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 gymnast performing acrobatics in the air and identifying the conserved quantity, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Motion**:
The gymnast performs acrobatic movements in the air, which involves rotation and changes in body position.

2. **Identifying Relevant Physics Concepts**:
In rotational motion, one key principle is the conservation of angular momentum. Angular momentum (L) is given by the product of the moment of inertia (I) and angular velocity (ω):
\[ L = I \cdot \omega \]

3. **Moment of Inertia and Angular Velocity**:
As the gymnast changes position (for example, by folding their arms), the moment of inertia changes. When the arms are extended, the moment of inertia is larger. When the gymnast folds their arms, the moment of inertia decreases.

4. **Applying Conservation of Angular Momentum**:
According to the conservation of angular momentum:
\[ I_1 \cdot \omega_1 = I_2 \cdot \omega_2 \]
where \(I_1\) and \(I_2\) are the moments of inertia before and after the gymnast folds their arms, and \(\omega_1\) and \(\omega_2\) are the corresponding angular velocities.

5. **Conclusion**:
When the gymnast folds their arms, the moment of inertia decreases, which causes the angular velocity to increase in order to conserve angular momentum. Thus, the quantity that is conserved during the gymnast's motion is angular momentum.

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

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