Question

Comment on the statement “Rotational kinetic energy is equal to half of the moment of inertia into angular velocity”

Answer 1

Rotational kinetic energy:

1. The kinetic energy of a rigid body is a form of energy possessed by a moving body by means of its motion.
2. If work is done on an object by applying a net force, the object gains speed which in turn increases its kinetic energy.
3. The kinetic energy of a body in motion is dependent on its mass and speed.
4. When an item rotates around an axis, it has rotational kinetic energy.
5. A rotating body's kinetic energy is equivalent to linear kinetic energy and is determined by the following factors:
6. The rotational speed of the object; the greater the rotational speed, the greater the energy.
7. The angular kinetic energy of a rotating object is exactly proportional to its mass.
8. The energy of a point mass is also determined by its position relative to the axis of rotation.
9. The particles further away from the rotation axis have higher rotational kinetic energy than the particles closer to the rotation axis.

Moment of inertia:

1. The total of ${\mathrm{mr}}^2$for all the point masses that make up an object's moment of inertia I, where m is the mass and r is the distance of the mass from the center of mass, may be described as the object's moment of inertia $\mathrm{I}$.
2. It may be mathematically stated as $\mathrm{I}=\sum _{{\mathrm{mr}}^2}$ . Here, $\mathrm{I}$ is analogous to m in translational motion. In translational motion, $\mathrm{I}$ is comparable to $\mathrm{m}$.
3. To describe the Rotational Energy formula of a rotating item, we must first characterize the mass distribution of the object along the axis of rotation, which is denoted by the moment of inertia kinetic energy, $\mathrm{I}$.
4. The moment of inertia is a measure of the difficulty in changing a body's rotational motion around the axis of rotation.
5. The kinetic energy moment of inertia is affected by the mass of the body and its distribution around the axis of rotation.