Answer to Question #189358 in Classical Mechanics for Chinmoy Das

Question

Let's assume a rigid body of mass "m" has a velocity(ai^+bj^) in two dimensional plane and is now at the position (x1,y1) . It is experiencing a constant force "F" towards the origin(0,0).

What are the conditions for the body to orbit the origin?

Answer 1

Given,

Mass of rigid body $=m$

Velocity $(v)=(a \hat{i}+b\hat{j})$

Position of the body $(x_1, y_1)$

$\hat{r}=x_1\hat{i}+y_1\hat{j}$

Constant force = F is towards the origin (0,0)

$\Rightarrow F=m\frac{(\sqrt{a^2+b^2})^2}{\sqrt{(x_1)^2+(y_1)^2}}$

$\Rightarrow F = m\frac{a^2+b^2}{\sqrt{x_1^2+y_1^2}}$

Hence, the centripetal force will be F.