Central Force. Umiatin,M.Si. The aim : to evaluate characteristic of motion under central force field. A. Introduction. Central Force always directed along the line connecting the center of the two bodies Occurs in : motion of celestial bodies and nuclear interaction.
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No external forces are acting on the system, so the motion of the center of mass is uniform translational motion.
R** = 0.
If mass :m2 >> m1, then reduced mass:
The eq of motion :
If p is the linear momentum of a particle of mass µ, the torque τ about an axis passing through the center of force is :
2. Angular Momentum and Energy are Constant dimensional problem can be reduced into two dimensional. Using polar coordinate system :
The angular momentum of a particle of mass µat a distance r from the force center is :
Consider a mass µ at a distance r(θ) at time t from the force center O :
From the previous description :
1. Find the force law for a central force field that allow a particle to move in logarithmic spiral orbit given by (k and α are constant) :
First determine :
The equation for the path of a particle moving under the influence of a central force whose magnitude is inversely proportional to the distance between the particle can be obtain from :