# Find the kinetic energy stored in the flywheel

• persephone
In summary, the conversation discusses a problem involving a car powered by a rotating flywheel. The flywheel has a radius of 1.00 m and a mass of 425 kg, and is attached to an electric motor to bring its rotational speed up to 4000 rev/min. The question asks for the kinetic energy stored in the flywheel and the length of time it could run as a 15.0-hp motor. The incorrect use of the moment of inertia for a circular hoop was identified and the correct equation, I=(1/2)MR^2, was suggested. This led to the successful solution of the problem.
persephone

## Homework Statement

A car is designed to get its energy from a rotating flywheel (solid disk) with a radius of 1.00 m and a mass of 425 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 4000 rev/min.

(a) Find the kinetic energy stored in the flywheel.

(b) If the flywheel is to supply energy to the car as would a 15.0-hp motor, find the length of time the car could run before the flywheel would have to be brought back up to speed.

KE=(1/2)Iw^2
where I=Mr^2

P=KE/t

## The Attempt at a Solution

First I used the equation to find the moment of inertia: I=(425kg)(1)^2=425
I know that the angular velocity is 4000 rev/min, so I converted that to 418.879 rad/s
Then I plugged that into the the equation for KE: 1/2(425)(418.879 rad/s)^2 =3.73e7
This was wrong...

For part b, I used the equation relating power to kinetic energy, so I converted 15 hp to 11185.5 Watt

So, 3.73e7/11185.5 = t = 3334.67s
Also wrong..

Is there something I'm missing here? I can't figure out for the life of me what I'm doing wrong.

At first glance, I noticed that you are using the wrong moment of inertia.

You are using the moment of inertia for a circular hoop, not a solid disc. The moment of inertia for a disc is:

$$I=\frac{1}{2}MR^2$$

Try working the problem with this moment of inertia and see if it helps.

ah ha! that equation worked! I'm a total newb at physics so I wasn't aware there was a separate equation for the moment of inertia for a disc

Thank you so much!

No problem. I'm glad to be of help!

## What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion.

## What is a flywheel?

A flywheel is a mechanical device used to store rotational energy.

## How do you calculate the kinetic energy stored in a flywheel?

The formula for calculating the kinetic energy of a flywheel is KE = 1/2 * I * ω^2, where I is the moment of inertia and ω is the angular velocity.

## What factors affect the kinetic energy stored in a flywheel?

The kinetic energy stored in a flywheel is affected by its mass, shape, and angular velocity.

## What are some real-life applications of flywheels and their kinetic energy?

Flywheels are commonly used in vehicles, such as cars and trains, to store energy and provide a smoother ride. They are also used in energy storage systems to store energy from renewable sources for later use.

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