Question

The centrifugal force acting on a body of mass $m\,$moving with an angular acceleration$w\,$ in a circle of radius $r$ is equal to:
(A) $\dfrac{m{{w}^{2}}}{r}\,$
(B) $m{{w}^{2}}r$
(C) $mwr$
(D) $\dfrac{mw}{r}$

Answer 1

Hint: We should know that the centrifugal force has very real effects on objects in a rotating reference frame and is therefore real. But the centrifugal force is not fundamental. Rather it is caused by the rotation of the reference frame. The centrifugal force is not some psychological oddity humans experience. The concept of centrifugal force can be applied in rotating devices, such as centrifuges, centrifugal pumps, centrifugal governors, and centrifugal clutches, and in centrifugal railways, planetary orbits and banked curves, when they are analysed in a rotating coordinate system.

Complete step-by step answer:

We should know that centrifugal force is a force that arises from the body's inertia and appears to act on a body that is moving in a circular path which is directed away from the centre around which the body is moving. Centrifugal force unit is Newton. The centrifugal force drives the object away from the centre.
When we swing an object around on a string or rope, the object will pull outward on the rope. The force we feel is called the centrifugal force and is caused by the inertia of the object, where it seeks to follow a straight-line path.
We know that the centrifugal force acting on a body is equal to the centripetal force $\dfrac{m{{w}^{2}}}{r}\,$
Now, $v=wr$
$\Rightarrow {{C}_{F}}=\dfrac{m{{(wr)}^{2}}}{r}$
$\Rightarrow {{C}_{F}}=m{{w}^{2}}r$
So, we can conclude that the centrifugal force acting on a body of mass $m\,$ moving with an angular acceleration $w\,$ in a circle of radius $r$ is equal to $m{{w}^{2}}r$.

Hence, the correct answer is Option B.

Note: We should know that the angular acceleration is the time rate of change of the angular velocity and is usually designated by $\alpha$ and expressed in radians per second per second. It should also be known to us that rotational velocity and acceleration is shared by all points on a rigid body. We only state that a body rotated about a point because the linear velocity is zero at that point. The vector direction of the acceleration is perpendicular to the plane where the rotation takes place. Increase in angular velocity clockwise, then the angular acceleration velocity points away from the observer.
It should also be known that angular velocity is the rate of change of angular displacement and it is also a vector quantity. In S.I. its unit is radian per second. Angular acceleration is the rate of change of angular velocity and it is also a vector quantity.