# Q & A: where is the effect of the equal opposite reaction?

Q:
If for every action there is an equal and opposite reaction, then if I push a pen with my hand, the force of my hand on the pen is the same as the force of the pen on my hand. So why does my pen move forward but my hand not move backward?
- Brian (age 24)
Champaign, IL USA
A:

Brian- I bet that question is one that lots of people wonder about.

Say you gave the pen a little push East. It pushes back on you West. While it's heading East, shouldn't you head West? You should, but since you're much more massive than the pencil you pick up much less velocity. Even worse,  you're pretty firmly connected to the Earth, and you and the Earth together are much, much more massive than the pen. So yes, you and the Earth will head West but not enough to notice.

One way to look at this is to describe Newton's third law as conservation of momentum, mv, where m is mass and v is the velocity vector, including direction. You can see that canceling the momentum of a small mass one way  requires much smaller v for a big mass going the other way.

Mike W.

(published on 06/20/2013)