Kinetic Energy

Work must be done to set any object in motion, and any moving object can do work. Energy is the ability to do work and 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 - Kinetic Energy in a Car

The kinetic energy of a car with mass of 1000 kg at speed 70 km/h can be calculated 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 of a car is increased with 28% (from 70 to 90 km/h ) - the kinetic energy of the car is increased with 65% (from 189043 to 312500 J ). 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 fatal.

Download and print Kinetic Energy in a Moving Car chart

Example - Kinetic Energy in a Steel Cube moving on a Conveyor Belt

A steel cube with weight 500 lb is moved on a conveyor belt with a speed of 9 ft/s .  The steel cube mass can be calculated as

m = (500 lb ) / (32.1740 ft/s ² )

= 15.54 slugs

• mass and weight

The kinetic energy of the steel cube can be calculated as

E _t = 1/2 (15.54 slugs) (9 ft/s) ²

= 629 ft lbs

Example - Kinetic Energy in a Flywheel

A flywheel with Moment of Inertia I = 0.15 kg m ² is rotating with 1000 rpm (revolutions/min) . The angular velocity can be calculated as

ω = (1000 revolutions /min) (0.01667 min/s) (2 π rad/ revolution )

= 104 rad/s

The flywheel kinetic energy can be calculated

E _r = 1/2 (0.15 kg m ² ) (104 rad/s) ²

= 821 J

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm