__Flywheel Power Calculator:__

__Flywheel Power Calculator:__

Enter the values of moment of inertia, I_{(kg.m2)}, angular velocity, ω_{(rad/s)} and time, t_{(s)} to determine the value of Flywheel power, P_{fw(W)}.

__Flywheel Power Formula:__

__Flywheel Power Formula:__

Flywheel power (Pfw) signifies the rate at which a flywheel stores and releases energy. Flywheels are used in various mechanical systems to smooth out the delivery of power from an energy source to a mechanical load, storing excess energy and releasing it when needed.

Moment of inertia is a measure of how much torque is needed for a desired angular acceleration about a rotational axis, dependent on the mass distribution of the flywheel.

The rate of rotation of the flywheel, measured in radians per second. The duration over which the power is considered.

Energy is supplied to the flywheel, causing it to rotate and increase its angular velocity (ω).

The moment of inertia (I) determines how much of this energy is stored within the flywheel’s rotation.

The formula helps calculate the rate at which this energy is transferred during a specific time interval (t). A positive Pfw indicates energy is being charged into the flywheel, while negative Pfw signifies energy is being discharged.

Flywheel power, P_{fw(W)} in watts is calculated by dividing the product of 0.5, moment of inertia, I_{(kg.m2)} in kilogram metre square and square angular velocity, ω_{(rad/s)} in radians per second by time, t_{(s)} in seconds.

Flywheel power, P_{fw(W)} = 0.5 * I_{(kg.m2)} * ω^{2}_{(rad/s)} / t_{(s)}

P_{fw(W)} = flywheel power in watts, W.

I_{(kg.m2)} = moment of inertia in kilogram metre square, kg.m^{2}.

ω_{(rad/s)} = angular speed in radians per second, rad/s.

t_{(s)} = time in seconds, s.

__Flywheel Power Calculation:__

__Flywheel Power Calculation:__

#### 1. Finding Flywheel Power (Pfw)

Given:

Moment of Inertia I_{(kg.m2)} = 10 kg·m^{2}

Angular Velocity ω_{(rad/s)} = 5 rad/s

Time t_{(s)} = 2 s

Flywheel power, P_{fw(W)} = 0.5 * I_{(kg.m2)} * ω^{2}_{(rad/s)} / t_{(s)}

P_{fw(W)} = 0.5 * 10 * 5^{2} / 2

P_{fw(W)} = 125 / 2

P_{fw(W)} = 62.5W.

#### 2. Determining the Moment of Inertia (I)

Given:

Flywheel power, P_{fw(W)} = 80W

Angular Velocity ω_{(rad/s)} = 4 rad/s

Time t_{(s)} = 1.5s

Flywheel power, P_{fw(W)} = 0.5 * I_{(kg.m2)} * ω^{2}_{(rad/s)} / t_{(s)}

I_{(kg.m2)} = P_{fw(W)} * t_{(s)} / 0.5 * ω^{2}_{(rad/s)}

I_{(kg.m2)} = 80 * 1.5 / 0.5 * 4^{2}

I_{(kg.m2)} = 120 / 8

I_{(kg.m2)} = 15kg.m^{2}.