g=4 pi (l/t square)
Maybe you mean:
g = 4 pi^2 (L/T^2)
simple pendulum length L, all mass
m at end, small angle
m g L theta = m L^2 omega^2 theta
omega^2 = g/L
but omega = 2 pi f = 2 pi/T
4 pi^2/T^2 = g/L
g = 4 pi^2 L / T^2
The equation you provided is g = 4π(l/t^2), where g represents acceleration due to gravity, π is a mathematical constant approximately equal to 3.14159, l represents the length, and t represents the time.
To understand this equation better, let's break it down step by step:
1. First, we have 4π. The value of π is a constant ratio of a circle's circumference to its diameter, approximately equal to 3.14159. Multiplying by 4π is a way of incorporating this constant factor into the equation.
2. Next, we have (l/t^2). This represents the ratio of the length (l) to the square of the time (t^2).
To compute g using this equation, follow these steps:
Step 1: Measure the length (l) of the object or distance you are interested in. Make sure the length is given in a consistent unit of measurement (e.g., meters, feet, etc.).
Step 2: Measure the time (t) it takes for the object to perform a specific motion, such as falling from a certain height. Ensure that time is measured in seconds (s) for consistent units.
Step 3: Square the value of time (t) by multiplying it by itself (t^2). This step accounts for the "square" in the equation.
Step 4: Multiply the squared time (t^2) by the length (l).
Step 5: Multiply the result from step 4 by 4π (approximately 12.56637).
The final value obtained from these calculations will represent the acceleration due to gravity (g) for the given length and time.