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

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:

$K=\frac{1}{2}m{v}^2$

• Where:

  • $K$ = translational kinetic energy, measured in $\mathrm{J}$

  • $m$ = mass, measured in $\mathrm{kg}$

  • $v$ = velocity, measured in $\mathrm{m}/\mathrm{s}$

• 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 $1500\mathrm{kg}$ travelling with a constant velocity of $5\mathrm{m}/\mathrm{s}$ and a truck of mass $4500\mathrm{kg}$ travelling in the same direction at a constant velocity of $10\mathrm{m}/\mathrm{s}$

• Person A measures:

  • themselves to be stationary

  • the velocity of the car to be $5\mathrm{m}/\mathrm{s}$

  • the velocity of the truck to be $10\mathrm{m}/\mathrm{s}$

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

$K_{car}=\frac{1}{2}\left(1500\right){\left(5\right)}^2=18750\mathrm{J}$

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

$K_{truck}=\frac{1}{2}\left(4500\right){\left(10\right)}^2=225000\mathrm{J}$

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

  • themselves to be stationary

  • the velocity of the truck to be $5\mathrm{m}/\mathrm{s}$

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

$K_{truck}=\frac{1}{2}\left(4500\right){\left(5\right)}^2=56250\mathrm{J}$

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

  • themselves to be stationary

  • the velocity of the car to be $-5\mathrm{m}/\mathrm{s}$

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

$K_{truck}=\frac{1}{2}\left(1500\right){\left(-5\right)}^2=18750\mathrm{J}$

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