Spacial Units

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Last updated: Oct 29, 2021 by Mayurakhi Khan

Metre

The metre (m) is the SI base unit for measuring length. The metre, as of 2002, is defined as the length traveled by light in a vacuum in 1·299,792,458-1 of a second [1].

Square Metre

The square metre (m2) is the SI derived unit for measuring area. The square metre is already expressed in SI base units [2].

Since the square metre is exponential, the quantity grows exponentially by the corresponding power of 10 when using SI prefixes. For example, 1 kilometre (km) is 103 times the legnth of 1 metre (m), but 1 square kilometre (km2) is (103)2 times the area of 1 square metre [2].

Cubic Metre

The cubic metre (m3) is the SI derived unit used for measuring volume. The cubic metre is already expressed in SI base units [3].

A cubic metre can also be converted to litres, 1 cubic metre is equal to 1000 litres. This also means that 1 cubic metre of water at the temperature of maximum density (3.98 °C) and standard atmospheric pressure (101.325 kPa) has a mass of 1000 kg [3].

Since the cubic metre is an exponential unit, the quantity grows exponentially by the corresponding power of 10 when using prefixes. For example, 1cubic kilometre (km3) is (103)3 times the volume of 1 cubic metre [2].

Metre per Second

The metre per second (m/s) is a SI derived unit used for measuring speed (scalar quantity) and velocity (vector quantity). The metre per second is already expressed in SI base units and is equal to the speed of a body covering a distance of one metre in a time of one second [4].

Metre per Second Squared

The metre per second squared (m/s2) is the SI derived unit used for measuring acceleration. The metre per second squared is already expressed in SI based units and is interpreted physically as the change in velocity or speed per time interval and is treated as a vector quantity [5].

The most common example of a metre per second squared, or acceleration, measurement is the acceleration due to the gravitational force which is equal to 9.8 m/s2 [5].

Radian

The radian (rad) is a SI derived unit used for measuring angles and is the standard unit of angular measures. The radian in SI base units is 1 rad = 1 m/m [6].

Radians can be converted to degrees. One radian is equal to 180/π or angle in degrees is equal to angle in radians multiplied by 180/π [6].

Radian per Second

The radian per second (rad/s) is the SI derived unit for measuring angular velocity (ω) and angular frequency. The radian per second is defined as the change in the orientation of an object, in radians every second. Since the radian is dimensionless, the radian per second is dimensionally equivalent to the hertz, both being defined as s-1 [7].

Radian per Second Squared

The radian per second squared (rad/s2) is the SI derived unit used for measuring the magnitude of angular acceleration. The angular acceleration is also defined as the rate of change of angular velocity [8].

References

[1] “Metre,” Wikipedia, 05-Aug-2021. [Online]. Available: https://en.wikipedia.org/wiki/Metre. [Accessed: 18-Aug-2021].

[2] “Square metre,” Wikipedia, 14-Aug-2021. [Online]. Available: https://en.wikipedia.org/wiki/Square_metre. [Accessed: 18-Aug-2021].

[3] “Cubic metre,” Wikipedia, 21-Feb-2021. [Online]. Available: https://en.wikipedia.org/wiki/Cubic_metre. [Accessed: 18-Aug-2021].

[4] “Metre per second,” Wikipedia, 12-Jun-2021. [Online]. Available: https://en.wikipedia.org/wiki/Metre_per_second. [Accessed: 18-Aug-2021].

[5] “Metre per second squared,” Wikipedia, 25-May-2021. [Online]. Available: https://en.wikipedia.org/wiki/Metre_per_second_squared. [Accessed: 18-Aug-2021].

[6] “Radian,” Wikipedia, 06-Aug-2021. [Online]. Available: https://en.wikipedia.org/wiki/Radian. [Accessed: 19-Aug-2021].

[7] “Radian per second,” Wikipedia, 21-Feb-2021. [Online]. Available: https://en.wikipedia.org/wiki/Radian_per_second. [Accessed: 19-Aug-2021].

[8] T. T. Contributor, “What is radian per second squared? - definition from whatis.com,” WhatIs.com, 21-Sep-2005. [Online]. Available: https://whatis.techtarget.com/definition/radian-per-second-squared. [Accessed: 19-Aug-2021].