Question

Consider a flywheel that is a solid cylindrical disk 0.2 meters in radius with a mass of 40 kg. The flywheel turns at 700 rpm until acceleration is applied by an external torque; in 6 seconds the flywheel turns at 2500 rpm.

(a) What magnitude of torque was applied, assuming constant angular acceleration?

Answer 1

To calculate the magnitude of the torque applied to the flywheel, you can use the equation Torque = Moment of inertia * Angular acceleration. By substituting the given values into the equations, the torque applied to the flywheel is found to be 139.7 N·m.

Step-by-step explanation:

To calculate the magnitude of torque applied to the flywheel, we can use the equation:

Torque = Moment of inertia * Angular acceleration

First, we need to calculate the moment of inertia (I) of the flywheel. The moment of inertia for a solid cylindrical disk is given by:
I = (1/2) * mass * radius^2

Substituting the given values:
I = (1/2) * 40 kg * (0.2 m)^2 = 0.8 kg·m²

Next, we can use the formula for angular acceleration:
Angular acceleration = (Change in angular velocity) / Time

Substituting the given values:
Angular acceleration = (2500 rpm - 700 rpm) / 6 s = 166.67 rpm/s = 174.63 rad/s²

Finally, we can calculate the torque applied:
Torque = 0.8 kg·m² * 174.63 rad/s² = 139.7 N·m