|Can you give me an example of when the angular acceleration is in a different direction from the torque applied?
When an object isn't symmetric, it can rotate in very peculiar ways. If you throw a tennis racket into the air so that it is spinning about an axis that isn't along the handle or at right angles to the handle, it will wobble in flight. Its axis of rotation will actually change with time as it wobbles. If you were to exert a torque on this wobbling tennis racket, its angular acceleration wouldn't necessarily be along the direction of the torque.