How To Calculate Frictional Torque

Torque is described as a force acting a measured distance from a fixed axis, such as a door rotating on a hinge or a mass suspended from a rope that is hung across a pulley. The torque can be affected by an opposing force that results from a resistant surface. This opposing force is referred to as friction. The frictional torque, therefore, is calculated as the difference between the applied torque and the resulting net, or observed, torque.

Step 1

Determine the net torque of a frictionless mass pulley system with a pulley of a given radius, R, a given pulley mass, m1, and mass suspended from the system, m2. The net torque is equal to the angular acceleration of the mass suspended from the pulley, multiplied by the rotational inertia of the pulley.
Net Torque = Angular Acceleration Inertia of Pulley Angular Acceleration = (acceleration of mass, m2) / (radius of pulley) Inertia of Pulley = (1/2 mass of pulley) (radius of pulley)^2

Step 2

Determine the applied, or observed, torque of the same system with friction. The calculation will be the exact same as above, however, the observed acceleration of the mass will be less due to the friction now added to the pulley. Applied Torque = Angular Acceleration (with friction) * Inertia of Pulley

Step 3

Find the frictional torque by subtracting the applied torque from the net torque. Net Torque = Applied Torque + Frictional Torque Frictional Torque = Net Torque – Applied Torque