I find it helpful to think about the anaolgy between equations of linear motion and equations of rotational motion. If you wanted to determine acceleration of a mass that is initially moving at velocity v that comes to a stop over distance d you would use the equation:
Well in this problem you use an analogous equation, but with rotation components:
where
= final rotational velocity, which is 0 rad/s;
= initial radial velocity in radians/second;
= rotational acceleration, and
= the angle the mass rotates through, in radians. You'll have to covert the data you were given - 3600 RPM to radians/second, and 50 rotations to radians - then plug and chug.