Explain, why dancers are able to increasetheir angular speed by pulling in theirextended arms, while dancing

Dancers are able to increase their angular speed by pulling in their extended arms while dancing due to the principle of conservation of angular momentum.

1. Angular momentum is a property of rotating objects and is defined as the product of the moment of inertia and angular velocity. It is a measure of how fast an object is rotating and how difficult it is to change its rotation.

2. When dancers extend their arms, their moment of inertia increases. Moment of inertia is a measure of an object's resistance to changes in its rotation. By extending their arms, dancers increase the distribution of mass away from their axis of rotation, which increases their moment of inertia.

3. According to the conservation of angular momentum, the total angular momentum of a system remains constant unless acted upon by an external torque. In this case, the dancer is the system, and their extended arms contribute to their total angular momentum.

4. When dancers pull in their extended arms, they decrease their moment of inertia. This reduction in moment of inertia causes an increase in angular velocity to maintain the conservation of angular momentum. In other words, as the moment of inertia decreases, the angular velocity increases to keep the total angular momentum constant.

5. By increasing their angular velocity, dancers are able to spin faster and perform more intricate movements. This technique is commonly used in various dance styles, such as ballet and contemporary dance, to create visually stunning and dynamic performances.

In conclusion, dancers are able to increase their angular speed by pulling in their extended arms while dancing because it reduces their moment of inertia, leading to an increase in angular velocity as per the conservation of angular momentum.