Angular Dimensional Formula For Power

Power Dimensional Formula:

\[ [P] = [M L² T^{-3}] \]

Power Dimensional Value:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Dimensional Formula for Power?

Definition: The dimensional formula for power represents its dependence on fundamental quantities: mass (M), length (L), and time (T).

Purpose: It helps in understanding the relationship between power and other physical quantities and in verifying the correctness of physical equations.

2. How Does the Dimensional Formula Work?

The dimensional formula is expressed as:

\[ [P] = [M L² T^{-3}] \]

Where:

\( M \) — Mass (kilograms)
\( L \) — Length (meters)
\( T \) — Time (seconds)

Explanation: Power is work done per unit time. Work is force × distance, and force is mass × acceleration, leading to this dimensional relationship.

3. Importance of Dimensional Analysis

Details: Dimensional analysis helps verify equations, convert between unit systems, and understand physical relationships between quantities.

4. Using the Calculator

Tips: Enter values for mass (kg), length (m), and time (s) to calculate the dimensional value of power in kg·m²/s³ (equivalent to watts).

5. Frequently Asked Questions (FAQ)

Q1: Why is length squared in the formula?
A: Because work (and thus power) involves force acting over a distance, and force itself involves acceleration (distance/time²).

Q2: What are the SI units of power?
A: The SI unit is the watt (W), which equals 1 kg·m²/s³.

Q3: How is this different from angular power?
A: Angular power would involve angular velocity (T⁻¹) and torque (M L² T⁻²), but has the same dimensional formula.

Q4: Can I use this for other power calculations?
A: Yes, the dimensional formula applies to all forms of power - mechanical, electrical, etc.

Q5: What if I get negative values?
A: The calculator requires positive values as physical quantities can't be negative in this context.