The Description of Motion: Kinematics
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Part I
2
The Description of Motion: Kinematics Definition of Motion. Frames of Reference
Motion refers to a change in the location of an object with time, as seen from a fixed, rigid frame, the “frame of reference”. This supplementary specification is quite essential. We can see this from a randomly-chosen example: A bicyclist looks down at her feet and sees them moving in circular paths with the pedals. An observer standing on the sidewalk sees a very different picture of the motion of the bicyclist’s feet; for her or him, the feet follow a wavelike path, namely the cycloids which are sketched in Fig. 2.1. The rigid solid body which is our frame of reference for the description of motion in the rest of this chapter is the earth or the floor of the room where we are located. We leave the daily rotation of the earth out of consideration. (In reality, we are practicing physics on a large carousel. The earth is also not really rigid, but instead is deformable.) Later, we will occasionally change the standpoint of our observations, i.e. our frame of reference. We will take the earth’s rotation into account in some discussions, and sometimes also the deformation of the earth. This will always be mentioned explicitly. Otherwise we would have an endless confusion, especially when we treat rotational motions. For the description of all motions, also called kinematics, we require the concepts of velocity and acceleration. We will begin with them.
“Otherwise we would have an endless confusion, especially when we treat rotational motions”.
Figure 2.1 The path followed by the pedals of a bicycle as seen by a station-
ary observer
© Springer International Publishing Switzerland 2017 K. Lüders, R.O. Pohl (Eds.), Pohl’s Introduction to Physics, DOI 10.1007/978-3-319-40046-4_2
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2 The Description of Motion: Kinematics
Part I
2.2
Definition of Velocity. Example of a Velocity Measurement
Suppose that an object moves through a distance l within the time interval t. Then we define um D
Distance moved l Time interval t
(2.1)
as the mean velocity along the direction of the distance l. This quotient changes in general if one successively decreases the distance l. However, the changes gradually decrease to below the precision of the measurements. The value of um which is then measured, which depends only on the starting point, is denoted as the velocity u at the starting point. Mathematically, one thus finds the velocity u as the limiting value of um by taking the limit t ! 0. The symbol is conventionally replaced by d, giving for the definition of the velocity
uD
dl dt
(2.2)
i.e. the differential quotient of the distance travelled divided by the time interval. This definition in many cases requires the measurement of rather short times. As an example, we consider the measurement of the muzzle velocity of a bullet from a pistol. Figure 2.2 shows a suitable setup for this measurement. The distance interval l is fixed by two thin cardboard disks; its length could be for example 22.5 cm. The time measureme
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