Finding change in momentum in 2-dimensions.

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SUMMARY

To calculate the change in momentum for an object in two dimensions, one must first determine the initial momentum vectors in both the x and y directions. The final momentum vectors are then calculated similarly. The change in momentum is found by applying vector subtraction to these momentum vectors, specifically using the formula for magnitude: Δp = √((p₁x - p₂x)² + (p₁y - p₂y)²). This approach effectively utilizes the Pythagorean theorem to quantify the difference between initial and final momentum.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with momentum concepts in physics
  • Knowledge of Cartesian coordinates
  • Basic proficiency in applying the Pythagorean theorem
NEXT STEPS
  • Research "vector subtraction Cartesian coordinates" for practical examples
  • Study the concept of momentum in physics, focusing on vector quantities
  • Explore advanced applications of the Pythagorean theorem in physics
  • Learn about momentum conservation in two-dimensional collisions
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Physics students, educators, and anyone interested in understanding momentum changes in two-dimensional motion.

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To find the momentum change for an object in 2 dimensions do I find the initial momentum in both the x & y direction then apply the Pythagorean theorem, and then do the same for the final momentum and then find the difference between the two?
 
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Momentum is a vector, so when you're looking for the change in momentum you're really looking for the difference between the initial an dthe final momentum vectors. Google for "vector subtraction Cartesian coordinates" and you'll find plenty of examples.
 
If you just want the magnitude,
##\Delta p = \sqrt{(p_{1x} - p_{2x})^2 + (p_{1y}-p_{2y})^2}##
 

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