Tag: Motion in 3 Dimensions

Frame of Reference | Motion in One Dimension

Motion in One Dimension

Frame Of Reference-

 

A frame of reference is a frame in which an observer sits and makes observations.

 

  • A Cartesian Coordinate System is attached with the frame of reference.
  • A clock is positioned in this system to measure time.
  • An observer is always considered to be present at the origin O.

 

 

At any time, the position of a particle is described with the help of its three position coordinates (x, y, z).

 

Position Vector-

 

Consider the particle is present at any point P in the space whose coordinates are (x, y, z).

 

 

The position vector of point P is a vector drawn from the origin O of the coordinate system to point P.

It is given by-

 

 

Types of Frame of Reference-

 

Frame of reference can be of two types-

 

 

  1. Inertial Frame of Reference
  2. Non-Inertial Frame of Reference

 

1. Inertial Frame of Reference-

 

  • A frame of reference which is either at rest or moving with constant velocity is known as inertial frame of reference.
  • Newton’s laws are valid in this frame.

 

2. Non-Inertial Frame of Reference-

 

  • A frame of reference moving with some acceleration is known as non-inertial frame of reference.
  • Newton’s laws are not valid in this frame.

 

Rest and Motion-

 

A body is said to be at rest if it does not change its position with time.

A body is said to be in motion if it continually change its position with time.

 

  • Rest and motion are relative terms.
  • When a particle moves, its position coordinates change with time.
  • At one time, one or two or all three position coordinates may change.

 

Accordingly, we have following three types of motion-

 

 

  1. Motion in one dimension
  2. Motion in two dimensions
  3. Motion in three dimensions

 

1. Motion in One Dimension-

 

The motion of a particle is said to be in one dimension if

only one out of the three coordinates specifying the position of the particle change with time.

 

  • In such a motion, the particle moves along a straight line.
  • One dimensional motion is sometimes known as rectilinear or linear motion.

 

Examples-

 

Examples of motion in 1 dimension are-

  • A car moving on a straight road
  • A ball thrown vertically up
  • A stone dropped into a well
  • A ball dropped from a certain height above the ground

 

2. Motion in Two Dimensions-

 

The motion of a particle is said to be in two dimensions if

any two out of the three coordinates specifying the position of the particle change with time.

 

In such a motion, the particle moves in a plane.

 

Examples-

 

Examples of motion in two dimensions are-

  • Projectile motion
  • Circular motion
  • A carom coin rebounding smoothly from the side of the board
  • Motion of a boat in a river
  • Motion of an insect on a floor

 

3. Motion in Three Dimensions-

 

The motion of a particle is said to be in three dimensions if

all the three coordinates specifying the position of the particle change with time.

 

In such a motion, the particle moves in a space.

 

Examples-

 

Examples of motion in three dimensions are-

  • Random motion of a gas molecule
  • A kite flying in the sky
  • A bird flying in the sky

 

Terms Regarding Motion-

 

We discuss the following parameters in detail while studying the motion of any particle-

 

 

  1. Distance
  2. Displacement
  3. Speed
  4. Velocity
  5. Acceleration

 

PRACTICE PROBLEMS BASED ON REST AND MOTION-

 

Problem-01:

 

“Rest and Motion are relative terms.” Justify this statement.

 

Solution-

 

  • It is rightly mentioned that the rest and motion are relative terms.
  • This is because they depend on the observer’s frame of reference.
  • A body at rest with respect to one observer might be in motion with respect to another observer.
  • A body in motion with respect to one observer might be at rest with respect to another observer.

 

Consider the following examples-

 

Example-01:

 

  • A person sitting in a moving train is at rest with respect to fellow passengers.
  • While person sitting in a moving train is in motion with respect to a person standing on the platform.

 

Example-02:

 

Consider the following scenario-

  • Two persons A and B are standing in a truck moving with velocity v.
  • Person C is standing on the ground.

 

 

Here,

  • A and B are at rest with respect to each other.
  • A and B moves with velocity V in the positive X direction with respect to C.
  • C moves with velocity V in the negative X direction with respect to A and B.

 

Problem-02:

 

Is it possible to achieve state of absolute rest or absolute motion?

 

Solution-

 

  • A body at rest with respect to all other bodies is called in state of absolute rest.
  • A body moving with respect to all other bodies is called in state of absolute motion.

 

Talking about absolute rest,

  • It is impossible to achieve the state of absolute rest.
  • This is because all heavenly bodies are moving with respect to each other.

 

Talking about absolute motion,

  • It is impossible to achieve the state of absolute motion.
  • This is because there exists no reference point which is absolutely fixed in the space.

 

To gain better understanding about Rest and Motion,

Watch this Video Lecture

 

Next Article- Distance and Displacement

 

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