Physics / Mechanics

# Physical Quantities and Units and Dimensions

Physics deals with matter and energy and also deal with their inter conversions. Physics is a science of measurements. Physical quantities are those quantities, which can be measured. All the physical quantities are classified into two categories, fundamental physical quantities and derived physical quantities. The examples of fundamental quantities are length, mass and time and the examples of derived quantities are area, speed, acceleration, etc.

## Units and Dimensions of Physical Quantities

• Units are the standards of measurement of physical quantities. The systems of measurement of physical quantities are FPS (Foot, Pound, Second), MKS (Meter, Kilogram, Second) and CGS (Centimeter, Gram, Second).

• There is another system called SI (International System of Units) in which there are 7 fundamental quantities. The units of measurement of these fundamental quantities are Meter (for Length), Kilogram (for Mass), Second (for Time), Ampere (for Current), Kelvin (for Temperature), Mole (for Amount of substance) and Candela (for Luminous Intensity).

• The dimension of a derived physical quantity can be termed as the powers to which the fundamental units of mass, length and time are raised to represent that derived physical quantity.

• Study of objects in motion is called Mechanics. Physical quantities that depict the motion of objects are classified into two categories, scalars and vectors. Scalars are those physical quantities that have only magnitude and vectors are those physical quantities that have both magnitude and direction.

Examples of scalars are Mass, Speed, Distance, etc. and examples of vectors are Displacement, Velocity, Force, etc.

• Time (t) rate of change of distance of a body is called speed. Time rate of change of displacement (s) is called velocity. Uniform motion means uniform velocity (v). Time rate of change of velocity is called acceleration (a).

Velocity, v = ( sf – si )/( tf - ti ) ( m/s ), where 'f' represents final quantity and 'i' represents initial quantity

Acceleration, a = ( vf – vi )/( tf – ti ) ( m/s2 )

Momentum, p = mv ( kg m/s ), where m is the mass of the body.

Force, F = ma ( kg m/s2 or N ), where N is Newton.

• The dimensions of fundamental physical quantities: Mass is M1, Length is L1 and Time is T1.

The dimensions of some of the derived physical quantities: velocity is L1 T-1, acceleration is L1 T-2, momentum is M1 L1 T-1 and force is M1 L1 T-2.