference frames and relative motion

• Since velocity is relative and translational kinetic energy is dependent upon an object's velocity, the translational kinetic energy of an object is also relative

• For example, Person A is a stationary observer standing on the side of a road who sees a car of mass travelling with a constant velocity of and a truck of mass travelling in the same direction at a constant velocity of

• Person A measures:

  • themselves to be stationary

  • the velocity of the car to be

  • the velocity of the truck to be

• Therefore, Person A measures the translational kinetic energy of the car to be:

• And Person A measures the translational kinetic energy of the truck to be:

• From the reference frame of the car, the driver measures:

  • themselves to be stationary

  • the velocity of the truck to be

• Therefore, the car measures the translational kinetic energy of the truck to be:

• From the reference frame of the truck, the driver measures:

  • themselves to be stationary

  • the velocity of the car to be

• Therefore, the car measures the translational kinetic energy of the truck to be:

• The relative velocities are calculated in the study guide Reference frames and relative motion