Motion in a Plane

Introduction

Motion in a plane refers to motion in two dimensions because a plane has just two dimensions. In light of the previous, we’ll look at two axes: the X-axis and the Y-axis. To establish the equation of motion on a plane, we must first understand motion in one direction.

To understand motion in a plane, let’s discuss the following parameters of motion:

• Distance– It is the total distance covered by a body from the starting point to its terminating point
• Velocity– It is defined as the rate of change of an object’s position to time in a particular direction
• Displacement– It is the shortest distance a body covers to travel from one point to another

Motion Parameters in a Plane

We mentioned three motion characteristics in the previous heading: distance, velocity, displacement and acceleration. Let’s take a closer look at the concept of motion in a plane: 

Following are the important parameters of motion in a plane to understand the topic easily:

• Distance: Distance can be described as the length from one destination to another. We won’t know which direction we’re travelling on the train because it’s a scalar physical quantity; all we’ll know is the distance we covered from one place to another
• Time: Because we move with time, we may use it to calculate an object’s velocity and acceleration; however, because time is a scalar variable, we only know how long it will take us to go from one place to another, not which direction the train will travel
• Velocity: Velocity, a physical quantity, describes the magnitude and direction of a moving item. A velocity depicts how the rate of change of an object’s position to a frame of reference and time can be expressed. Well, it may appear tough because velocity is the speed of an object in a specific direction
• Displacement: It is a physical number that specifies both the size and direction of a body’s motion; however, it is the minimum distance a body can travel to reach another point

Plain Motion

We already learn that velocity is a vector quantity, hence the magnitude of the velocity vector is determined by Pythagoras theorem:

We measured the velocity along both axes and then used the Pythagoras theorem to calculate the magnitude of a velocity vector because we are discussing motion in a plane.

v =v =vx2+vy2…. (1)

We get the following two equations for acceleration along both axes:

ax = dvxdt

ay = dvydt

Two quantities that are essential to know while learning motion in a plane are:

Scalar quantities

Scalar quantities are those that have merely a magnitude but no direction. For instance, mass, length, duration, speed, temperature, and so forth.

Vector Quantities: 

These are quantities that have both a magnitude and a direction and follow vector laws such as addition, multiplication, and division. Displacement, velocity, acceleration, force, momentum, and so on are some examples.

The two main motions in a plane are as follows:

Projectile Motion:

Projectile motion is the name given to someone who, after being hurled into space with a certain initial velocity, moves through space under the pull of gravity alone, without the aid of any motor or fuel. The trajectory of a projectile is the path it takes.

Circular Motion:

When a body moves in such a way that it stays at a constant distance from a given point, it is said to be moving in a circular motion. The fixed distance is known as the circular path’s radius, and the fixed location is known as the circular path’s centre.

Uniform Circular Motion– When an object moves in a circular path at a constant speed, it is said to be in a uniform circular motion. The object’s motion is referred to as uniform circular motion.

ac = v2/R is the magnitude of its acceleration.

Here v is linear velocity of the object

R is the radius of circular path

ac always points in the direction of the circle’s centre.

Angular Displacement – 

The angle swept by the radius vector of a particle travelling on a circular route is referred to as the particle’s angular displacement. The angle whereby a point rotates around a centre or a given axis in a specified sense is known as angular displacement of a body. When a body rotates about its axis, the motion cannot be treated as a particle because, in a circular motion, the velocity and acceleration change at every given instant.

Conclusion:

To sum up, everything we have learnt till now, we would say that the term “motion in a plane” refers to motion in two dimensions. A few examples include circular motion, projectile motion, and so on. The origin and the two coordinate axes, X and Y, will serve as the reference point for such motion analysis. The main parameters of plain motion are distance, time, velocity and displacement.