|If every force always has an equal and opposite force pushing against it (like the bowling ball and your arm in today's lecture), how can anything at all accelerate? Wouldn't forces always cancel each other out?
The two equal but opposite forces are being exerted on different objects! In many cases, those two objects are free to accelerate independently and they will accelerate—in opposite directions! For example, when I push on a bowling ball, it pushes back on me with an equal but opposite force. If my force on the bowling ball is the only force it experiences, it will accelerate in the direction of my force on it. Since it exerts an opposite force on me, I will accelerate in the opposite direction—we will push apart!