Heisenberg's Uncertainty Principle for 2 bodies connected by a spring Take two identical particles, measure there mass and let them spring apart. Now the two particles will move in opposite direction. If I calculate accurately position of first particle and velocity of second particle, I can easily calculate velocity of first particle as they are mathematically related.
Consider this figure for reference

So what about the uncertainty principle here?
 A: First, it is subtle to apply quantum mechanical reasoning on classical scales, i.e. we shouldn't think about this in a macroscopic "two balls and a string" way. Nevertheless, your question makes perfect sense quantumly: We assume that we start with two states subject to the constraint that their total momentum is zero. We may assume they start in states of definite momentum, but we need not (they could also be an entangled state of indefinite momentum subject to this constraint). We now make a position measurement on the first state and a momentum measurement on the second state. You seem to think that there's a violation of the uncertainty principle here because we now know both position and momentum of the first state exactly. It isn't, and here's why:
What you calculate is not the velocity of the first particle because quantum measurements change the state. When you measure the position of the first particle, you are changing its state to one where it has a definite position. It is no longer in the state that it had when it parted from the other particle, but the velocity you're computing for it relies on the idea of momentum conservation, i.e. nothing external having interacted with the first particle in the mean time, which is false due to the measurement. Therefore we don't know the velocity/momentum of the first particle after its position measurement.
If you do not measure the position of the first particle, then it will have the velocity/momentum you computed, but we don't know its position.
Either way, the uncertainty principle is not violated.
A: What is Heisenberg's Uncertainty Principle (HUP)?
$ΔxΔp>h/{2π}$
note, larger.
$h/{2π}$ is a very small number order of $10^{-15}$ evs, so the inequality is fulfilled  for all macroscopic observations , even for elementary particles traveling in a bubble chamber, see my answer to a related question here.
