Question

With what angular velocity and in what direction does the turntable rotate?
A. The table rotates anticlockwise (in direction of the man motion) with angular velocity \[0.05\text{ }rad{{s}^{-1}}\]
B. The table rotates clockwise (opposite to the man) with angular velocity \[0.1\text{ }rad{{s}^{-1}}\].
C. The table rotates clockwise (opposite to the man) with angular velocity \[0.05\text{ }rad{{s}^{-1}}\].
D. The table rotates anticlockwise (in the direction of the man motion) with angular velocity \[0.1\text{ }rad{{s}^{-1}}\].

Answer 1

Hint: Here, we will use the relation between linear moment and angular moment to get the required answer. We also know that the angular momentum of a particle is conserved.
Remember that the direction of the turntable is opposite to the direction of the man.
Formula used:
\[L=mvr\]

Complete answer:
Angular velocity is the rate of velocity at which an object or a particle is rotating around the specific point in a given time period.
Let the angular velocity of the turntable be w in clockwise direction, v is the velocity, m is the mass and r is the radius.
We know that there is no external torque, thus angular momentum is conserved.
\[{{L}_{i}}={{L}_{f}}\]
As the initial angular moment is zero, the final angular moment is also zero.
Therefore, if a man moves anticlockwise, the turntable will rotate in clockwise direction.
\[\begin{align}
  & 0={{I}_{w}}-mvr \\
 & \Rightarrow 400w=100\times 1\times 2 \\
 & \therefore w=0.05\text{ }rad{{s}^{-1}} \\
\end{align}\]
Therefore, the table rotates clockwise (opposite to the man) with angular velocity 0.05rad/sec.
Additional information:
Angular velocity is also known as rotational velocity. It is measured in angle per unit time or radian per second (rad/sec).
The rate of change of angular velocity is angular acceleration.
Angular momentum is the rotational equivalent to linear momentum, given by:
\[L=mvr\]
Here, L is linear momentum, m is mass, v is velocity and r is the radius of an object.
It is a conserved quantity. The total angular momentum of a closed system remains constant.
Angular momentum is also the product of inertia and angular velocity.
If angular momentum remains constant then the angular velocity of the object must increase.

Note:
The direction of the turntable is opposite to the direction of man.
The initial and final linear momentum is equal when there is no torque i.e., conserved angular moment.
The relation between linear moment and angular moment need to remember.