Question

A boy comes and sits suddenly on a circular rotating table. What will remain conserved for the table-boy system?
A. Angular velocity
B. Angular momentum
C. Linear momentum
D. All of these

Answer 1

Hint: For every option observe how the quantities are changing with time. If a quantity is changing with time, then it will not remain conserved. And there is no external force acting on the system.

Complete Step by step answer:Given, a boy comes and sits suddenly on a circular rotating table.
When the boy sits on the rotating table, then he starts rotating too with the table.
Now, we check the options one by one
-For option (A)
Let \[\omega \] be the angular velocity, which is how fast the system rotates,
\[\omega = \dfrac{{d\theta }}{{dt}}\] where \[d\theta \] is the angle swept in the time interval \[dt\]
Therefore, angular velocity is not constant and changes with time.
-For option (B)
Let \[L\] be the angular momentum. We have the formula for torque as,
\[
\tau _{net}} = \dfrac{{dL}}{{dt}}\]
There are no other forces acting on the system, therefore for the rotating system net torque \[{\tau _{net}}\] is zero. This implies,
\[\dfrac{{dL}}{{dt}} = 0 \\
 \Rightarrow L = {\text{constant}} \\
\]
Hence, angular momentum will remain conserved for the table-boy system.
-For option (C)
Let \[p\] be the linear momentum. Linear momentum can be written as,
\[\dfrac{{dp}}{{dt}} = F\]
Since, the net force \[F\] is not zero, the linear momentum is not conserved and changes with time. We observe that only angular momentum remains conserved for the table-boy system.

Hence, the correct answer is option (B) angular momentum.

Note: Remember that for a rotational motion or closed system, angular momentum is always conserved. Therefore, for such questions without any calculations, we can say that angular momentum is conserved. However, for other quantities we need to check their dependency on time.