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Kinematics: frames and vectors
Styding the motion of objects
The whole goal of mechanics is to study the motion of objects. This is not an easy task and it requires some appropriates tools! Defining the tools to describe motion is the subpart of mechanics called “kinematics”, that we will study now.
The need to define a frame.
If you think about it, you will realise that it is absolutely meaningless to talk about the motion of bodies without refering with respect to what they are moving. This fact, perhaps a bit confusing, means that daily sentences as “I go in straight line at 50 km/h” are absolutely meaningless! Indeed, you are moving in straight line at 50 km/h, with respect to the road! With respect to the Sun, you are doing a much more complicated motion composed of the rotation of Earth on itself, of our planet around the Sun and of yourself on the road! Defining which object we are studying the motion is called a choice of frame. The object considered as motionless (the road, the sun …) is hence called – you guessed it – the frame.
Axis/coordinates: quantifying motion
Once you defined a frame, you a way to quantify the position of a moving body relative to that frame. This is done by choosing some axis, which are like gigantic rulers on which you can measure the position. For objects moving in the three dimensional space, three axis (i.e. three rulers) are required to completely label the object (see the wonderful picture of the kiwi below).
A flying Kiwi in the position $(x=5,y=4,z=3)$ with respect to the reference frame of the road.