Question

Why is centripetal force equal to weight?

Answer 1

Step 1: Centripetal Force

1. It is the force which acts on an object which moves in a circle.
2. It acts along the center of the motion and attracts the object towards the center of the motion.

Step 2: Formula used

$F=ma,whereF=force,m=mass,a=acceleration$

$a_c=r{\omega }^2,where{a}_c=angularacceleration,r=radiusofcurvatureofthemotion,\omega =angularvelocity$

Step 3: Explanation

When an object is subjected to circular motion then the net force which acts on the object to keep it in circular motion is centripetal force.

From Newton's law of motion, we know that, $F=ma$

Now in circular motion acceleration is centripetal acceleration($a_c$),

which is defined as $a_c=r{\omega }^2$

Now, the centripetal force can be written as $F_c=mr{\omega }^2......\left(1\right)$

When the centripetal force will be equal to the weight of the object. Let $W$ be the weight of the object then $W=mg........\left(2\right)$

Now when the centripetal force is equal to the weight of the object-

By comparing equation $\left(1\right)$ and equation $\left(2\right)$ we get that

$mg=mr{\omega }^2$

By eliminating m from both the sides we get

$g=r{\omega }^2$

When the angular acceleration of the object will become equal to the gravitational acceleration then the centripetal force will be equal to the weight of the object.

Thus, the centripetal force is equal to the weight.