# Physical Quantities and Units

## Physical Quantities and Units

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# Physical Quantities and Units

There are only 7 basic physical quantities in the universe.
All other physical quantities are a combination of these 7.

For example time, length and mass are basic physical quantities. Velocity is also a physical quantity but it is a combination of length and time: velocity = length / time.  So velocity is not a basic physical quantity.

All physical quantities are either basic physical quantities or they are a combination of basic physical quantities.

Professional organizations define units to measure each of the basic physical quantities. These are called base units.  For example the base unit of second (s) measures time, the base unit of meter (m) measures length and the base unit of kilogram (kg) measures mass.

Some examples of base unit definitions:

• A second is the time it takes for 1,192,631,770 cycles of a specific atomic transition in the cesium 133 atom.
• A meter is the length that light travels in a vacuum in 1/299,792,458 of a second.
• A kg is the mass of a platinum-iridium cylinder kept in a museum in France.

The units for anything other than a base unit are called derived units.  One example of a derived unit is the metric unit of energy called the Joule (J). It is a combination of the base units for mass, length and time:  1J = 1 kg m2/s2

 PHYSICAL QUANTITIES WITH CORRESPONDING METRIC AND ENGLISH UNITS Physical quantity Common Metric System units Common English System units length meter (m), kilometer (km) inch (in), foot (ft), yard time second second mass kilogram (kg), gram (g) slug*, pound (lbm)*** NOTE: These are NOT base units in the English system. They are derived units. temperature Degrees Celsius (oC) or Kelvin (oK) degrees Farenheit (oF) or Rankin (oR) charge current** Ampere (A) Ampere (A) amount of a substance mole mole lunimous intensity candela candela force Newton (N)* NOTE: This is NOT a base unit in the metric system. It is a derived unit. pound (lbf)

*All of the units in this table are base units except for the units of mass in the English system, and the units of force in the metric system. These are derived units.

The English system defines force to be a basic physical quantity. Hence the unit for force is a base unit and the unit for mass becomes a derived unit. The base unit of force defined in the English system is called a pound (lbf).  From Newton’s second Law:  F = ma  or  force = (mass) x [(length) / (time2)] we see that mass is a combination of force, length and time. The derived unit of mass in the English system is called a slug: 1slug = (l lbf) / (1ft/s2)

There is also a unit of mass in the English system called the pound (lbm):  1lbm=(32.2 lbf) / (1ft/s2)   Hence 1 lbm= 32.2 slugs

The metric system defines mass to be a basic physical quantity. Hence the unit for mass is a base unit and the unit for force becomes a derived unit. The base unit of mass defined in the Metric system is called a kilogram (kg). From Newton’s second Law:  F = ma  or  force = (mass) x [(length) / (time2)]  we see that force is a combination of mass, length and time.  The derived unit of force in the metric system is called a Newton (N):  1 N = 1kg m/s2

The English system is called a gravitational system because the definition of the base unit of force (l lbf) relys on the gravity of the earth and is defined at a specific sea level. The metric system is called an absolute system because the definitions of the units are not dependant on gravity.

**Intuitively, it would seem that charge is a more appropriate basic physical quantity.  But it is easier to measure current in the lab and so current is taken to be the basic physical quantity.  So Ampere, which measures current is a base unit and charge is a derived unit.  The unit for charge is the Coulomb: 1C = 1A-sec

***There are two different units called pound (lb). One is a unit of force (sometimes called “pound-force” and the other is a unit of mass (sometimes called “pound-mass”. To distinguish between the two, a subscript f or m is used. (lbf , lbm)  However, if there is no subscript, you must assume that the unit is pound-force.

Conversions you might need

12 inches = 1 foot

3 feet = 1 yard

5280 feet = 1 mile

1 in = 2.54 cm

1 gram = 0.03527 ounces

32.2 lbm  = 1 slug

1 lbf = 16 oz

2000 lbs = 1 ton

1000 kg = 1 metric ton

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