In view of the coronavirus pandemic, we are making LIVE CLASSES and VIDEO CLASSES completely FREE to prevent interruption in studies
Physics > Motion in a Plane > Introduction to Motion in a Plane
Motion in a Plane

Introduction to Motion in a Plane

The physical quantities like work, temperature and distance can be represented in day to day life wholly by their magnitude alone. However, the relation of these physical quantities can be explained by the laws of arithmetic. In order to represent physical quantities like acceleration, displacement, and force, the direction is equally essential along with the magnitude. Let us now study Plane Motion.

Suggested Videos

Play
Play
Play
Arrow
Arrow
ArrowArrow
Scalar and vector quantities
Motion in plane with constant acceleration
Uniform Circular Motion
Slider

 

Introduction to Plane Motion

Velocity refers to a physical vector quantity which is described by both magnitude and direction. The magnitude or scalar absolute value of velocity is referred to as speed. As stated by the Pythagorean Theorem, the magnitude of the velocity vector is given by –

| v | = v =  √ ( vx ²+ vy ² )

Acceleration is defined by the rate of change of velocity of an object with respect to time. Numerically or in terms of components, it can be presented as –

ax =   \( \frac{d}{dt} \)   vx

a=    \( \frac{d}{dt} \)   vy

Motion in a Plane

Motion in a plane is also referred to as a motion in two dimensions. For example, circular motion, projectile motion, etc. For the analysis of such type of motion, the reference point will be made of an origin and the two coordinate axes X and Y.

Motion in a plane refers to the point where we consider motion in two dimensions as only two dimensions makes a plane. Here, considering the above, we take two axes into consideration – generally X-axis or Y – axes. In an attempt to derive the equation of the motion in a plane, we must know about motion in one direction.

Equations of Plane Motion

The equations of motion in a straight line are:

v = u+at

s = ut+1/2 at²

v2 = u² + 2as

Where,

  • v = final velocity of the particle
  • u = initial velocity of the particle
  • s = displacement of the particle
  • a = acceleration of the particle
  • t = the time interval in which the particle is in consideration

In a plane, we have to apply the same equations separately in both the directions: Y axis and Y-axis. This would give us the equations for motion in a plane.

vy   = u+ ayt

sy = ut +1/2 ay

  = u²y+2as

Where,

  • vy = final velocity of the particle in the y-direction
  • uy = initial velocity of the particle in the y-direction
  • sy = displacement of the particle in the y-direction
  • ay = acceleration of the particle in the y-direction

Similarly, for the X-axis :

vx = u+ at

sx=  ux t+1/2 ax

v²x = u²x+2 axs

Where,

  • v= final velocity of the particle in the x-direction
  • ux = initial velocity of the particle in the x-direction
  • sx= displacement of the particle in the x-direction
  • a= acceleration of the particle in x-direction

You can download Motion in a Plane Cheat Sheet by clicking on the download button below
motion in plane

Projectile Motion: Plane Motion

One of the most common examples of motion in a plane is Projectile motion. In a projectile motion, the only acceleration acting is in the vertical direction which is acceleration due to gravity (g). Therefore, equations of motion can be applied separately in the X-axis and Y-axis to find the unknown parameters. Plane Motion

The above diagram represents the motion of an object under the influence of gravity. It is an example of projectile motion (an special case of motion in a plane).

Examples of  Two-Dimensional Plane Motion

  •  Throwing a ball or a cannonball
  •  The motion of a billiard ball on the billiard table.
  •  A motion of a shell fired from a gun.
  •  A motion of a boat in a river.
  •  The motion of the earth around the sun.

Solved Examples for You

Question 1.  The state with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:

  1. adding any two scalars,
  2. adding a scalar to a vector of the same dimensions,
  3. multiplying any vector by any scalar,
  4. multiplying any two scalars,
  5. adding any two vectors,
  6. adding a component of a vector to the same vector.

Solution.

  1. Meaningful; The addition of two scalar quantities is meaningful only if they both represent the same physical quantity.
  2. Not Meaningful; The addition of a vector quantity with a scalar quantity is not meaningful.
  3. Meaningful; A scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse.
  4. It’s meaningful; A scalar, irrespective of the physical quantity it represents, can be multiplied by another scalar having the same or different dimensions.
  5. Meaningful; The addition of two vector quantities is meaningful only if they both represent the same physical quantity.
  6. Meaningful; A component of a vector can be added to the same vector as they both have the same dimensions.

Question 2: Read each statement below carefully and state with reasons, if it is true or false:

(a) The magnitude of a vector is always a scalar,
(b) each component of a vector is always a scalar,

Solution :

(a) True. The magnitude of a vector is a number. Hence, it is a scalar.
(b) False. Each component of a vector is also a vector.

Share with friends

Customize your course in 30 seconds

Which class are you in?
5th
6th
7th
8th
9th
10th
11th
12th
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
tutor
tutor
Ashhar Firdausi
IIT Roorkee
Biology
tutor
tutor
Dr. Nazma Shaik
VTU
Chemistry
tutor
tutor
Gaurav Tiwari
APJAKTU
Physics
Get Started

2
Leave a Reply

avatar
2 Comment threads
0 Thread replies
1 Followers
 
Most reacted comment
Hottest comment thread
2 Comment authors
optionalAWAIS Recent comment authors
  Subscribe  
newest oldest most voted
Notify of
AWAIS
Guest
AWAIS

which situation we use vectors subtraction?

Aditya
Guest
Aditya

When we give same magnitude but different direction then we use the substraction of method R bar=[p]-[Q] when its is whenever theta =180°

optional
Guest
optional

What are there applications in real life?

Stuck with a

Question Mark?

Have a doubt at 3 am? Our experts are available 24x7. Connect with a tutor instantly and get your concepts cleared in less than 3 steps.
toppr Code

chance to win a

study tour
to ISRO

Download the App

Watch lectures, practise questions and take tests on the go.

Get Question Papers of Last 10 Years

Which class are you in?
No thanks.