I am trying to understand conservation linear momentum with in angular momentum
Herewith i just explain what i am looking for.
Imagine an object of mass(M), velocity(V), is undergoing circular motion
with radius(R)
Angular momentum L = RMV (R-radius M-mass- V- tangential velocity)
Mass is constant here
Since L is conserved so when R is decreased tangential velocity(V)
has to be increased to keep angular momentum constant.
Does this mean linear momentum not conserved when radius of rotation changes?
When linear momentum is not conserved then what is the force that increases the velocity of object when R decreases.
Could anyone clarify this. or could any one say is my basic understanding about momentum is wrong. for easy understanding i am only considered magnitude of momentum's not cross product of vectors
Best Answer
The thing you are overlooking is that something else must be applying an equal and opposite force in order to pull something into the circle you mention.
Consider the case of two astronauts each holding an end of a rope in between them. If they are both moving in a circle around their common center of mass, then when they pull the rope in, their rotational motion increases, the momentum of each increases in magnitude, but the total momentum stays the same.