Question

Suppose that a disk is rotated at a constant speed of 100 rad/s, and we wish to stop it in 2 minutes. Assuming the moment of inertia (J) of the disk is 6 kgm^2, determine the torque necessary to stop the rotation. Assume no friction in the system.

a) 300 Nm
b) 600 Nm
c) 900 Nm
d) 1200 Nm

Answer 1

The torque required to stop a 6 kg·m² disk rotating at 100 rad/s in 2 minutes is 5 N·m, not 300 Nm, 600 Nm, 900 Nm, or 1200 Nm as suggested in the options provided.

Step-by-step explanation:

To determine the torque necessary to stop a disk rotating at 100 rad/s in 2 minutes (120 seconds), we can use the formula τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular deceleration. Given that the moment of inertia (J) is 6 kg·m² and that angular deceleration (α) can be found by dividing the angular velocity (100 rad/s) by the time interval for deceleration (120 s), we calculate α to be 100 rad/s ÷ 120 s = 0.8333 rad/s². Substituting these values into the torque formula, we get: τ = 6 kg·m² × 0.8333 rad/s², which equals 5 N·m. Therefore, option a) 300 Nm is incorrect, as the correct value for the torque necessary to stop the rotation is 5 N·m.