Name: dimensional checks for physics equations
Uploaded: 2023-05-16T08:18:40.000Z
Duration: 1 min 8 s
Channel: JoVE

Supongamos que un péndulo simple de masa m está unido a una cuerda de longitud L, que oscila bajo la influencia de la gravedad g. ¿Cuál es la forma de la ecuación para el período de tiempo del péndulo?
Inicialmente, identifique y enumere las variables involucradas en el problema. El período de tiempo T se puede expresar como el producto de estas variables, cada una elevada a un exponente desconocido. Aquí, k es una constante adimensional.
Excluyendo la constante adimensional, se obtiene una ecuación que relaciona las dimensiones de las variables con el período de tiempo.
Ahora, igualando los exponentes de las dimensiones de ambos lados y resolviendo las ecuaciones, se determinan los valores de los exponentes desconocidos.
Al sustituir los exponentes, se obtiene la expresión final del período de tiempo, que es un producto de la constante k y la raíz cuadrada de la longitud sobre la aceleración gravitatoria.
Una de las limitaciones del análisis dimensional es que no nos permite encontrar el valor de la constante adimensional k.

<ol>
	<li>OpenStax. (2019). Física Universitaria Vol. 1. [Versión web]. Obtenido de <a href="https://openstax.org/books/university-physics-volume-1/pages/1-4-dimensional-analysis">https://openstax.org/books/university-physics-volume-1/pages/1-4-dimensional-analysis</a>; Sección 1.4; páginas 22-25.</li>
</ol>

resolución de problemas: análisis dimensional

Toda ecuación matemática que conecta magnitudes físicas separadas y distintas debe ser dimensionalmente consistente, lo que implica que debe cumplir con dos reglas. Por esta razón, el concepto de dimensión es crucial. La primera regla es que las expresiones de una ecuación a ambos lados de una igualdad deben tener la misma dimensión exacta, es decir, magnitudes de la misma dimensión pueden ser sumadas o eliminadas. La segunda regla estipula que todas las funciones matemáticas populares, como las funciones exponenciales, logarítmicas y trigonométricas, deben tener argumentos adimensionales en una ecuación. Es dimensionalmente inconsistente que una ecuación rompa cualquiera de estas dos reglas, por lo que una ecuación no puede ser una representación precisa de ninguna ley física. El análisis dimensional puede ayudar a recordar las diferentes leyes de la física, verificar errores algebraicos o erratas e incluso especular sobre la forma que podrían tener las futuras leyes de la física. Las magnitudes fundamentales se pueden usar para crear cualquier magnitud física deseada. Una magnitud se expresa como el producto de varias potencias de las magnitudes fundamentales cuando se expresa en términos de las magnitudes fundamentales. La dimensión de la magnitud en esa base es el exponente de una magnitud base que aparece en la ecuación. Considera la magnitud física fuerza, que se define como la masa multiplicada por la aceleración. La aceleración se calcula como el cambio de velocidad dividido por un intervalo de tiempo, mientras que la longitud dividida por el intervalo de tiempo es igual a la velocidad. Como resultado, la fuerza tiene las siguientes dimensiones: una en masa, una en longitud y menos dos en tiempo.

Resolución de problemas: Análisis dimensional

Cada ecuación matemática que conecta cantidades físicas distintas por separado debe ser dimensionalmente consistente, lo que implica que debe cumplir con dos ...

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Education

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JoVE Core

Physics

Física

Unit 1

Unidad 1

Units, Dimensions, and Measurements

Unidades, dimensiones y mediciones

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Problem Solving: Dimensional Analysis

dimensional checks for physics equations

Dimensional analysis helps check whether physics equations make sense. It compares the dimensions on each side of an equation and shows whether the units are consistent. This method is useful for spotting algebra errors, typos, and for remembering physical laws.

A valid equation must follow two rules. First, both sides of an equality must have the same dimension, so only quantities with matching dimensions can be added or subtracted. Second, common math functions such as exponential, logarithmic, and trigonometric functions must use dimensionless arguments.

If an equation breaks either rule, it is dimensionally inconsistent. That means the equation cannot correctly represent a physical law. Dimensional analysis also helps scientists think about the form future laws of physics might take.

Base quantities are the building blocks for other physical quantities. A quantity can be written as a product of powers of the base quantities. In that form, the dimension of a quantity is given by the exponent of each base quantity.

Force is a useful example. Force is defined as mass multiplied by acceleration. Acceleration is the change in velocity divided by time, and velocity is length divided by time. From these relationships, force has dimensions of mass to the first power, length to the first power, and time to the minus second power.

Dimensional Checks for Physics Equations

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Dimensional Checks for Physics Equations | JoVE K12

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JoVE Core Física presenta la teoría y la aplicación de conceptos físicos fundamentales, como la cinemática, dinámica, mecánica de fluidos, estática, ondas y acústica, mediante animaciones audiovisuales concisas y fáciles de entender. Además, los vídeos de científicos en acción muestran la aplicación de los conceptos relacionados en experimentos de investigación clásicos y originales, realizados en laboratorios de todo el mundo.

Dimensional Checks for Physics Equations

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