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physics

 In addition to the three fundamental quantities, classical mechanics also deals with derived quantities, such as velocity, acceleration, momentum, angular momentum, etc. Each of these derived quantities can be reduced to some particular combination of length, mass, and time. The mks units of these derived quantities are, therefore, the corresponding combinations of the mks units of length, mass, and time. For instance, a velocity can be reduced to a length divided by a time. Hence, the mks units of velocity are meters per second:

Here, v stands for a velocity, L for a length, and T for a time, whereas the operator[….] represents the units, or dimensions, of the quantity contained within the brackets. Momentum can be reduced to a mass times a velocity. Hence, the mks units of momentum are kilogram-meters per second:

[p] = [M][v] =[M][L]/[T]  = kgms^-1                                                          

Here, p stands for a momentum, and M for a mass. In this manner, the mks units

of all derived quantities appearing in classical dynamics can easily be obtained.

Volume =[L³]         (m³)

Density = [M]/[V] = = [M]/[L³]    (kg/m³)

Additional non-standard units of length include the inch (1 ft = 12 in), the yard (1 ya = 3 ft), and the mile (1 mi = 5280 ft). Additional non-standard units of mass include the ton (in the US, 1 ton = 2.000 lb; in the UK, 1 ton = 2240 lb), and the metric ton (1 tonne = 1000 kg). Finally, additional non-standard units of time include the minute (1 min = 60 s), the hour (1 hr = 3600 s), the day (1 da = 86400 s), and the year (1 yr = 365.26 da = 31558464 s).

                                               2          Conversion of Units

   Sometimes it is necessary to convert units from one measurement system to another, or to convert within a system, for example, from kilometers to meters. Equalities between SI and U.S. customary units of length are as follows:

1 mile = 1609 m =  1.609 km              1 ft = 0.3048 m =  30.48 cm

1 m = 39.37 in. =  3.281 ft                  1 in. =  0.0254 m =  2.54 cm (exactly)

     Units can be treated as algebraic quantities that can cancel each other. For example, suppose we wish to convert 80 km/hr  to m/s, because 1 km  is defined as exactly 1000 m, and 1h = 3600 s, we find that: