Question

a bead of mass m rests on a vertical smooth parabola x2=cy at (-a,b).The required value of angular velocity is-

Answer 1

The needed angular velocity value is $w^{2}R=w^{2}(-a,b)$

Explanation:

• Angular velocity, also known as rotational velocity or angular frequency vector, is a vector measure of rotation rate that relates to how fast an object spins or revolves relative to another point, i.e. how quickly the angular position or orientation of an object changes with time.

Solution:

• The equation of the parabola is given to be as $x^{2}=cy$

• The mass is positioned at $x=(-a,b)$

• The mass is a distance from the axis, and it moves in a circular motion with a radius $(-a,b)$

As a result, the centripetal acceleration is: $w^{2}R=w^{2}(-a,b)$