Kinetic Energy of a Rigid Body

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

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

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.

Translational Kinetic Energy

Translational kinetic energy can be expressed as

Et = 1/2 mv2 (1)

where

Et = kinetic translation energy (Joule, ft lb)

m = mass (kg, slugs)

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

Rotational Kinetic Energy

Rotational kinetic energy can be expressed as

Er = 1/2 Ioω2 (2)

where

Em = kinetic rotation energy (Joule, ft lb)

Io = 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

Et = 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

Et = 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.

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Related Topics

  • Mechanics Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects

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