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Base units and derived units
When reading about SI units, you will find that they are often divided into base units and derived units. I will put the base units in Figure 1 and some sample derivedunits in Figure 2 .
| Figure 1 . SI base units. |
|---|
Base Quantity Name Symbol
length meter mmass kilogram kg
time second selectric current ampere A
thermodynamic temperature kelvin Kamount of substance mole mol
luminous intensity candela cd |
Note that the list of derived units in Figure 2 is only a sampling of different units that can be derived from the base units.
The exponentiation indicator
As is the case throughout these modules, the character "^" that you see used extensively in Figure 2 indicates that the character following the ^ is an exponent. Note also that when the exponent is negative, itis enclosed along with its minus sign in parentheses for clarity.
| Figure 2 . Examples of SI derived units. |
|---|
force newton kg*m/s^2
area square meter m^2volume cubic meter m^3
speed, velocity meter per second m/sacceleration meter per second squared m/s^2
wave number reciprocal meter m^(-1)mass density kilogram per cubic meter kg/m^3
specific volume cubic meter per kilogram m^3/kgcurrent density ampere per square meter A/m^2 |
The newton
The first derived unit listed in Figure 2 is the newton, which is the product of the base unit for mass (kg) and the base unit for acceleration (m/s^2). Thus,the units for the newton are
kg*m/s^2
A newton is a unit of force that causes a mass of one kilogram to be accelerated by one meter per second squared (1 m/s^2).
When making physics calculations, It is extremely important that you understand and keep track of the units that you are using. The Google search boxcan serve your needs as a scientific calculator if you are careful how you use it. For example, if you enter an expression such as3+5 in the Google search box and press the Enter key, the result of evaluating that expression will be displayed immediately below the search box.
A physics problem
A typical problem in a physics textbook states that a 2-kg mass is moving in a circular path with a constant angular velocity of 5 radians per second and with a tangential velocity of 3 m/sec.The objective is to find the centripetal force on the mass.
You will learn all that you need to know to solve this problem in future modules. For now, just bear with me and concentrate on the use of the Googlesearch box as a scientific calculator.
As you will learn in a future module, a radian is a dimensionless quantity, and the proper units for an angular velocity of 5 radians per second is simply 5/s.(It also works to spell radians out, but abbreviations for radians may not work in the Google calculator.)
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