A gymnast does many acrobats in air before descending on the floor. The quantity conserved, consequent to motion, is:

Options

A. angular velocity
B. M.I.
C. linear momentum
D. angular momentum

Answer

To solve the question regarding the conservation of quantities during a gymnast's acrobatic movements in the air, we need to analyze the situation with respect to the principles of physics, particularly focusing on angular momentum.

### Step-by-Step Solution:

1. **Understanding the Motion**:
- When a gymnast performs acrobatic movements in the air, they rotate and change their body position. This motion can be analyzed in terms of angular momentum.

2. **Angular Momentum Definition**:
- Angular momentum (L) is defined as the product of the moment of inertia (I) and the angular velocity (ω):
\[ L = I \cdot \omega \]

3. **Initial State of the Gymnast**:
- Initially, the gymnast has a certain moment of inertia (I) and rotates with an angular velocity (ω). Therefore, the initial angular momentum can be expressed as:
\[ L_{initial} = I \cdot \omega \]

4. **Changing Body Position**:
- As the gymnast performs acrobats, they may pull their arms and legs closer to their body. This action decreases their moment of inertia (I decreases to I') because the mass distribution is now closer to the axis of rotation.

5. **Conservation of Angular Momentum**:
- According to the principle of conservation of angular momentum, if no external torque acts on the system, the total angular momentum before and after the change must remain constant:
\[ L_{initial} = L_{final} \]
- This means:
\[ I \cdot \omega = I' \cdot \omega' \]
- Here, I' is the new moment of inertia after the gymnast pulls in their limbs, and ω' is the new angular velocity.

6. **Effect of Decreased Moment of Inertia**:
- Since I' < I, to keep the angular momentum constant, the angular velocity must increase (ω' > ω). This results in the gymnast spinning faster.

7. **Conclusion**:
- The quantity that is conserved during the gymnast's motion is **angular momentum**. This conservation allows the gymnast to control their rotation speed and perform various acrobatic maneuvers effectively.

### Final Answer:
The quantity conserved, consequent to motion, is **angular momentum**.