# Newton's Third Law: Action and Reaction

Newton’s third law of motion is famous, especially in wrestling and drivers’ ed circles, but you may not recognize it in all its physics glory: “Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body.”

The more popular version of this, which you’ve probably heard many times, is “For every action, there’s an equal and opposite reaction.” But for physics, it’s better to express the originally intended version, in terms of forces, not actions (which can apparently mean everything from voting trends to temperature forecasts!).

Here’s a real-world example to show you how Newton’s third law of motion works. Say that you’re in your car, speeding up with constant acceleration. To do this, your car has to exert a force against the road; otherwise, the car wouldn’t be accelerating. And the road has to exert the same force on your car. You can see what this looks like, tire-wise, in the figure.

The two forces in the figure are equal in magnitude but opposite in direction. However, they do not cancel out because the two forces are acting on different bodies — one on the car and the other on the road. The force that the tire exerts on the road (F_{car}) is equal and opposite to the force the road exerts on the tire (F_{road}). The force of the road on the tire accelerates the car.

So why doesn’t the road accelerate? The car accelerates, so shouldn’t the road accelerate in the opposite direction? Believe it or not, it does; Newton’s law is in full effect. Your car pushes the Earth, affecting the motion of the Earth in just the tiniest amount. Given the fact that the Earth is about 6,000,000,000,000,000,000,000 times as massive as your car, however, any effects aren’t too noticeable!

Similarly, when a hockey player slaps a puck, the puck accelerates away from the spot of contact, and so does the hockey player. If hockey pucks weighed 1,000 pounds — with a mass of about 31 slugs, or 450 kilograms — you’d notice this effect much more; in fact, the puck wouldn’t move much at all, but the player would hurtle off in the opposite direction after striking it.