Rotational Kinetic Energy Formula

Rotational Kinetic Energy Formula

Kinetic energy is always the energy of a moving object. This movement can also be linear or rotational, and a rotating object also has kinetic energy. This energy is called the kinetic energy of rotation. The kinetic energy of a rotating object depends on the angle of the object. From the rotational speed expressed in radians/sec. It also depends on the moment of inertia of the object, and the moment of inertia is a measure of how easy it is to change the rotational state of an object. Students can visit the Extramarks website and learn more about the Rotational Kinetic Energy Formula.

A rigid body has two types of energy: kinetic energy and potential energy. Rigid body potential energy is the energy stored in a rigid body due to its position and other loads, and the kinetic energy of a rigid body is the form of energy that a moving body has as a result of its motion. When work is done on an object by applying a net force, the object speeds up, thereby increasing its kinetic energy and the kinetic energy of a moving body depends on its mass and speed. In this article, we will look at the kinetic energy of rotational motion and learn about the formula for rotational energy. When an object rotates about an axis, it has rotational kinetic energy. 

  • Kinetic energy of rotation concept

Rotational Kinetic Energy Formula is the energy absorbed by a body due to its rotation. The linear and Rotational Kinetic Energy Formula  equations can be expressed in the same way as the work-energy principle. Imagine the following parallel lines between the constant torque applied to the flywheel with a moment of inertia(I) and the constant force applied to the mass(m). Both start from a resting state. For linear starting at rest, Newton’s second law acceleration is equal to terminal velocity divided by time, and average velocity is half terminal velocity. That is, the work done on the block gives the block the same kinetic energy. I’m done with my work. In the case of rotational motion, which also starts at rest, the rotational work is:


And the angular acceleration α of the flywheel is obtained from Newton’s second law of rotation, and angular acceleration equals final angular velocity divided by time. Also, the average angular velocity is equal to half the final angular velocity. Furthermore, the Rotational Kinetic Energy Formula

transferred to the flywheel is equivalent to the work done by the torque.

The Formula For Rotational Kinetic Energy

It can be calculated using the following formula for rotational kinetic energy:

Rotational Kinetic Energy Formula = 12 x (moment of inertia) x (angular velocity) 2

In other words, mathematically


Ek Rotational kinetic energy

I moment of inertia

ω Angular velocity of rotating body

The Rotational Kinetic Energy Formula helps calculate the rotational kinetic energy of a body undergoing rotational motion. Moment of inertia is denoted by the letter I and is expressed in units of kg·m2, and the unit of kinetic energy is the joule (J). In other units, 1 joule is equivalent to 1 square kilometre per square second. H. kgm2s−2. Solution 

Solved Examples For Rotational Kinetic Energy Formula

Q.1: Calculate the Rotational Kinetic Energy Formula when the angular velocity is ω=7.29×10−5 rad per sec and the moment of inertia is 8.04×1037 kgm2. 

Solution: The known parameters are:

angular velocity, ω=7.29×10−5rd per sec,

Moment of inertia, I = 8.04 × 1037 kgm2. The kinetic energy of rotation is Ek=12Iω2

=12×8.04×1037kgm2×(7.29×10−5 rad/s)2

= 2.13 × 1029 J

So the rotational kinetic energy is 2.13 × 1029 J. 

Q.2: Find the Rotational Kinetic Energy Formula of the motor when the angular velocity is 100π rad/s and the moment of inertia is 50 kgm2.


angular velocity, omega = 100πradprosec

Moment of inertia I=50kgm2

Kinetic energy of rotation is Ek=12Iw2


= 2500 years

So the kinetic energy of rotation is 2500 J. More examples of the Rotational Kinetic Energy Formula can be checked on the Extramarks website.

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