# What Moves In Kinetic Energy?

## Definition of Kinetic Energy

Kinetic energy is the energy of motion. An object that has motion – whether it is vertical or horizontal motion – has kinetic energy. The amount of kinetic energy depends on the object’s mass and velocity. The greater the mass and the greater the velocity of the object, the more kinetic energy it possesses.

For example, a Mack truck moving at 65 mph has a much greater amount of kinetic energy than a Hot Wheels car moving at the same speed. This is because the Mack truck has a much greater mass. However, if both the Mack truck and Hot Wheels car were moving at the same velocity, the Mack truck would have much more kinetic energy simply because it has more mass.

Kinetic energy is directly proportional to mass and the square of velocity. This means that an object moving faster gains much more kinetic energy than an object with more mass. Doubling the velocity quadruples the kinetic energy, while doubling the mass only doubles the kinetic energy.

## Calculating Kinetic Energy

Kinetic energy depends directly on an object’s mass and velocity. The formula for calculating kinetic energy is:

KE = 1/2 x m x v^{2}

Where KE is kinetic energy, m is mass, and v is velocity. Kinetic energy is directly proportional to both mass and the square of velocity. This means that if the mass or velocity increases, the kinetic energy will also increase. However, because velocity is squared in the formula, changes to velocity have a greater impact on kinetic energy than changes to mass alone. Doubling the velocity of an object will quadruple its kinetic energy, while doubling the mass will only double the kinetic energy.

The units for kinetic energy are typically joules (J) in the SI system. The formula shows that an increase in either mass or velocity will result in an exponential increase in kinetic energy. This is why large, fast moving objects like trucks or asteroids have tremendous amounts of kinetic energy.

## Forms of Kinetic Energy

Kinetic energy comes in several different forms including:

### Vibrational Kinetic Energy

Vibrational kinetic energy refers to the kinetic energy associated with vibrational motion. This includes the vibration of atoms in solids, liquids, and gases as well as larger oscillating systems like pendulums. The atoms or molecules in these systems exhibit kinetic energy as they oscillate around their equilibrium positions. Greater amplitude of vibration corresponds to higher vibrational kinetic energy.

### Rotational Kinetic Energy

Rotational kinetic energy refers to the kinetic energy possessed by a rotating object. Any object that spins, orbits, or rotates exhibits rotational kinetic energy. Examples include spinning flywheels, rotating gears, orbiting planets, spinning electrons, and tumbling molecules. The rotational kinetic energy depends on the object’s moment of inertia and its angular velocity. Greater moment of inertia and faster angular velocity mean higher rotational kinetic energy.

### Translational Kinetic Energy

Translational kinetic energy refers to the kinetic energy an object possesses due to its straight-line motion. Any object moving with a velocity exhibits translational kinetic energy, like a car driving down a road, a bullet being fired, or a runner sprinting. The translational kinetic energy depends on the object’s mass and its speed. Heavier and faster objects have greater translational kinetic energy.

## Real World Examples of Kinetic Energy

Kinetic energy is all around us in the real world. Here are some common examples:

**Sports:** Many sports rely heavily on kinetic energy. A moving soccer ball contains kinetic energy that allows it to be kicked and travel through the air. A tennis ball hit by a racket contains kinetic energy that propels it across the court. Runners and sprinters generate kinetic energy with each stride to move forward.

**Vehicles:** All moving vehicles have kinetic energy. Cars, trucks, trains, planes, and rockets convert potential energy from fuel into kinetic energy of motion. The faster a vehicle moves, the more kinetic energy it possesses.

**Heat:** On the atomic level, heat is the result of increased molecular motion, which can be described as kinetic energy at a microscopic scale. Higher temperatures mean faster molecular motion and greater kinetic energy.

**Explosions:** Explosions release tremendous kinetic energy very rapidly in the form of expanding gases and shock waves. This generates high velocities and extreme force.

**Falling objects:** When an object falls due to gravity, it accelerates and gains kinetic energy that is released upon impact. The higher the fall, the greater the kinetic energy buildup.

## Converting Between Potential and Kinetic

Potential energy and kinetic energy are two forms of mechanical energy that are closely related. Kinetic energy is the energy of motion and potential energy is stored energy that depends on an object’s position or shape. According to the law of conservation of energy, energy cannot be created or destroyed, only converted from one form to another. This means that potential energy can be converted into kinetic energy and vice versa.

For example, when you hold a ball at a height above the ground, it has gravitational potential energy equal to mgh, where m is the mass of the ball, g is the gravitational acceleration, and h is the height. If you drop the ball, this potential energy will be converted into kinetic energy as the ball falls and gains speed. The kinetic energy of the ball will be equal to 1/2mv^2, where v is the final velocity right before the ball hits the ground. The total mechanical energy remains constant, even as the potential energy is converted into kinetic energy.

This transfer between potential and kinetic energy explains phenomena like swinging pendulums, roller coasters going over hills, and even how hydraulic dams generate electricity from the potential energy of water held at a height. Understanding the relationship between these two forms of energy provides great insight into many mechanical processes and systems.

