Conservation of linear/angluar momentum

Question

How is it that someone is able to walk? I mean, when you push against the surface of the earth, you're really applying a torque, and thus giving the earth angular momentum rather than linear momentum. So where does a person's linear momentum come from? I've given this some thought, and the explanation I came up with is that we don't gain linear momentum, we gain angular momentum; basically, we push against the earth with one foot, and the rest of our body rotates around our ankle, which makes some sense. But this explanation doesn't seem to work in all cases. Consider a car, how is its momentum conserved? Well, I would say that when the wheels of a car push against the earth, the angular momentum lost by the earth is transferred to the car's wheels. Everything seems to make sense, until the body of the car is considered: where does it's linear momentum come from? Finally, let's say someone jumps against a wall, while the earth gains angular momentum, the person in question gains linear momentum. How is this possible? Thanks in advance.

Answer 1

The problem is the earth is so large, what you're calling "angular momentum" is actually neglected and linear momentum is instead used because it's much more practical and obvious. The linear momentum of a car comes from the car moving. It has no momentum when it's stationary. I also don't quite get what you're trying to say when a person jumping against a wall is gaining linear momentum.  

Answer 2

The simple definition of torque T=r^F for this case describes that the force from a human walking will be imparted tangential to the earth. This will give rise to a linear momentum of the human and a corresponding angular momentum of the earth. It is a simple case of Newton's Third Law. Think of it in this way when thinking of the car too.

You can't say that in either of the cases of the car and jumping against a wall that the earth has gained or lost angular momentum. Angular momentum is a vector and so a corresponding loss or gain will be as a result of the sum of the angular momentum vectors of the two bodies considered in the system.