r'' = A*s/r^2 and r = (A*s/(r''))^0.5 is the same equation.s = sin(atan(r*θ' / r'))
(A = constant)
r'' = A*s/r^2
System of equations:
r'' = A*s/r^2
r = (A*s/(r''))^0.5
The spiral shape produced by an attractive (1/r^2)sin(theta) force is called an Archimedean spiral. It is a logarithmic spiral that expands outward at a constant rate while also rotating at a constant angle.
The spiral shape is formed by the combination of an attractive force and a rotational force. The attractive force, represented by the (1/r^2) term, pulls particles towards the center while the rotational force, represented by the sin(theta) term, causes the particles to move in a circular motion around the center.
The (1/r^2)sin(theta) force is a fundamental force in physics known as the inverse-square law force. It is a common force seen in many natural phenomena, such as the force of gravity and the force of electric charges.
Yes, the spiral shape produced by an (1/r^2)sin(theta) force can be seen in various natural phenomena, such as the spiral arms of galaxies, the shape of hurricanes, and the growth pattern of certain plants.
As the distance from the center increases, the strength of the spiral shape decreases. This is because the (1/r^2) term in the force equation indicates that the force decreases with the square of the distance. Therefore, the further away from the center, the weaker the force and the less pronounced the spiral shape.