How to Calculate the Constant Torque to Stop a Flywheel?

What is the constant torque required to stop a flywheel?

Given a flywheel with a mass of 24.1 kg, radius of 1.83 m, and spinning counterclockwise at 217 rpm, how do we calculate the constant torque needed to bring it to rest in 2.25 minutes?

Answer:

The constant torque required to bring a flywheel of mass 24.1 kg and radius 1.83 m spinning at 217 rpm to rest in 135 seconds is approximately -6.78 N·m.

Explanation:

The question pertains to the principles of circular motion and angular momentum. It requires calculating the torque needed to stop a spinning flywheel. Torque can be equated to the change in angular momentum divided by the time it takes for that change to occur. Firstly, given the spinning speed of 217 rpm, we need to convert this to rad/s. After the conversion, we have an angular velocity ω of about 22.7 rad/s. The moment of inertia I of a uniformly thick disk is (1/2)*m*r^2, substituting m = 24.1 kg and r = 1.83 m, we get I to be approximately 40.3 kg·m². To find the final angular momentum, we multiply I by the final angular velocity, which is zero as the flywheel stops, and subtract from it the initial angular momentum. This results in a change in angular momentum of about -915.1 kg·m²/s. Dividing this by the time to stop in seconds (135s), we find the constant torque required to stop the flywheel to be approximately -6.78 N·m.