# You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to...

## Question:

You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to be a uniform disk with radius {eq}29.0{/eq} {eq}cm{/eq}. Starting from rest at {eq}t=0{/eq}. The flywheel rotates with constant angular acceleration {eq}3.00{/eq} {eq}rad/s^2{/eq} about an axis perpendicular to the flywheel at its center.

1. If the flywheel density (mass per unit volume) of {eq}8600{/eq} {eq}kg/m^3{/eq}, what thickness must it have to store {eq}800{/eq} {eq}J{/eq} of kinetic energy at {eq}t=8.00{/eq} {eq}s{/eq} ?

## Rotational Kinetic Energy:

The energy stored in a rotation flywheel is in the form of rotational kinetic energy given by the formula:

$$\begin{align*} &E_K = \frac{1}{2} I\omega^2 & \text{[Rotational Kinetic Energy of a Flywheel]]} \end{align*} $$

where {eq}\omega{/eq} is the angular velocity of the flywheel.

The moment of inertia {eq}I{/eq} of the flywheel about its axis of symmetry is given by the equation:

$$\begin{align*} &I = \frac{1}{2}mr^2 & \text{[Moment of Inertia of a Flywheel]} \end{align*} $$

where {eq}m{/eq} is the mass of the flywheel and {eq}r{/eq} is its radius.

## Answer and Explanation:

Given a rotating metal flywheel with radius {eq}r = 29 \,cm = 0.29\,m{/eq} and density {eq}\rho = 8600\,\frac{kg}{m^3}{/eq}.

The flywheel's mass...

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