# How Long Can a Flywheel-Powered Car Run on Stored Kinetic Energy?

• ba726
In summary, the car's flywheel has a radius of 1.85m and a mass of 678kg. Before a trip, an electric motor brings the flywheel's rotational speed up to 3610 rev/min, resulting in a kinetic energy of 82905777.99J stored in the flywheel. To run the car, the flywheel would need to supply energy like a 7.9hp motor, which can be converted to 746W. Using the relationship between power and time, you can calculate how long the car could run before the flywheel would need to be brought back up to speed.
ba726

## Homework Statement

A car is designed to get its energy from a rotating flywheel with a radius of 1.85 m and a mass of 678 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 3610 rev/min. Find the kinetic energy stored in the flywheel. Answer in units of J.

If the flywheel is to supply energy to the car as would a 7.9hp motor, how long could the car run before the flywheel would have to be brought back up to speed? Answer in units of h.

## Homework Equations

rotational KE= 1/2 I $$\omega$$2
I=1/2mr2
$$\omega$$=$$\omega$$o + $$\alpha$$t
$$\theta$$-$$\theta$$o=$$\omega$$ot+1/2$$\alpha$$t2

## The Attempt at a Solution

I found part 1 which was 82905777.99J but am stuck on how to approach part 2. I think I should use a rotational equation but I don't know angular position nor angular acceleration. Since they give me 7.9hp, I think I should convert it to work (1hp=746W) but don't know what to do with it. Any direction to take would be helpful.

Hi ba726,

ba726 said:

## Homework Statement

A car is designed to get its energy from a rotating flywheel with a radius of 1.85 m and a mass of 678 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 3610 rev/min. Find the kinetic energy stored in the flywheel. Answer in units of J.

If the flywheel is to supply energy to the car as would a 7.9hp motor, how long could the car run before the flywheel would have to be brought back up to speed? Answer in units of h.

## Homework Equations

rotational KE= 1/2 I $$\omega$$2
I=1/2mr2
$$\omega$$=$$\omega$$o + $$\alpha$$t
$$\theta$$-$$\theta$$o=$$\omega$$ot+1/2$$\alpha$$t2

## The Attempt at a Solution

I found part 1 which was 82905777.99J but am stuck on how to approach part 2. I think I should use a rotational equation but I don't know angular position nor angular acceleration. Since they give me 7.9hp, I think I should convert it to work (1hp=746W)

This is not converting to work; it is changing the units: that is, changing a power of 7.9 horsepower to the same power in units of watts.

Once you have the power in watts, what is the relationship between power and time?

To find the answer to part 2, you can use the equation for rotational work, W = \tau\theta, where \tau is the torque and \theta is the angular displacement. Since the flywheel is attached to an electric motor, we can assume that the torque is constant. The power output of the motor is given as 7.9hp, which is equivalent to 746*7.9 = 5893.4 W. We can then use the equation P = \tau\omega, where P is the power, \tau is the torque, and \omega is the angular velocity. Rearranging for \tau, we get \tau = P/\omega. We can now substitute this value for \tau into the equation for work, W = \tau\theta, to get W = (P/\omega)\theta. We can then solve for \theta, which gives us the angular displacement. Since we know the initial and final angular velocities, we can use the equation \theta-\thetao=(\omega-\omegao)t + 1/2\alpha t^2 to solve for the time, t, that the flywheel will run before it needs to be brought back up to speed.

## What is rotational motion of flywheel?

Rotational motion of flywheel refers to the movement of a spinning object, called a flywheel, around an axis. This type of motion is characterized by the rotation of the flywheel at a constant speed and direction.

## What is the purpose of a flywheel?

A flywheel is used to store rotational energy and maintain a constant speed of a machine or system. It also helps with the smoothing out of fluctuations in the rotational motion.

## How does the mass of a flywheel affect its rotational motion?

The mass of a flywheel affects its rotational motion by determining the amount of kinetic energy it possesses. A larger mass will have a greater rotational inertia and require more energy to change its speed or direction.

## What factors affect the rotational motion of a flywheel?

The rotational motion of a flywheel can be affected by various factors such as the mass of the flywheel, the speed at which it is rotating, the shape and size of the flywheel, and any external forces acting upon it.

## How is rotational motion of a flywheel calculated?

The rotational motion of a flywheel can be calculated using the formula for rotational kinetic energy, which is ½ * I * ω², where I is the moment of inertia and ω is the angular velocity. The moment of inertia can be calculated by multiplying the mass of the flywheel by the square of its radius.

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