Question

A uniform disk of radius 0.543 m and unknown mass is constrained to rotate about a perpendicular axis through its center. A ring with same mass as the disk\'s is attached around the disk\'s rim. A tangential force of 0.201 N applied at the rim causes an angular acceleration of 0.119 rad/s2. Find the mass of the disk.

Answer 1

Radius r = 0.543 m

Tangential force F = 0.201 N

angular acceleration = 0.119 rad/s²

Torque T = Fr

             = 0.201 x 0.543

            = 0.109143 Nm

We know T = I

From this moment of inertia of the system I = T /    

      I = 0.109143 / 0.119

       = 0.91716 kg m ²

Moment of inertia of the system = moment of inertia of disk + moment of inertia of the ring

                I = (1/2)mr ² + mr ²

                  = (3/2) mr ²

. From this the mass of the disk m = (2/3)(I/r ² )

     m = (2/3)(0.91716 / 0.543 ² )

         = 2.073 kg