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### What is the relationship between rotational energy and Moment of inertia?

### What is the formula for calculating the translation energy?

### What is the similarity between rotational and linear kinetic energies?

### What is an example of rotational energy?

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The **Rotational energy**, also known as angular kinetic energy is the kinetic energy produced because of the rotation of an object or an entity and is a fraction of its total kinetic energy. **Rotational energy** occurs when any form of matter rotates around a center of rotation. **Rotational energy** can be transformed into other forms of energy, particularly heat and translational (linear) energy. According to the law of conservation of energy, eventually, the total amount of energy in a remote system must stay constant. Loss in energy of one type must result in the gain in energy of another type. Energy transfer between the types mostly takes place through the swap over of momentum between the atomic particles of matter. Besides **rotational energy,** some other examples of various forms of energy consist of chemical, potential, and thermal. Hence, **rotational energy** is one of numerous potential ways that matter can take hold of energy.

Examining **rotational energy** individually around the axis of rotation of object, the reliance of rotational energy on the moment of inertia of the object is given by the relationship: **E _{rotational }= 1/2 I ω ^ 2, **where, ω is the angular speed, I is the moment of inertia around the axis of rotation and E is the kinetic energy. The mechanical work needed for or which is applied throughout rotation is the torque (a twisting force) times the rotation angle. The immediate power of an angularly accelerating body is the torque or twisting force times the angular frequency. In case of the free-floating or unattached entities or objects, the axis of rotation is usually in the region of its center of mass.

The relationship between the linear (or translational) and rotational motion is given as: **E _{translational} = 1/2 mv ^2**, where, m is the mass and v is the linear velocity. It should be noted that in the rotating system, the moment of inertia, I takes the function of the mass, m, and the angular velocity, ω, takes the function of the linear velocity, v. The

There are number of similarities between **rotational energy** and linear kinetic energy.

- As an alternative for mass, rotational systems encompass a moment of inertia. The moment of inertia can be considered as the resistance to angular acceleration, which is identical to how mass is the resistance to linear acceleration. Moments of inertia amplify when matter is further from the center of rotation. This is due to the fact that it is harder to get a system spinning if its matter is positioned faraway from the center.
- Correspondingly, rotational systems have an angular velocity in its place of a linear velocity. Angular velocity is deliberated in radians per second, which is equal to about 57.3 degrees per second. Together high moment of inertia and high angular velocity stands for high rotational energy. According to the law of conservation of energy, the equal amount of rotational energy can be got by reducing a system’s moment of inertia while escalating the angular velocity. Angular momentum is proportional to the moment of inertia, which depends on not just the mass of a spinning object, but also on how that mass is distributed relative to the axis of rotation.

A Flywheel battery is a best realistic application of **rotational energy**. A flywheel battery stocks up rotational energy, similar to how a standard battery stocks up the electrical energy. In a train using flywheel battery, the linear kinetic energy of the moving train can be shifted to the rotational energy of the aboard flywheel. The effect of this shift will be a decrease in the velocity of the train. If there is no energy loss as heat, all the energy of the train’s movement can be stored in the flywheel and utilized after a while for speeding up the train.