## In Elastic and Inelastic Collisions

Kinetic energy can transfer between objects during collisions. The amount of kinetic energy transferred depends on whether the collision is elastic or inelastic.

In an elastic collision, kinetic energy is conserved. This means the total kinetic energy of the system before and after the collision is the same. An example is two billiard balls colliding on a frictionless surface. The total kinetic energy before and after the collision is the same, but the balls exchange kinetic energy during the collision.

In an inelastic collision, kinetic energy is not conserved. Some of the initial kinetic energy is converted to other forms of energy like heat, sound, or potential energy during the collision. An example is a ball dropping and bouncing on the floor. The ball loses kinetic energy on each bounce due to energy dissipating as heat and sound.

Understanding how kinetic energy changes in collisions helps predict motion and calculate quantities like velocity. Real world examples include vehicle collisions, particle accelerators, and sports interactions.

## Kinetic Energy and Temperature

The kinetic energy of molecules is directly related to temperature. Temperature is a measure of the average kinetic energy of molecules. As kinetic energy increases, molecules vibrate faster and collide more, resulting in a higher temperature.

This relationship can be described mathematically. The average kinetic energy (E_kinetic) of molecules is proportional to absolute temperature (T) as shown in this formula:

E_kinetic = (3/2)kT

Where k is the Boltzmann constant.

This formula explains why temperature rises when kinetic energy increases. For example, when you heat up water on a stove, you’re adding kinetic energy to the water molecules, increasing their vibrational motion. This added kinetic energy is sensed as a rise in temperature.

The relationship also works in reverse – decreasing kinetic energy lowers temperature. This is why substances cool down over time as their molecules lose energy through collisions.

Kinetic molecular energy and temperature help explain states of matter as well. The kinetic energy of molecules increases from solid to liquid to gas. Solids have the least motion and lowest average kinetic energy. Gases have the highest amounts of molecular motion and kinetic energy.

The strong link between kinetic energy at the molecular level and temperature is a fundamental concept in physics and chemistry.

## Kinetic Energy and Work

There is a direct relationship between kinetic energy and the work done to accelerate an object. Work, in physics, is defined as force applied over a distance. When work is done to accelerate an object, that work goes into increasing the object’s speed and kinetic energy.

For example, imagine pushing a heavy box across the floor. As you apply force to the box over a distance, you are doing work on the box. That work gets transferred into kinetic energy, seen as the increased speed and motion of the box. The more work you do on the box by pushing it further, the more kinetic energy the box gains.

This relationship can be described mathematically. The work done on an object equals the change in its kinetic energy. So if you do 100 Joules of work to accelerate a 10kg object, its kinetic energy will increase by 100 Joules. This shows the direct transfer between work and kinetic energy.

Understanding this connection helps explain how doing work on objects gives them kinetic energy. Any process that applies force to accelerate something – whether a person pushing a box or a rocket engine propelling a spaceship – is transferring energy that shows up as increased kinetic energy and motion.

## Power and Kinetic Energy

Power is defined as the rate at which work is done or energy is transferred. In physics, power is the rate of change of kinetic energy in a system. Kinetic energy is directly proportional to power, which means if kinetic energy changes quickly, power is high. If kinetic energy changes slowly, power is low.

The relationship can be described mathematically as:

Power = Change in Kinetic Energy / Time

Or:

P = ΔKE/Δt

Where P is power, ΔKE is the change in kinetic energy, and Δt is the change in time. So if an object speeds up or slows down quickly, it requires a lot of power to cause that rapid change in kinetic energy. But if the change occurs slowly over time, less power is needed.

Understanding the relationship between power and kinetic energy is useful in many areas of physics and engineering. For example, the power output of engines and motors depends on how quickly they can accelerate an object to increase its kinetic energy. The rate at which kinetic energy is removed by brakes is related to the stopping power. Even in biomechanics, the muscles’ ability to generate power determines how much force and kinetic energy they can produce quickly for running and jumping.

## Kinetic Energy and Momentum

Kinetic energy and momentum are closely related concepts in physics. The momentum of an object is directly proportional to its mass and velocity. Momentum is defined as the product of an object’s mass (m) and velocity (v).

Kinetic energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. The kinetic energy (KE) of an object is calculated as:

KE = 1/2 mv^{2}

Where m is mass and v is velocity. This shows that kinetic energy increases exponentially with velocity, while momentum increases linearly with velocity. Additionally, kinetic energy is scalar (has magnitude only) while momentum is a vector quantity with both magnitude and direction.

While they are distinct properties, kinetic energy and momentum are directly proportional. As one increases and decreases, so does the other. This relationship can be summarized in the following mathematical equation:

KE = p^{2}/2m

Where p is momentum. This equation demonstrates that as momentum increases, so does kinetic energy by the square of momentum divided by two times mass. When an object is in motion, it has both momentum and kinetic energy directly linked to its mass and velocity.