A cylinder rotating at an angular speed of 50 rev/s is brought into contact with an identical stationary cylinder. Due to kinetic friction, torques act on the two cylinders, accelerating the stationary one and decelerating the moving one. If the common magnitude of the acceleration and deceleration is 1 rev/s ^2 , how much time will it take before the two cylinders attain equal angular speed?

Step-by-step solution

Let the initial angular speed of the first cylinder be ₁ = 50 rev/s and the second cylinder be ₂ = 0 . The angular deceleration of the first cylinder is ₁ = 1 rev/s ^2 and the angular acceleration of the second cylinder is ₂ = 1 rev/s ^2 . Let t be the time taken for the two cylinders to attain equal angular speed . Using the first equation of rotational motion for both cylinders: For the first cylinder: = ₁ - ₁ t = 50 - t For the second cylinder: = ₂ + ₂ t = 0 + t Equating the final angular speeds: 50 - t = t 2t =