Patrick Teaches Physics

When solving physics problems we always have the benefit of choosing our frame of reference.  Not only can we chose where the origin of our coordinate is, but we can also chose which part of our system is stationary.  Consider the following simple kinematic problem: A car is travelling along, and we want to know how long it takes to travel some distance.  We can plug numbers into a kinematic equation and get the answer.  If the car is accelerating then the problem is mathematically a bit more fiddly (a quadratic equation, or do it in two steps with two equations) but it's not conceptually harder. But now consider a similar problem with two moving bodies: Now there's two cars at different speeds, and the question is: how long will it take the red car to overtake the blue car?  This looks rather harder because the distance the red car has to travel is not immediately clear.  But that's only because of our choice of reference frame, which up till now has been ...

There is probably no habit that a physics student can learn that has a higher return on investment than including units in calculations.  To see what I mean, consider this routine momentum calculation: Can't remember the units for momentum?  Don't have to, they're already there on the page!  This is particularly useful if you are not using base SI units: you don't get confused or forget which units you're using along the way. Better than that, this method gives us a powerful way to check our own calculations.  In the next example, I calculate the time required for an object to fall a distance: What!?  Metres per second isn't a unit of time!  I've made a silly mistake re-arranging the equation; the kind of mistake it's easy for a student to make, and even pros do occasionally.  But pros tend to catch such mistakes because they have kept track of the units.  That means we can fix it: The unit being right gives us some confidence the number is right....