# Can Angles Be Assigned Dimension in Scientific Calculations?

• HappyFeynman
In summary, adding units and counters is crucial in scientific experiments as it enables accurate measurements of quantities and ensures the validity of results. Units can be converted using conversion factors or dimensional analysis, while counters are used to keep track of events. These two terms cannot be used interchangeably in experiments and play distinct roles. Finally, adding units and counters aids in data analysis and interpretation by providing standardized measurements and facilitating communication within the scientific community.
HappyFeynman
Homework Statement
In class, we had determined that radians are a form of a count of distance in terms of radius units. We stated this is different from other units such as m, s, etc. I am having an issue in determining whether two values can be added. Lets say we have the equation (6.7 rad^2 * m) + (3 m) = z. Since we defined radians as a count of distance, we can put it in terms such as 1 rad^2 = m^2 / m^2 = 1, so it is dimensionless. Because of this, can I add the two values to simply state that z= 9.7 m?
Relevant Equations
1 rad^2 = m^2 / m^2 =1
(6.7 rad^2 * m) + (3 m) = 9.7 m

You might find this interesting: https://www.physicsforums.com/insights/can-angles-assigned-dimension/.
The bottom line is that rad2 is certainly dimensionless, but if you find you are adding terms that have a mix of radians to an even power and radians to an odd power then you have very likely gone wrong. E.g. energy, ##ML^2T^{-2}##, cannot equal angular momentum, ##ML^2T^{-2}\Omega##, where ##\Omega## represents the 'angular' dimension.

BvU

## What is the purpose of adding units and counters in scientific experiments?

Adding units and counters is essential in scientific experiments to accurately measure and record quantities. Units provide a standard of measurement, while counters help keep track of the number of times an event occurs.

## What are the common units used in scientific experiments?

The most common units used in scientific experiments are the International System of Units (SI). These include units for length (meter), mass (kilogram), time (second), temperature (kelvin), and many others.

## How do you convert between different units?

To convert between units, you can use conversion factors. These are ratios that relate different units of measurement. For example, to convert from meters to centimeters, you would multiply the number of meters by 100.

## Why is it important to use units consistently in scientific experiments?

Using units consistently is crucial in scientific experiments to ensure accuracy and reproducibility. It also allows for easier comparison and communication of results among scientists.

## What is the purpose of using counters in scientific experiments?

Counters are used in scientific experiments to keep track of the number of times an event occurs. This helps in obtaining more precise and reliable results, especially when dealing with large quantities or repetitive processes.

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