function calculateMotgage() {
var mass = parseFloat(document.getElementById('objectMass').value);
var velocity = parseFloat(document.getElementById('velocityVector').value);
var radius = parseFloat(document.getElementById('rotationRadius').value);
var resultsDiv = document.getElementById('motgage-results');
if (isNaN(mass) || isNaN(velocity) || isNaN(radius) || radius <= 0) {
alert("Please enter valid positive numbers for all fields.");
return;
}
// Calculations
var momentum = mass * velocity;
var force = (mass * Math.pow(velocity, 2)) / radius;
var energy = 0.5 * mass * Math.pow(velocity, 2);
// Display Results
document.getElementById('momentumRes').innerText = momentum.toFixed(2);
document.getElementById('forceRes').innerText = force.toFixed(2);
document.getElementById('energyRes').innerText = energy.toFixed(2);
resultsDiv.style.display = 'block';
}
Understanding the Motgage Calculation in Dynamics
The term "Motgage" (a portmanteau of Motion and Gauge) refers to the comprehensive measurement of a physical body's dynamic properties. Unlike financial assessments, a Motgage calculation focuses on the interplay between mass, velocity, and orbital constraints to determine the energy state of an object in motion.
The Core Components of Motgage Analysis
To accurately gauge the "Motgage" of a system, three primary variables are required:
Object Mass (kg): The total amount of matter within the body being analyzed. This is the fundamental inertia component.
Velocity Vector (m/s): The rate of change of position. In Motgage dynamics, we treat this as the instantaneous speed acting upon the mass.
Rotation Radius (m): The distance from the center of mass to the pivot point or orbital center. This is critical for determining centripetal influence.
Mathematical Formulas Involved
Our Motgage calculator utilizes three standard Newtonian equations to provide a full profile of the object's state:
Linear Momentum (p = m * v): This determines the "quantity of motion" the object possesses.
Centripetal Force (Fc = mv² / r): This calculates the inward force required to maintain the object's circular path at the specified radius.
Kinetic Energy (Ek = ½mv²): This represents the work required to accelerate the body from rest to its stated velocity.
Practical Example of a Motgage Calculation
Imagine a mechanical component with a Mass of 10 kg moving at a Velocity of 5 m/s while tethered to a Radius of 2 meters. The Motgage profile would be calculated as follows:
Momentum: 10 kg * 5 m/s = 50 kg·m/s.
Centripetal Force: (10 * 5²) / 2 = 125 Newtons.
Kinetic Energy: 0.5 * 10 * 5² = 125 Joules.
Applications in Engineering
Engineers use these Motgage metrics to design safer rotating machinery, such as turbines and centrifuges. By gauging the motion and the resulting forces, designers can select materials that withstand the centripetal stress and manage the kinetic energy transfer effectively during operation.