Which of the following statements are correct when a gymnast sitting o...
Explanation:
- When the gymnast lowers his hands while sitting on a rotating stool, the moment of inertia decreases. This is because the distribution of mass is closer to the axis of rotation, leading to a decrease in moment of inertia.
- As the moment of inertia decreases, according to the conservation of angular momentum, the angular velocity of the gymnast increases. This is because angular momentum is conserved and is the product of moment of inertia and angular velocity.
Therefore, the correct statements are:
2. The angular velocity increases.
3. The moment of inertia decreases.
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Which of the following statements are correct when a gymnast sitting o...
Explanation:
When a gymnast sitting on a rotating stool with his arms outstretched suddenly lowers his hands, there are changes in the angular velocity and moment of inertia. Let us discuss these changes in detail.
Angular Velocity:
Angular velocity is defined as the rate of change of angular displacement with respect to time. It is a vector quantity and its direction is perpendicular to the plane of rotation. In this case, when the gymnast lowers his hands, the moment of inertia decreases, which means that the angular velocity increases. This is due to the conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque. Therefore, when the moment of inertia decreases, the angular velocity increases to maintain the conservation of angular momentum.
Moment of Inertia:
Moment of inertia is defined as the resistance of a body to rotational motion about a particular axis. It depends on the mass of the body and the distribution of mass with respect to the axis of rotation. In this case, when the gymnast lowers his hands, the moment of inertia decreases. This is because the arms are closer to the axis of rotation, which reduces the distribution of mass and hence the moment of inertia.
Conclusion:
Therefore, it can be concluded that when a gymnast sitting on a rotating stool with his arms outstretched, suddenly lowers his hands, the angular velocity increases and the moment of inertia decreases.