Fly wheels used in automobiles and steam engines producing rotational motion have discs with a large moment of inertia. Explain why?
Q 113
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A flywheel is used as
(i) a mechanical energy storage, the energy being stored in the form of rotational kinetic energy
(ii) a direction and speed stabilizer. A flywheel rotor is typically in the form of a disc. Rotational kinetic energy, $E_{\text {rot }}=\frac{1}{2} I \omega^2$, where 1 is the moment of inertia and $\omega$ is the angular speed. That is, $E_{\text {rot }} \propto \mathrm{L}$. Therefore, higher the moment of inertia, the higher is the rotational kinetic energy that can be stored or recovered.Also, angular momentum, $\vec{L}=I \vec{\omega}$, i.e, $|\vec{L}| \propto I$. A torque aligned with the symmetry axis of a flywheel can change its angular velocity and thereby its angular momentum. A flywheel with a large angular momentum will require a greater torque to change its angular velocity. Thus, a flywheel can be used to stabilize direction and magnitude of its angular velocity by undesired torques.
(i) a mechanical energy storage, the energy being stored in the form of rotational kinetic energy
(ii) a direction and speed stabilizer. A flywheel rotor is typically in the form of a disc. Rotational kinetic energy, $E_{\text {rot }}=\frac{1}{2} I \omega^2$, where 1 is the moment of inertia and $\omega$ is the angular speed. That is, $E_{\text {rot }} \propto \mathrm{L}$. Therefore, higher the moment of inertia, the higher is the rotational kinetic energy that can be stored or recovered.Also, angular momentum, $\vec{L}=I \vec{\omega}$, i.e, $|\vec{L}| \propto I$. A torque aligned with the symmetry axis of a flywheel can change its angular velocity and thereby its angular momentum. A flywheel with a large angular momentum will require a greater torque to change its angular velocity. Thus, a flywheel can be used to stabilize direction and magnitude of its angular velocity by undesired torques.
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