A cylinder rotating at an angular speed of 50 rev/s is brought into...

Let the initial angular speed of the first cylinder be $\omega_1 = 50 \text{ rev/s}$ and the second cylinder be $\omega_2 = 0$.

The angular deceleration of the first cylinder is $\alpha_1 = 1 \text{ rev/s}^2$ and the angular acceleration of the second cylinder is $\alpha_2 = 1 \text{ rev/s}^2$.

Let $t$ be the time taken for the two cylinders to attain equal angular speed $\omega$.

Using the first equation of rotational motion for both cylinders:

For the first cylinder: $\omega = \omega_1 - \alpha_1 t = 50 - t$

For the second cylinder: $\omega = \omega_2 + \alpha_2 t = 0 + t$

Equating the final angular speeds:

$50 - t = t$

$2t = 50$

$t = 25 \text{ s}$