Units and Dimensional Analysis
Newtonian Mechanics 8.01
Units and Dimensional Analysis
1
Dimensions in Mechanics
Physical quantities have dimensions. These quantities are the basic dimensions: - mass, length, time with dimension symbols M, L, T Other quantities’ dimensions are more complex:
- [velocity] = length/time = LT-1 - [force] = (mass)(length) /(time)2 = MLT-2 - [any mechanical quantity] = Ma Lb Tc where a b, and c can be negative and/or non-integer
2
Base Quantities
Name Length Time Mass Electric current Thermodynamic Temperature Amount of substance Luminous intensity Symbol for quantity l t m I T n IV Symbol for dimension L T M I Θ N J SI base unit meter second kilogram ampere kelvin mole candela 3
SI Base Units:
Second: The second (s) is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. Meter: The meter (m) is now defined as the distance traveled by a light wave in vacuum in 1/299,792,458 seconds. Mass: The SI standard of mass is a platinum-iridium cylinder assigned a mass of 1 kg
Image courtesy of the National Bureau of Standards
4
Speed of Light
In 1983 the General Conference on Weights and Measures defined the speed of light to be the best measured value at that time:
c = 299, 792, 458 meters/second
This had the effect that length became a derived quantity, but the meter was kept around for practicality
5
Meter
The meter was originally defined as 1/10,000,000 of the arc from the Equator to the North Pole along the meridian passing through Paris. To aid in calibration and ease of comparison, the meter was redefined in terms of a length scale etched into a platinum bar preserved near Paris. Once laser light was engineered, the meter was redefined to be a certain number of wavelengths of a particular monochromatic laser beam. The meter (m) is now defined as the distance traveled by a light wave in vacuum in 1/299,792,458
Units and Dimensional Analysis
1
Dimensions in Mechanics
Physical quantities have dimensions. These quantities are the basic dimensions: - mass, length, time with dimension symbols M, L, T Other quantities’ dimensions are more complex:
- [velocity] = length/time = LT-1 - [force] = (mass)(length) /(time)2 = MLT-2 - [any mechanical quantity] = Ma Lb Tc where a b, and c can be negative and/or non-integer
2
Base Quantities
Name Length Time Mass Electric current Thermodynamic Temperature Amount of substance Luminous intensity Symbol for quantity l t m I T n IV Symbol for dimension L T M I Θ N J SI base unit meter second kilogram ampere kelvin mole candela 3
SI Base Units:
Second: The second (s) is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. Meter: The meter (m) is now defined as the distance traveled by a light wave in vacuum in 1/299,792,458 seconds. Mass: The SI standard of mass is a platinum-iridium cylinder assigned a mass of 1 kg
Image courtesy of the National Bureau of Standards
4
Speed of Light
In 1983 the General Conference on Weights and Measures defined the speed of light to be the best measured value at that time:
c = 299, 792, 458 meters/second
This had the effect that length became a derived quantity, but the meter was kept around for practicality
5
Meter
The meter was originally defined as 1/10,000,000 of the arc from the Equator to the North Pole along the meridian passing through Paris. To aid in calibration and ease of comparison, the meter was redefined in terms of a length scale etched into a platinum bar preserved near Paris. Once laser light was engineered, the meter was redefined to be a certain number of wavelengths of a particular monochromatic laser beam. The meter (m) is now defined as the distance traveled by a light wave in vacuum in 1/299,792,458