Playing marbles on ice (part I)

5 min readMar 28, 2022

Recap of the previous story: https://medium.com/@AstroFederica/a-small-point-to-describe-the-universe-a6087f104230

Various types of motion
The point particle
The Cartesian plane as reference system
Coordinates and vectors
Difference between kinematics and dynamics

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If you wish to read this article in full webcomic format, you can follow this link: https://www.webtoons.com/en/challenge/physictionary/playing-marbles-on-ice-part-i/viewer?title_no=748139&episode_no=2 .

Scalar and vector quantities

In kinematics we can represent the physical quantities of position, time, speed and acceleration on the Cartesian axes. They are fundamental for describing motion. As Leo and Mia will highlight below, we distinguish between scalar quantities, such as distance and time, and vector quantities, like velocity and acceleration.

The difference is that:

position and time are numerical values accompanied by a unit of measurement, which indicate where and when a certain phenomenon occurs.
speed and acceleration, on the other hand, are vectors: what distinguishes them is not only their length (called magnitude and indicated by a number), but also a direction and a head.

In physics, other examples of scalar quantities are the mass, temperature and pressure, density and volume of an object, while other important vector quantities are the forces that act ons bodies and causes their motion.

The uniform rectilinear motion

The simplest of all is rectilinear motion, occurring along a linear trajectory.

In daily life we observe an object in motion slows down due to the force of friction. For example, a ball rolling on grass or sand stops after a few seconds. We will deal with friction in the chapter about dynamics. For now we will consider examples where the frictional force is negligible. Let’s think for example of a marble rolling on ice: this surface is so slippery that we can consider the motion of the marble as frictionless. The ball proceeds without decelerating and therefore at a constant speed. This concept is summarised in the figure below.

The law of motion

When the speed is constant, the point particle moves in a uniform rectilinear motion. In this case the speed is the ratio between the displacement and the time taken to travel it.

On the Cartesian plane, equal displacements correspond to time intervals of equal duration. This translates into a linear relationship between space, time and speed, i.e. in a straight line. This relationship is called the law of motion.

Physics uses the language of math to describe the law of motion. The uniform rectilinear motion is modelled with a function called line, whose equation is:

y = mx+q.

In this context, y corresponds to space, the variable which depends from time that runs along the x-axis.
The quantity mx corresponds tothe product between velocity and time, vt, as reported in the figure above.
m is the slope (or angular coefficient) of the line. It represents the inclination of the line from the horizontal axis. In the uniform rectilinear motion, it corresponds to the velocity. The steeper is the line, the higher the speed!
What about q? If mx=vt is the space traveled within a certain amount of time, q is the initial position which sums up to the final one. If the initial position is at the origin of the Cartesian axes, then it will be equal to zero, exactly as in the figure below.

In this type of motion, the speed is always the same and so it represents the constant ratio between portions of space and the time intervals needed to cover them. In this scenario we say there is a direct proportionality between space and time.

Comparison of motions

We can use this linear relationship between space, time and velocity to compare two motions. A working example is proposed and solved in the comics below.