Know about motion in two Dimension

As defined by physics, motion is the phenomenon in which an object changes its position over time. Mathematical terminology like displacement, distance, velocity, acceleration, speed, and time are used to explain motion. An observer is given a frame of reference, and the change in position of the body in relation to that frame is tracked over time. Kinematics is the discipline of physics that studies motion without regard to its source, while dynamics is the branch that analyses forces and their effects on motion. Absolute motion cannot be determined since there is no absolute frame of reference.As a result, everything in the universe can be thought of as being in motion.

Displacement

Displacement is a one-dimensional variable that represents the gap between two known positions. It is also known as length or distance. In the SI (International System of Units) units, the metre is the standard unit of displacement.

Displacement = x=xf-xi

Here,

xf = Final Position

xi = Initial Position

Velocity

Velocity is considered as a Physical Vector Quantity. Velocity has both magnitude and direction also. Velocity in calculus is defined as the first derivative of the position with respect to time period. Velocity is also defined as the rate of change in the position of an object w.r.t time.

Unit of velocity metre per second which is determined as m/s.

Velocity = Displacement/Time

Velocity = (Final Position – initial position)/Time

Acceleration

Because acceleration has both magnitude and direction, so it is a vector quantity. It is also known as the first derivative of velocity with respect to time or the second derivative of point with regard to time.

acceleration = (change in velocity)/time

Laws of Motion:

The laws of motion are three assertions which define the relationship between the forces acting on a body and its motion. They form the foundation of classical mechanics. Isaac Newton, an English physicist and mathematician, was the first to express them.

Newton ‘s three classical mechanics laws:

Newton’s First Law: According to Newton’s first law of motion, things cannot initiate (or initiate), stop, or change direction on their own and for this they need some external force. 

Newton’s Second Law: Relationship between force and acceleration is the subject of Newton’s second law of motion. S second law of motion is that  the acceleration of an item caused by a net force is proportional to its magnitude, in the same direction of the force, and inversely to the mass of the object.

Newton’s Third Law: When one body exerts force on another, Newton’s third law of motion states that every action has an equal and opposite response.

As a result, every action has an equal and opposite reaction, according to the third rule of motion. All natural forces act in pairs, according to this theory.

Motion in two dimension:

When we talk about motion, we should talk about it in terms of a fixed frame of reference. When we view two objects in the sky, one a moon and the other a cloud, one’s eyes are drawn to the clouds due to the relative larger size of clouds (as seen by us), and therefore one’s frame of reference is fixated on the clouds. It’s as if we’re sitting on the clouds themselves, which appear to be motionless to us, and the sensation arises that the moon is moving across this fixed cloud in the opposite direction as the clouds’ motion. When we travel on a road, we observe things going backwards in the same way.

What is a frame of reference in a two dimensional motion?

A frame of reference is a collection of coordinate axes that is fixed with regard to a space point (a body or other item can also be treated as a point mass and therefore become a site for fixing a reference frame), which we have arbitrarily chosen based on our observer’s needs. It is made up of two different parts:

(i) The origin, or the body on which the spectator appears to be sitting to witness the motion.

(ii) A coordinate system fixed to this body, allowing whatever is being viewed to be measured or mathematically calculated using the coordinates of space points defined by a unique set of coordinates (x, y, z).

To fix a frame of reference, one must first fix the origin to a selected space point, then the coordinate system on top of that. We have completed the exercise of fixing the frame of reference after the origin and coordinate system have been fixed, and we may now proceed to solve problems and analyse other parameters such as location, velocity, and accelerations as functions of time.

One thing to keep in mind is that the earth becomes a natural choice for the frame of reference because it is quite easy to imagine motion in relation to it in most circumstances. We innocently (even in early childhood) refer to and observe all motion phenomena with relation to the earth just because it is a routine in our everyday lives.

The coordinate system will be applicable while defining any motion. Because we will refer to all points in this coordinate system fixed on that body, this is called a frame of reference. Remember that the three axes of the coordinate system, namely the X-axis, Y-axis, and Z-axis, as well as the origin, are fixed on the body, and the origin coordinates are (0, 0, 0). It’s the point where we presume the observer is sitting, watching the motion in the relevant reference frame.

Choosing a Reference Frame:

Let us return to the subject of motion. Do you believe that everything you see moving is moving, and everything you don’t see moving is at rest? On the road, like autos! You should be aware that motion or motion observation is far from simple!

Let’s look at an example: The moon in the sky at night! You may notice the moon passing through the clouds to the east or west at night. And on some nights, it doesn’t even move! We’ll all agree that it’s not possible. It cannot alternate between moving faster and slower, as well as becoming still at times. So, what exactly is this phenomenon? It’s the reference point.

Conclusion:

One of the most ubiquitous phenomena we encounter in our daily lives is motion. A moving car, a child jogging down the street, or a fly flying through the air, for example, are all considered to be in motion. In general, a body is considered to be in motion if its location varies in relation to a reference point and time. The motion of a particle can vary depending on its path, such as projectile motion, rectilinear motion, rotating motion, and so on. Apart from this motion occurs in more than one dimension as described above.