Question

A girl sits near the edge of a rotating circular platform. If the girl moves from circumference towards the center of the platform, then the angular velocity of the platform will:
(A). decrease
(B). increase
(C). remain same
(D). becomes zero

Answer 1

Hint: All particles of the moving body have different angular velocities and their angular velocities depend on the translational velocity and distance from the axis of rotation. Using this relation we can determine whether angular velocity will increase or decrease as we move towards the center.

Formula used: \[\omega =\dfrac{v}{r}\]

Complete step by step answer:
Angular velocity is defined as the angular displacement travelled in unit time. It is denoted by\[\omega \]and SI unit is\[rad\,{{s}^{-1}}\]
\[\omega =\dfrac{\theta }{t}\]
Here,
\[\theta \]is the angular displacement
\[t\] is the time taken
Relation between velocity (\[v\] ) and angular displacement is-
\[\omega =\dfrac{v}{r}\] - (1)
Here, \[r\]is the distance from the axis of rotation.
By the above relation we can say that,\[\omega \] is directly proportional to magnitude of \[v\] but inversely proportional to \[r\].
For a rotating circular platform, the axis of rotation (\[r\]) is in the center. Therefore as we move towards the center the distance from the axis of rotation (\[r\]) decreases and from the relation in eq (1), the angular velocity increases.

So, the correct answer is “Option B”.

Note: Velocity is always tangential to the rotating body. The axis of rotation is an imaginary axis around which the body rotates. Forces acting on a rotating body are centripetal forces which attract the body towards the center and centrifugal force which is directed away from the center of rotation.