Science Behind Rotational Kinetic Energy: Concepts, Examples

This article discusses about rotational kinetic energy of Earth. The Earth like every other planet rotates about its own axis. In this article we will discuss about its rotational kinetic energy.

Earth revolves around the Sun with certain kinetic energy. But in this article we will focus on the rotational kinetic energy, that is the kinetic energy with which the Earth rotates around its own axis. We shall discuss about the reasons behind Earth’s rotation and other facts about rotational kinetic energy.

What is kinetic energy?

Kinetic energy is the energy possesed by an object by the virtue if its motion. The object will have kinetic energy only when it is moving.

The kinetic energy depends on the object’s mass and square of velocity. We can use the value of change in kinetic energy to find the work done. Kinetic energy of the object can be converted into other forms of energies such as potential energy , heat energy etc.

Rotational kinetic energy

When the object follows a circular motion, the associated kinetic energy is called as rotational kinetic energy. To calculate rotational kinetic energy we require two quantities.

The first quantity is moment of inertia. The moment of inertia is analogous to mass that is instead of mass, we have inertia in rotational motion. The second quantity is rotational speed or angular velocity. Angular velocity of an object is the velocity with which the object is rotating.

What is the rotational kinetic energy?

The rotational kinetic energy of Earth is the kinetic energy of Earth’s surface while rotating. In the next section we will study how to find the rotational kinetic energy of Earth.

To find the rotational kinetic energy of Earth we require the value of moment if inertia of Earth and the angular velocity with which Earth rotates. In next section we will calculate the value of rotational kinetic energy of Earth using the values of moment of inertia and angular velocity.

How to calculate rotational kinetic energy of Earth

The rotational kinetic energy of Earth in simple terms is the kinetic energy with which the surface of Earth is rotating around a center of rotation.

The angular velocity of Earth is 7.29 x 10^(-5) rad/s, moment of inertia is 8.04 x 10^37 kg m2. Using the values of angular velocity and moment of inertia we can find the value of rotational kinetic energy. After substituting the values we get rotational kinetic of energy of Earth = 2.138 x 10^29 J.

The formula used here is given in the section below

R.K.E=1/2Iω²

Where,

I is the moment of inertia of Earth

Omega is the angular velocity of Earth

Image credits: Wikipedia

Where did the rotational kinetic energy of Earth come from?

The rotational kinetic energy of Earth comes from its rotational motion. The otational motion of Earth dates back to the time when Earth was formed.

The Earth was formed by continuous collisions of asteroids and comets with a rock. Due to collisions on the surface of the rock, the rock started rotating, due to addition of mass of comets and asteroids, the value of inertia kept increasing. This is how rotational motion of Earth was born.

Rotational Kinetic energy examples

There are many instances in which we can see objects having rotational kinetic energy. The list of examples are given in the section below-

Ball rolling down a ramp – A ball follows translational motion while moving forward but the ball rotates around its centre. Due to rotation it will have rotational kinetic energy. The center of rotation is the radial center of the ball.
Wheels of a car – When the car is moving, the wheels of car follow rotational motion. The wheels rotate in order to move the car forward. The wheels will have rotational kinetic energy due to its rotational motion.
Wheels of a cycle – Similar to the wheels of car, even the wheels of a cycle follow rotational motion. The wheels rotate to move the cycle in forward direction. The wheels will have rotational kinetic energy due to its rotational motion. The centre of wheels is the centre of rotation.
Earth’s rotation– As discussed in the above sections, we all know that Earth rotates around its axis and has certain amount of rotational kinetic energy. We also know how the Earth started its rotation.
Frisbee– When kids play frisbee, they throw the frisbee in such a way that the frisbee starts rotating around its centre. Due to the rotation, frisbee will have rotational kinetic energy as well. The magnitude of rotational kinetic energy will depend on the moment of inertia and the angular speed with which the frisbee is rotating.
Fan’s blade – When a fan is switched ON, the blades of fan starts following a rotational motion. Due to the rotational motion, the fan blades will have rotational kinetic energy. The magnitude of rotational kinetic energy will depend on the moment of inertia and the angular speed with which the blades are rotating.
Hammer throw– A hammer thrower rotates to gain angular momentum, due to his rotational motion he gains rotational kinetic energy which is then transferred to the hammer. The hammer will follow a parabolic path after the hammer throws the hammer. The magnitude of rotational kinetic energy will depend on the moment of inertia and the angular speed with which the hammer thrower is rotating.
Ballerina – Ballerina usually rotate their bodies while dancing. The keep their toes as center of rotation. This way they gain rotational kinetic energy.
Satellite orbiting Earth– Satellites orbit around the Earth by maintaining equilibrium between gravitational force and centrifugal force. The satellite has rotational kinetic energy as it revolves around the planet. The magnitude of rotational kinetic energy will depend on the moment of inertia and the angular speed with which the satellite is rotating.
Toys having rotational elements – Some toys have rotating elements inside them. Due to their rotational motion they attain rotational kinetic energy. The magnitude of rotational kinetic energy will depend on the moment of inertia and the angular speed with which the rotational elements are rotating.

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Abhishek

Hi ….I am Abhishek Khambhata, have pursued B. Tech in Mechanical Engineering. Throughout four years of my engineering, I have designed and flown unmanned aerial vehicles. My forte is fluid mechanics and thermal engineering. My fourth-year project was based on the performance enhancement of unmanned aerial vehicles using solar technology. I would like to connect with like-minded people.