Certainly physics can help, but it depends greatly on the kind of game programming you're doing. Obviously, if you're working on a physics engine for a 3d game, then a solid understanding of the physics of mechanical motion will be a great help. However, I would say for most cases, game programmers probably don't deal with this kind of thing very often. Many companies use 3rd party company physics engines, and any physics that you would be doing would probably be pretty elementary.
I do not mean to discourage you from physics necessarily, and in fact, I think it's the better choice. It's a highly structured and interesting (and probably, though this is arguable, more useful) option for games programming...especially since you'll probably start on the mechanical motions area. But evaluate each class carefully, unless it's contributing to your major, since many higher end physics courses (such as electromagnetics, wave motion, quantum theory, relativity, etc.), while interesting, would not contribute much, in a direct way, to games programming.
EDIT, responding to a comment: To be a bit simplistic, the physics of mechanics is the study of how things react when forces are applied to them. The reason that understanding and replicating the physics of the real world is important is that you, as a human, already have a very intuitive sense of how the physics of mechanical motion work. You know that when you push a ball, it will roll, and you can make some guesses about where it will roll, and how far, depending on how you hard you push it, how heavy it is, etc. You have an idea that when you throw a stick, it will rotate through the air, and if it hits something it won't simply stop, but will bounce away in some direction. These are things that you know from just being alive for some time, and interacting with your environment, and a game that doesn't model these things correctly is very easy to spot, because it violates your innate sense of how things work. You may not understand exactly why something looks unrealistic, but you can spot it immediately. This is why it is so difficult to model a human walking, for instance, and movies and video games use motion capture when they want to make it look right: because our brains are very, very good at picking up a lot of subtleties in motion.
So, how does this affect you as a programmer? In many cases, if you can model the physics of what is happening, you don't need to worry about bizarre input: you can just let things happen, and they'll look good. As an example in a game, if I drop a ball in a street, and let it bounce, what happens? Realistically, it might hit a parked car, bounce at a strange angle, hit a moving car, gain some speed and launch itself over a building. Or, if it were dropped at a slightly different angle, an entirely different scenario might result. How can you possibly program in every possibility? You can't...but you can let physics do the work for you. During each cycle of the physics engine, it looks at all of the objects, and decides what happens to them. The ball, hitting the parked car, hits at velocity vector x, the car part it hits has a normal vector theta, and a speed vector z, resulting in a new velocity for the ball y. This sounds complex, boils down to a set of physics formulas that are well understood, and are relatively straightforward. You put those formulas into a physics engine, enter the various values for your objects, and start 'er up...and if you've done things right, things just look right...because they're modeled after what is going on in the real world.
Inertia, momentum, mass, force...these are all things that can be included in a physics engine, and understanding how they work and how you can model, or when and how you can fake them, is critical in handling realistic physics.
Does that help? If you're looking for something more specific, or a different example, just ask.