Can an Electron Rotate a Brick?

In The Theory of Almost Everything,1 Robert Oerter asserts the following: “Take a beam of electrons that are all spinning in the same direction and fire it at, say, a brick. If you could keep this up for long enough, and if there were no other forces acting on the brick, the electrons would transfer their rotation to the brick, and it would begin to rotate.” Although this may awe credulous readers, skeptical physics students and their teachers ought to ask: Is it true that an electron can rotate a brick? To answer this requires bringing together elementary concepts from several areas of physics and doing the kind of back-of-the-envelope calculations students should be taught to do early on in their scientific education.