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# 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.

### 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

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 )

The flywheel kinetic energy can be calculated

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

= 821 J

## Related Topics

### • Dynamics

Motion - velocity and acceleration, forces and torque.

### • Mechanics

Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

## Related Documents

### Angular Motion - Power and Torque

Angular velocity and acceleration vs. power and torque.

### Car Acceleration

Car acceleration calculator.

### Car Fuel Consumption - liter/100 km

Calculate fuel consumption in liter per km - consumption chart and calculator.

### Conservation of Momentum

The momentum of a body is the product of its mass and velocity - recoil calculator.

### Conveyors - Belt Speed

Maximum conveyor belt speed.

### Distance Traveled vs. Speed and Time - Calculator and Chart

Velocity plotted in time used diagram.

### Dynamic Pressure

Dynamic pressure is the kinetic energy per unit volume of a fluid in movement.

### Energy Storage Density

Energy density - by weight and volume - for some ways to store energy

### Flywheels - Kinetic Energy

The kinetic energy stored in flywheels - the moment of inertia.

### Formulas of Motion - Linear and Circular

Linear and angular (rotation) acceleration, velocity, speed and distance.

### Fuel Consumption - mpg

Calculate fuel consumption in miles per gallon - mpg - calculator and consumption charts.

### Heat, Work and Energy

Heat vs. work vs. energy.

### Impact Force

Impact forces acting on falling objects hitting the ground, cars crashing and similar cases.

### Impulse and Impulse Force

Forces acting a very short time are called impulse forces.

### Pitot Tubes

Pitot tubes can be used to measure fluid flow velocities by measuring the difference between static and dynamic pressure in the flow.

### Potential Energy - Hydropower

Elevation and potential energy in hydropower.

### Projectile Range

Calculate the range of a projectile - a motion in two dimensions.

### Rolling Resistance

Rolling friction and rolling resistance.

### Salt Hydrates - Melting points and Latent Melting Energy

Melting points and latent energy of salt hydrates.

### Vehicle - Distance Traveled vs. Velcocity and Time Used (mph)

Speed (mph) and time (hours) and distance traveled (miles) chart.

### Vehicle - Distance Traveled vs. Velocity and Time (km/h)

Speed (km/h) vs. time (hours) and distance traveled (km).

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