# Kinetic Energy

## The kinetic energy of a rigid 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

- 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* - *Nm* 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 m v^{2 }(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 ω^{2 }(2)

where

E_{m}= kinetic rotation energy (Joule, ft lb)

I = moment of inertia, an object's resistance to changes in rotation direction (kg m^{2}, slug ft^{2})

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 km/h) (1000 m/km) / (3600 s/h))^{2}

= 189043 (Joule)

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

E_{t}= 1/2 (1000 kg) ((90 km/h) (1000 m/km) / (3600 s/h))^{2}

= 312500 (Joule)

**Note!** When the speed is increased with *28%* (from* 70* to *90 km/h*) - the kinetic energy is increased with *65% *(from *189043* to *312500 J*). Be aware that this huge rise in kinetic energy must be absorbed by the safety construction of the car to provide the same protection in a crash - which is very hard to achieve. In a modern car it is possible to survive a crash at 70 km/h. A crash at 90 km/h is more likely death.

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