A boy comes running and sits on a rotating platform. What is conserved ?

Options

A. Linear momentum
B. Kinetic energy
C. Angular momentum
D. None of the above

Answer

To solve the question of what is conserved when a boy comes running and sits on a rotating platform, we can analyze the situation step by step.

### Step 1: Understand the System
We have a rotating platform (like a merry-go-round) and a boy who runs and sits on it. Initially, the platform is rotating with some angular velocity, and the boy is running towards it.

**Hint:** Consider the properties of the system before and after the boy sits on the platform.

### Step 2: Identify the Forces and Motion
When the boy runs and sits on the platform, he exerts a force on the platform, but this does not change the total angular momentum of the system. The boy's motion affects the distribution of mass but not the total angular momentum.

**Hint:** Think about how the boy's mass and speed affect the system's motion.

### Step 3: Apply the Principle of Conservation of Angular Momentum
In an isolated system where no external torque acts, the total angular momentum before an event must equal the total angular momentum after the event. Here, the boy's entry onto the platform does not introduce any external torques.

**Hint:** Recall the formula for angular momentum: \( L = I \omega \), where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

### Step 4: Analyze the System Before and After
Before the boy sits down, the angular momentum of the system is due to the rotating platform alone. After the boy sits down, the total angular momentum is the sum of the angular momentum of the platform and the boy.

**Hint:** Consider how the moment of inertia changes when the boy sits on the platform.

### Step 5: Conclude the Conservation
Since there are no external torques acting on the system, we conclude that the angular momentum of the system is conserved. Therefore, the total angular momentum before the boy sits on the platform equals the total angular momentum after he sits down.

**Final Answer:** The quantity that is conserved when the boy comes running and sits on the rotating platform is **angular momentum**.