Motion in a Plane: Types and Examples

The motion in a plane is generally referred to as the motion of the body in a two-dimensional plane. 

• In the case of plane motion, position, velocity, displacement, and acceleration of the particle have two components (say x and y).
• Examples of motion in a plane are circular motion, projectile motion, etc.

The different physical quantities in physics can be classified into two categories.

• They are called scalar and vector quantities. 
• There is a difference between both quantities. 
• The scalar quantity has magnitude whereas the vector quantity has both magnitude and direction. 
• Examples of scalar quantities are mass, density, work, speed, length, etc.
• Vector quantity represents both the magnitude and direction. 
• A vector quantity is represented by the symbol starting from bold-faced letters having an arrow over them.

Key Terms: Motion, Circular motion, Projectile motion, Velocity, Accelerated motion, Scalar and vector quantities, One-dimensional motion, Frame of reference, Equations of motion

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What is Motion in a Plane?

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Motion means a change in the position of a body with respect to time and with respect to a frame of reference.

• A reference point is needed to describe the motion of a body.
• The motion of the body can be in one dimension, two dimensions, or three dimensions.
• When the motion of the body is along the two dimensions, then the motion is said to be two-dimensional motion or motion in a plane.
• For a particle moving in a straight line direction of velocity and acceleration of the particle always comes along the same line.
• If there is an angle θ between velocity and acceleration vectors such that θ will not equal 0^o and 180^o then the particle will move along a curve, known as plane motion.

Motion in a plane

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Equations of Motion in a Plane

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The equation for the motion in a plane is given for both axes (x and y).

For the Y-axis, the equation will be.

v_y = u_y + a_yt

s_y = u_yt + 1/2a_yt²

v²_y = u²_y + 2a_ys

Here 

• v_y is referred to as the final velocity of the object in the y-direction.
• u_y = initial velocity 
• a_y = acceleration 
• t = time interval 
• s_y = displacement 

For the X-axis, the equation will be.

v_x = u_x + a_xt

s_x = u_xt + 1/2a_xt²

v²_x = u²_x + 2a_xs_x

Apart from this, there are different parameters of motion in a plane. They are interrelated to the motion of an object in 1-dimensional and 2-dimensional planes. 

• Distance
• Velocity
• Acceleration
• Displacement

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Relative Motion

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A frame of reference is required to describe the relative motion of a body.

• Relative motion occurs in one dimension as well as two dimensions in a plane.
• When the particular body has a certain velocity, then this velocity is with respect to the reference frame.
• For example, if a person is traveling in a bus and the bus is moving at a speed of 70 km/hr, then the speed according to another passenger sitting on the bus would be zero. 
• It shows that the bus is moving and it makes the person move while sitting. 
• It is known as relative motion.

Relative Motion in One-Dimension

Relative Motion occurs with an object while moving.

• When the body moves in a straight line, it is said to be one-dimensional. 
• This can happen when the body moves in the same direction or in the opposite direction. 
• A simple example of this is, if a person is traveling in a bus with a speed of 80 km/h, then the bus is moving in the forward direction and the trees outside would seem to be going in the backward direction.

Relative Motion in Two-Dimension

The concept regarding the motion of two different bodies is the same as for one dimension. 

• The velocity of body A can be identified with respect to B. 
• It can be assumed that body B is at rest and can give its velocity to A in the opposite direction.
• The velocities of both bodies are given as V_a and V_b.

To find out the velocity of A with respect to B, this equation can be used.

V_ab = V_a – V_b

The equation will be the same in order to find out the velocity of body B.

V_ba = V_b – V_a

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Types of Motion in a Plane

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On the basis of the direction of the motion, it is divided into various parts.

• There are different types of motion created on both axes in a plane.
• It can be understood with the help of day-to-day life examples.

Projectile Motion

It is the most common example of motion that occurs in a plane.

• It is known as projectile motion. 
• In a plane, the acceleration occurs in the vertical direction and it happens due to the force of gravity.
• Gravity is denoted with the symbol (g).
• Hence, the equation of motion is calculated separately for both axes. 
• Example of projectile motion is kicking a ball, tossing a coin, etc.

Oscillatory Motion

It is another form of motion in a plane.

• The to-and-fro movement of the object from its mean position is known as oscillatory motion. 
• It happens in the absence of friction force. 
• Some of the common examples of oscillatory motion are the simple pendulum, movement of spring, vibrating strings of musical instruments, etc.

Circular Motion

The motion occurs when there is a movement of a particular object along the circumference of the circle or in a circular path. 

• This is uniform in nature. 
• It has a constant angular rate of rotation with constant speed. 
• Some examples are the revolution of Earth, a car moving in a circular orbit, etc.

Accelerated Motion

This is another form of motion on a plane.

• It is defined as the rate of change of velocity with the change in position and time according to the speed and direction and is called accelerated motion. 
• Examples of accelerated motion are the falling of an apple, a vehicle moving on the road, etc.

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Examples of 2-D Motion in a Plane

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Motion can be seen every day. Motion is the movement of the body which occurs in a plane. It can be one - dimensional and 2 - dimensional. The examples of motion in the two-dimensional plane are given here 

• The motion of an ant on the floor or table.
• The motion of the Earth revolving around the Sun.
• Moving a boat in the river.
• Throwing a ball on the billiard table.

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Principle of Motion

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Motion occurs on the body if the external force acts upon it.

• It tends an object to move from its actual place.
• There are some principles or laws of motion given by the scientist named Isaac Newton.

They are discussed here. 

• When the body remains at rest or moves at a constant speed in a straight line, then it will remain at rest or keep moving in a straight path unless any external force acts upon the body.
• The second principle of motion states that the force on an object is equal to its mass, time, and its acceleration.
• The third principle states that when two objects interact with each other, they apply forces to each other of equal magnitude and opposite direction.

Read more: Force and Motion

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Things to Remember

• Motion is defined as the change in position of a body with respect to time.
• There are various types of motion executed by an object along the X and Y - axis.
• They are linear motion, circular motion, projectile motion, oscillatory motion, accelerated motion, etc.
• The motion occurs in either a straight path or a curved path, so the distance and displacement and their velocity are calculated.
• Linear motion is the movement of the body in a straight line whereas circular motion is referred to as the executing movement by the body in a circular path.
• The to-and-fro movement of the object from its mean position is known as oscillatory motion