I have a question about the phrase "life can turn on a dime." I know what it means, but what is its literal meaning? How did it come to mean that life can change for the better or worse any moment? What does "turning on a dime" refer to exactly?
To "turn on a dime" is usually an expression you hear when referring to high performance cars, airplanes, boats, etc. Since a dime is the smallest U.S. coin, the ability to "turn on it" is a figure of speech meaning you can change direction very quickly in a very small space.
In this case, it means that life can change course very quickly. Depending on the circumstances, it can be either good or bad, but either way it will be rapid.
The expression "can turn on a dime" means "has a very tight turning radius". A dime is a very small American coin, 17.91 mm diameter. In this expression, it illustrates just how small the turning radius is. (A tight or small turning radius is an advantage in handling a car.)
By extension, anything that can "turn on a dime" can make a radical change in direction very quickly.
In the Dutch language we have a similar phrase, which might shed an interesting light on this. Transaleted it says: "It's a dime on its edge". Literally it means, it's hard to balance a dime on its edge (since it is so small and thin) and one can't tell to which side it will fall over. Metaphorically, it refers to something unpredictable. It's often used to express a narrow escape from a perrilous situation by sheer luck.