Dimensional motion as defined in a College Physics Book is movement of an object in certain planes. Motion in physics can be in one, two or three dimensions.
One dimensional motion in the College Physics Book. Engineering in Kenya has more articles
One dimension in motion means that the body is moving in only one plane and that therefore implies that the body moves in a straight line. If one rolls a marble on a flat surface and in a straight line (not easily done), the marble would be undergoing one dimensional motion as defined in the College Physics Book.
There are four acute variables which when put together in an equation describe one dimensional motion. These are;
ü Velocity (V);
- Initial velocity (u)
- Final Velocity (v)
ü Acceleration (a)
ü Displacement (s) and
ü Time elapsed (t).
The equations below show the relationship between these variables in one dimensional motion;
- V2 = u2 + 2as
- V = u + at
- S = ut + 1/2 at2
- Average velocity = (v + u)/ 2
With these equations found in the College Physics Book, one can calculate on any form of motion in a straight e.g. the acceleration of a car.
Two and three dimensional motion in the College Physics Book
The two forms of dimensional motion in the College Physics Book are better defined when divided into scalar and vector quantities. The difference between scalar and vector quantities as put in the College Physics Book is in the terms ‘magnitude’ and ‘direction’. Magnitude defines how much of the quantity is there. Direction is the way in which a certain magnitude moves. Scalars are physical quantities which are defined by their magnitude only. Scalars include mass, speed, volume, distance etc. Vectors are physical quantities defined by their magnitude and direction. Vectors include velocity, acceleration, force, momentum etc.
Vector Addition in the College Physics Book
Parallelogram law of vector addition
If one was to represent two vector quantities using the two adjacent sides of a parallelogram, the diagonal joining the two ends of the initial vectors becomes the resultant vector. The resultant vector combines the effects of the two initial vectors.
Resolution of vectors
Vectors as defined in the College Physics Book have components, and it is often advisable to split a vector into its components. The splitting of a vector into its constituent components is what is termed as the resolution of the vector. The initial vector forms the resultant of these components. When the vector components are perpendicular to each other, they are named the rectangular components of a vector.
Rectangular Components of a Vector
With the components of the vector at right angles, one can do mathematics on them as in the College Physics Book. This allows for the solving of many life problems. After all, the best part about physics is that it can be employed to solve real world issues/problems. Since it is hard to use vector notations on computer, we shall use bold letters to denote vector quantities and normal letters to denote scalar quantities. Subscripts of ‘x’ and ‘y’ will be used to show that the motion is either along the x or the y axes.
Let Ax and Ay be the rectangular components of the vector A
Then; A = Ax + Ay
This shows that the vector A is the resultant vector of vectors Ax and Ay, and Ax and Ay are the components.A is the magnitude of the vector A and similarly, the Ax and Ay are the magnitudes of the vectors Ax and Ay. We can therefore say that:
A = √(Ax + Ay)
Given that the angle made by the vector A and the x axis is Q;
Q = tan-1 (Ax / Ay)
Laws of Motion in the College Physics Book
The first law in Newton’s Laws of Motion
The law in the College Physics Book is stated as follows: – a body tends to remain at rest or in uniform motion in a straight line (with constant velocity) unless acted upon by a resultant force. The tendency of a body to continue in its initial state of motion (a state of rest or a state of uniform motion in a straight line) is called inertia in Newton’s Laws of Motion.
The second law in Newton’s Laws of Motion
The law in the College Physics Book is stated as follows: – if a net force acts on a body, it will cause an acceleration of that body. That acceleration in the direction of the net force and its magnitude is proportional to the magnitude of the net force and inversely proportional to the mass of the body i.e.
a α F/m, so that F = kma.
This vector equation is a relation between vector quantities F and a and thus applies to the x, y and z planes of the Cartesian plane. Motion defined by the three planes of the Cartesian plane is termed as three dimensional in the College Physics Book.
The third law in Newton’s Laws of Motion
The law in the College Physics Book is stated as follows: – action and reaction forces are always equal and opposite i.e. when a body in Newton’s Laws of Motion exerts a force on another, the second exerts an equal, oppositely directed force on the first. i.e.
F α R