Introduction:
In mechanics(motion, force, etc.), we come across various measurable, derivable and formulating quantities. To measure or calculate a particular set of quantities, you have to understand which category they belong to. In this session, we will discuss and understand those quantities by which we can calculate the motion.
Mainly we consider a quantity as
- Scalars
- Vectors
Explanation:
Scalar Quantity:
Scalars are the physical quantities that have only magnitude but not direction.
Scalars have only value but not direction.
For example, a car is moving at a speed of 35 m/s.
Here only the value of the speed is mentioned as 35 m/s, but it is not said in which direction the car is moving.
Examples of Scalar Quantity:
- Speed
- Distance
Vector Quantity:
A vector that has both directions as well as magnitude.
Example: A car is moving with a velocity of 35 m/s in the east direction.
Here unlike the scalar, the value and the direction are mentioned.
If we consider coordinates such as the x-axis and Y-axis, usually the direction is mentioned as positive or negative X-axis as well as positive or negative Y-axis.
Examples of Vector Quantity:
- Linear momentum
- Acceleration
- Displacement
Position Vectors
Consider using the coordinates say plane (2-dimension) or space (3-dimension).
Say there is a vector P present in the space, how can we locate the vector?
Using the position vector or representing the vectors in the Space by using some coordinates, we can say the position of the vector.
Let us consider i, j, k as the vectors coordinates for the axis (x, y, z). As we are taking the position vector in space, it has three dimensions (x, y, z).
Therefore,
The position vector
usually vector are denoted with “^” then,
Where,
= unit vector along x-direction.
= unit vector along the y-direction.
= unit vector along z-direction.
Where a, b, c are coordinates for x, y, z.
Using this equation, we can find the position vector in the given instance of time.
Displacement Vector:
In the formula mentioned earlier, we considered that the position vector is not moving, and it is at one point at the instance of time. What if the vector is moving from one point to another in the case of time?
We have to consider the displacement vector if the vector moves from one point to another in time.
Suppose a vector P is in position A in time t1 and moved to the position B in time t2. To find the position of the vector at different points at different instances of time,
we have,
at position A the vector
Therefore, position vector
is given by
Displacement:
Let us consider a person moving from his home to the park.
Assume his home is at point A and playground is at point B.
Displacement is defined as the path or length from the initial point to the final point. The displacement units are meters(m) in the SI system and centi-meter(cm) in the CGS system.
Note: Displacement is a vector quantity; it also should have direction along with the magnitude.
Example:
A car is moving from point A to point B, the displacement is 15 m in positive x-direction and moving from point B to point C 10 min negative x-direction. A B and C are colinear (which are in the same line).
What is the total displacement?
Displacement from A to B is 15 m in positive x-direction so consider it as +15 m.
Displacement from B to C is 10 m in negative x-direction so consider it as -10 m.
Total displacement = +15 m+(–10 m)
Displacement = +5 m towards positive × axis
Displacement = Final Position-Initial
Position=Change in position
We can say
Time and Time Interval:
Time is considered between the events. Time plays a very vital role in physics, especially in mechanics.
Unit of time is seconds(s) in both SI and CGS systems.
In physics, time appears as” rate”, like the rate of change.
Time interval is the phenomenon where we consider the events happening and changing with time.
Example: The time interval for traveling from one place to another place.
We can express time intervals for any occasion and any outcome.
Let us say an event started at the time t1 and completed at time t2.
So, the change in time is given by t = t2 – t1
Summary:
- Scalars: Scalar quantity is defined as the physical quantity with magnitude and no direction.
- Vectors: A vector quantity is defined as the physical quantity that has both direction as well as
magnitude. - Position Vectors: The position vector is used to specify the position of a certain body.
The position vector
usually vector is denoted with “^” then.
- Displacement Vector: The change in the position vector of an object is known as the displacement vector
Therefore position vector
- Displacement: Displacement is defined as the path or length from the initial point to the final point. Units of the displacement are meters(m) in the SI system and centi-meter(cm) in the CGS system.
Note: Displacement is a vector quantity; it also should have direction along with the magnitude.
- Time and Time Intervals: Time is considered between the events, time plays very vital role in
physics, especially in mechanics. - Unit of time is seconds(s) in both SI and CGS systems.
- Time interval is the phenomenon where we consider the events happening and changing with
time.
Related topics
Different Types of Waves and Their Examples
Introduction: We can’t directly observe many waves like light waves and sound waves. The mechanical waves on a rope, waves on the surface of the water, and a slinky are visible to us. So, these mechanical waves can serve as a model to understand the wave phenomenon. Explanation: Types of Waves: Fig:1 Types of waves […]
Read More >>Dispersion of Light and the Formation of Rainbow
Introduction: Visible Light: Visible light from the Sun comes to Earth as white light traveling through space in the form of waves. Visible light contains a mixture of wavelengths that the human eye can detect. Visible light has wavelengths between 0.7 and 0.4 millionths of a meter. The different colors you see are electromagnetic waves […]
Read More >>Force: Balanced and Unbalanced Forces
Introduction: In a tug of war, the one applying more force wins the game. In this session, we will calculate this force that makes one team win and one team lose. We will learn about it in terms of balanced force and unbalanced force. Explanation: Force Force is an external effort that may move a […]
Read More >>Magnets: Uses, Materials, and Their Interactions
Introduction: Nowadays magnets are widely used for many applications. In this session, we will discuss the basics of magnets and their properties, and the way they were and are used. Explanation: Magnets: Magnetic and Non-magnetic Materials: Poles of a Magnet: Fig No. 1.2: Poles of a magnet Compass: Interaction Between Magnets: The north pole of […]
Read More >>
Comments: