title: Changing an object's angle and velocity by a given angle and velocity
body: <p>I'm working on making a simple-ish physics engine for my game, but I'm not sure how to do the math on part of it.</p>
  
  <p>How I currently have my engine setup is as follows:</p>
  
  <p>Every object affected by physics has a "velocity" which consists of it's angle and force.</p>
  
  <p>Each object has an "push" function that takes a new velocity and affects the current velocity with it.</p>
  
  <p>The angle of velocity is global. So moving towards the right of the screen will always have an angle of 90. For example, if an object's velocity has a force of 10 and an angle of 90 and I adjust said velocity by an angle of 180 with a force of 10 it'll get a new velocity. This velocity will have a force of 0, so it's angle is irrelevant. Or if I take that earlier velocity with an angle of 90 and a force of 10 and adjust it by a velocity with an angle of 180 and a force of 5, the resulting velocity will have the angle of 90 but the force of 10.</p>
  
  <p>I'd provide more examples and test cases, but I don't know how to figure out the velocity of an object moving with a force of 13 and an angle of 32 when it's pushed by a velocity of 5 at an angle of 193.</p>
  
  <p>TLDR;</p>
  
  <p>I have objects with angular momentum. I want to be able to "push" them with a given force and angle and have them adjust accordingly(taking their current force and angle into account).</p>