Question

If a running boy jumps on a rotating table, which of the following is conserved?
A. Linear momentum
B. K.E
C. Angular momentum
D. None of these

Answer 1

We can solve this problem using two different concepts. The concepts being, the rotational motion and the torque. As in the case of the rotating platform, this rotating platform undergoes rotational motion and in turn, the angular momentum will be always conserved in the case of rotational motion. Torque will not be exerted by a boy jumping on the rotating platform. As the torque will be zero, thus, the angular momentum will remain conserved.

Complete step-by-step solution
The different concepts using which we can solve this problem are rotational motion and torque.
Concept 1: Rotational motion
The rotational motion is a type of motion in which the position of the object/body changes with respect to time.
When a boy comes running and sits on a rotating platform, the angular momentum is conserved.
The reason being, the rotating platform undergoes rotational motion and in the case of the rotational motion, the angular momentum is always conserved.
Concept 2: Torque
Torque at a point is the product of the force and the distance.
The boy does not exert a torque to the rotating table by jumping. Thus, the angular momentum will be conserved.
The mathematical representation of the same is given as follows.

& \dfrac{d\overset{\\_}{\mathop{L}}\,}{dt}=0 \\\ & \overset{\\_}{\mathop{L}}\,=\text{constant} \\\ \end{aligned}$$ The above equation represents that, the angular momentum will be conserved. $$\therefore $$ The angular momentum is conserved when a running boy jumps on a rotating table. **As, the angular momentum is conserved when a running boy jumps on a rotating table, thus, option (C) is correct.** **Note:** We can solve this problem using a trick, that is, using the given options, we can guess the correct one. All the given options, except the angular momentum, are related to the linear motion, whereas only the angular momentum is related to the rotational motion. In the given question, the term 'rotational' is used thus, we can say that the angular momentum is the correct option.