Kinetic Energy of a Rigid Body

The kinetic energy of a body is the energy possessed by the body motion

Kinetic energy is the energy of motion. There are several forms of kinetic energy

• vibration - the energy due to vibration motion
• rotational - the energy due to rotational motion
• translational - the energy due to motion from one location to another

Energy has the same units as work and work is force times distance. One joule is one Newton of force acting through one meter - N m or Joule in SI-units. The Imperial units are foot-pound.

• 1 ft lb = 1.356 N m (Joule)

Translational Kinetic Energy

Translational kinetic energy can be expressed as

E_t = 1/2 mv² (1)

where

E_t = kinetic translation energy (Joule, ft lb)

m = mass (kg, slugs)

v = velocity (m/s, ft/s)

• one slug = 32.1740 pounds (as mass) - lb_m

Rotational Kinetic Energy

Rotational kinetic energy can be expressed as

E_r = 1/2 I_oω² (2)

where

E_m = kinetic rotation energy (Joule, ft lb)

I_o = moment of inertia (kg m², slug ft²)

ω = angular velocity (rad/s)

Example - Car and Kinetic Energy

The kinetic energy of a car with mass of 1000 kg at speed 70 km/h can be expressed as

E_t = 1/2 1000 (kg) (70 1000/3600 (m/s))²

= 189,043 Joule

The kinetic energy of the same car at speed 90 km/h can be expressed as

E_t = 1/2 1000 (kg) (90 1000/3600 (m/s))²

= 312,500 Joule

Note! When the speed is increased with 28% the kinetic energy increases with 65%. This huge rise in kinetic energy must be absorbed by the safety construction of the car to provide the same protection in a crash. This is hard to achieve. In general it is today possible to survive a car crash in a modern car at 70 km/h. A car crash at 90 km/h is death.

Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Web The Engineering ToolBox