# Power Plants Storing Energy in Massive Flywheels

• Treefolk
In summary, we discussed the concept of using off-peak hours to generate and store mechanical energy in power plants, specifically through the use of large flywheels. We then applied this concept to a problem involving a flywheel made of iron and calculated the necessary diameter for it to store a specific amount of kinetic energy at a given angular velocity. The correct answer was found to be 14.1 meters.
Treefolk

## Homework Statement

It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle of the day. One suggestion has been to store the energy in large flywheels spinning on nearly frictionless ball-bearings. Consider a flywheel made of iron, with a density of 7800 kg/m^3 , in the shape of a uniform disk with a thickness of 10.6 cm.

What would the diameter of such a disk need to be if it is to store an amount of kinetic energy of 14.4 MJ when spinning at an angular velocity of 90.0 rpm about an axis perpendicular to the disk at its center?

## Homework Equations

V = h$\pi$r^2 <--Volume of a cylinder
I = .5mr^2 <-- Moment of an inertia of a solid cylinder
KE = .5I$\omega$^2 <-- Kinetic Energy of a Cylinder

## The Attempt at a Solution

$\delta$ = 7800
h = .106m
m = $\delta$*V = 7800*.106*$\pi$*r^2 = 2597.5r^2
I = .5(2597.5r^2)r^2 = 1298.7r^4
KE = .5(1298.7r^4)$\omega$^2 = 649.4r^4$\omega$^2
$\omega$ = 90rpm = 1.5rps = 3rad/s
KE = 649.4r^4(3)^2
KE = 14.4x10^6
14.4x10^6 = 649.4r^4*(3)^2
r^4 = 2463.9
r=7.05
diameter = 14.1

That sorts through my logic, but the online homework spits back the answer as wrong, so I'm rather at a loss for what I did wrong. Any advice would be quite welcome.

Hi Treefolk!

(try using the X2 button just above the Reply box )
Treefolk said:
$\omega$ = 90rpm = 1.5rps = 3rad/s

erm …

90 revolutions/minute => 1.5 Revolutions/Second => 3 Rad/s

Or did I muck this up?

yup!

Treefolk said:
diameter = 14.1

Furlongs?

tiny-tim said:
yup!

That would do it...lemme check that.

Borek said:
Furlongs?

Meters, the units weren't the issue here (online homework provides the unit next to the blank or asks for the units in the problem). Thank you anyways.

Treefolk said:
Meters, the units weren't the issue here (online homework provides the unit next to the blank or asks for the units in the problem). Thank you anyways.

We don't see the units you were shown, so we can't rule them out as a problem. Good practice to include them always

## 1. How do flywheels store energy in power plants?

Flywheels store energy through rotational inertia. When electricity is supplied to the flywheel, it spins faster and stores the energy as kinetic energy. When the energy is needed, the flywheel slows down and the kinetic energy is converted back into electricity.

## 2. What are the advantages of using flywheels for energy storage?

Flywheels have a high energy density, meaning they can store a large amount of energy in a small space. They also have a long lifespan and can be charged and discharged quickly. Additionally, they do not produce emissions or require fuel, making them a clean and sustainable form of energy storage.

## 3. Are there any disadvantages to using flywheels for energy storage?

One disadvantage of flywheel energy storage is the potential for mechanical failure. If the flywheel were to break or malfunction, it could release a large amount of energy in a short period of time. There is also the issue of energy loss due to friction, which can reduce the efficiency of the system.

## 4. How are flywheels used in power plants?

Flywheels are typically used in power plants as a form of grid energy storage. They can be charged during times of low energy demand and discharged during peak demand periods. This helps to balance out the fluctuations in energy supply and demand, making the grid more stable and efficient.

## 5. What is the future of flywheel energy storage in power plants?

Flywheel energy storage technology is constantly advancing, with new materials and designs being developed to improve efficiency and reliability. As renewable energy sources become more prevalent, the need for energy storage solutions like flywheels will also increase. It is likely that flywheel energy storage will continue to play an important role in the future of power plants and the energy industry as a whole.

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