Rotational Kinetic Energy

The kinetic energy of a body rotating can be compared to the linear kinetic energy and described in terms of the angular velocity. The extended object’s complete kinetic energy is described as the sum of translational kinetic energy of the centre of mass and rotational kinetic energy of centre of mass. The rotational kinetic energy is represented in the following manner for a constant axis of rotation.

Rotational Kinetic Energy Definition

Rotational energy occurs due to the object’s rotation and is a part of its total kinetic energy. If the rotational energy is considered separately across an object’s axis of rotation, the moment of inertia is observed as shown below.

ERotational = ½ I ω2

E is Kinetic energy

I is moment of inertia

ω is the angular velocity

The expression can be designed for linear and rotational kinetic energy parallelly from the principle of work and energy. Consider the particular parallel between a fixed exerted torque on a wheel with a moment of inertia and force on a mass m and both beginning from the rest.

According to Newton’s second law, the acceleration is equivalent to the resultant velocity divided by the time and average velocity is half of final velocity. In rotational case, the angular acceleration given to the wheel is fetched from Newton’s second law of rotation.

The mechanical work that is required during rotation is the number of torque of the rotation angle. The axis of rotation for unattached objects is mostly around its centre of mass.

Please note the relation between the result of rotational energy and the energy held by linear motion.

Etransitional = ½ mv2

The moment of inertia plays the role of the mass and angular velocity plays the role of linear velocity v in a rotating system.

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Practise This Question

3 A of current is flowing in a linear conductor having a length of 40 cm. The conductor is placed in a magnetic field of strength 500 gauss and makes an angle of 30 with the direction of the field. It experiences a force of magnitude