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What is the Resolution of a vector into two perpendicular components?

Resolution of a vector is the process of splitting up a vector (force) into two perpendicular component parts. They are called rectangular components because the two component forces are mutually perpendicular.
Resolution of a vector into two perpendicular components

At an angle θ with x axis, the force R acts at a point O. R can be resolved into two rectangular components along x and y axis. Two perpendicular lines CQ and CP are drawn to x and y axis. In the right angled triangle OQC,

Cos θ = OQ / OC

OQ = OC Cos θ

we know that  OC = R

OQ= R Cos θ

Therefore the horizontal component of the force R is R cosƟ.

In the right angled triangle OPC,

Cos (90-Ɵ) = OP / OC

SinƟ = OP / OC ——– Cos (90-Ɵ) = SinƟ

OP = OC SinƟ

we know that  OC = R

OP = R SinƟ

The vertical component of the force R is R sinƟ

posted in Scalars and Vectors | 0 Comments

What is the Law of parallelogram of two vector additions?

If two vectors are represented by two adjacent sides of parallelogram then diagonal of parallelogram through their common point will give the resultant of that vector in magnitude and direction.

Law of parallelogram of two vector additions

Angle between vector tan α = Q Sin Ɵ / P + Q Cos Ɵ

If two vector are in same direction Ɵ = 0
R = P + Q

If two vectors are opposite to each other Ɵ = 1800
R = P – Q

If two vectors are right angle to each otherƟ = 900
R =  law of parallelogram

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What are the formulas for magnitude for vectors in 2D and 3D plane?

A vector with a unit magnitude is a unit vector. The physical quantities which are described by its magnitude and direction are vector quantities.

Formula for Magnitude of vector A in 2D plane =Formula for Magnitude of vector A in 2D plane

Formula for Magnitude of vector A in 3D plane = Formula for Magnitude of vector A in 3D plane

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What are the conventions in writing the SI UNITS ?

1. When we write a unit in full, the first letter should not be in capital.
Example: metre and not as Metre kilogram and not as Kilogram

2. Name of scientist as the symbols of unit should be in upper case (capital) letter
Example: N for newton, J for joule.

3. The singular form of the unit should be used.
Example: km and not as kms, Kg and not as kgs

4. At the end of the abbreviations there should be no full stop.
Example: mm and not as mm, kg and not as kg.

5. The degree sign is omittedwhen temperature is expressed in Kelvin.
Example: 273K not as 2730 K

6. Accepted symbols should only be used.
Example: ampere is represented as ‘A’ and not ‘amp’
second is represented as ‘s’ and not ‘sec’

7. Not more than one solidus or slash should be employed. But effort should be made to avoid use of solidus or slash.
Example: J/k.mol or Jk.mol-1 but not J/k/mol
J kg-1K-1 but not J/kg/K

8. Between the number and the symbol of the unit, one letter space is always to be left.
Example: 2.3 m and not as 2.3m
Kg m s-1 and not kg ms-1

9. A physical quantity in numerical value should be expressed as p= a × 10m
Here ‘a’ is a number between 1 and 10 and ‘m’ is the appropriate power of 10.
Example: velocity of light c = 2.997 × 10 ms-1 .

posted in Dimensional Formulae | 0 Comments

What is Dimensional Formula of Latent Heat?

Latent Heat is defined as the heat absorbed or released per unit mass of the substance when the substance changes its phase at the constant temperature.

Latent heat of fusion is defined as the quantity of heat in calories required to transform 1 gm of solid substance at its melting point into liquid of the same temperature.

Mathematically,
Latent heat of fusion (L) = Heat (Q) / mass (m)

Dimensional formula of Heat(Q) = M1L2T-2
Dimensional formula of mass = M1L0T0

Putting these values in above equation we get,
Dimensional Formula of Latent Heat = M0L2T-2
SI unit of Latent Heat is Joule kg-1

Note:- Dimensional formula of latent heat of fusion is same as Latent heat. Similarly SI unit of Latent heat of fusion is same as Latent Heat.

posted in Dimensional Formulae | 0 Comments

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