Question

what are forces acting on a body in vertical circular motion?

Answer 1

Problem:

What are forces, acting on body in vertical circular motion.

Solution:

Let's consider some body, moving in vertical circle.

Forcer, acting on this body depends on the frame of reference, that we consider motion in.

In laboratory frame reference (or frame reference - Earth) forces are:

$F$ - normal reaction of the surface of the circle;

$m\vec{g}$ - gravitational force;

If to consider frame reference - axis O (perpendicular to the figure above), which rotate with angular speed $\omega = \frac{v}{R}$ (R - radius of the circle, $v$ - velocity of body), situation change. This frame reference is not inertial. Thus, new force appear - inertial force equal to $\vec{F}_i - m\vec{a}$ , where $\vec{a}$ - centripetal acceleration of the body ( $a = \frac{v^2}{R}$ ).

Thus, in frame reference - axis O, forces are:

$F$ - normal reaction of the surface of the circle;

$m\vec{g}$ - gravitational force;

$\vec{F}_i$ - inertial force;