Question

Why is centripetal force equal to weight?

Answer 1

Hint: Centripetal force is defined as a force which acts on a body which is moving circularly. It acts towards the center of the motion of a body and orthogonally to the position of the body. The centripetal force tends to attract the body towards the center of its motion.

Complete step by step answer:
The net force which acts on a body to keep it in a circular motion is known as centripetal force.From Newton’s Law of Motion we know that,
$F = ma$ where, $F = $ force, $m = $ mass of the body and $a = $ acceleration.
In case of circular motion,
Acceleration is known as centripetal acceleration, as ${a_c}$.
${a_c} = r{\omega ^2}$ where $r = $ radius of curvature for the motion of the body and $\omega = $ angular velocity.
So, the centripetal force can be written as,
${F_c} = mr{\omega ^2}$.

Let us now talk about when the centripetal force becomes equal to the weight of the body.
Let the weight of the body be $W$. And the formula of weight $ = mg$ where $m = $ mass of the body and $g = $ acceleration due to gravity.
Now let us now find what when centripetal force equals weight of the body.
$mg = mr{\omega ^2}$
Eliminating $m$ from both the equations we get,
$g = r{\omega ^2}$
So, when the angular acceleration will be equal to acceleration due to gravity then the weight of the body will be equal to the centripetal force.

Note: It must be noted that it has to be uniform circular motion in order to achieve the centripetal force equal to the weight of the body. The centripetal force causing rotation can be proved by Newton’s First Law which states that a body will continue to move in a straight line if it is not worked upon by an external force.