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# Derived quantities and their units

To measure a quantity, we always compare it with some reference standard. To say that a rope is 10 metres long is to say that it is 10 times as long as an object whose length is defined as 1 metre. Such a standard is called a unit of the quantity.

Unit

To measure a quantity, we always compare it with some reference standard. To say that a rope is 10 metres long is to say that it is 10 times as long as an object whose length is defined as 1 metre. Such a standard is called a unit of the quantity.

Therefore, unit of a physical quantity is defined as the established standard used for comparison of the given physical quantity.

The units in which the fundamental quantities are measured are called fundamental units and the units used to measure derived quantities are called derived units.

Uniqueness of SI system

The SI system is logically far superior to all other systems. The SI units have certain special features which make them more convenient in practice. Permanence and reproduceability are the two important characteristics of any unit standard. The SI standards do not vary with time as they are based on the properties of atoms. Further SI system of units are coherent system of units, in which the units of derived quantities are obtained as multiples or submultiples of certain basic units. List lists some of the derived quantities and their units.

Derived quantities and their units

Physical Quantity         Expression Unit

Area  :         length x breadth   m2

Volume  :    area x height        m3

Velocity  :   displacement/ time         m sâˆ'1

Acceleration  :      velocity / time       m sâˆ'2

Angular velocity  :         angular displacement / time     rad s-1

Angular acceleration  :   angular velocity / time   rad s-2

Density  :    mass / volume      kg mâˆ'3

Momentum  :        mass x velocity    kg m sâˆ'1

Moment of intertia  :      mass x (distance)2          kg m2

Force  :       mass x acceleration        kg m s-2 or N

Pressure  :   force / area  N m-2 or Pa

Energy (work)  :   force x distance    N m or J

Impulse  :    force x time N s

Surface tension  : force / length        N m-1

Moment of force (torque)  :     force x distance    N m

Electric charge  :   current x time       A s

Current density  :           current / area        A m-2

Magnetic induction  :     force / (current x length)          N A-1 m-1

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11th 12th std standard Class Physics sciense Higher secondary school College Notes : Derived quantities and their units |