Question

1. Her angular speed increases because by pulling in her arms she creates a net torque in the direction of rotation. 2. Her angular speed increases because air friction is reduced as her arms come in. 3. Her angular speed increases because her angular momentum is the same but her moment of inertia decreases. 4. Her angular speed increases because her potential energy increases as her arms come in. 5. Her angular speed increases due to a net torque exerted by her surroundings. 6. Her angular speed increases because her angular momentum increases.

Answer 1

Answer:

3. Her angular speed increases because her angular momentum is the same but her moment of inertia decreases

Explanation:

II ωi the intial angular momentum of the skater. Her angular momentum changes to If ωf after pulling her arms in.

It must be noted that If is less than II, then it is because her arms now go round not far from the rotation axis which brings down the mementos of inertia.

Angular momentum does not change since torque is O.

Note: the mathematical representations are better written on the attached diagram.

Answer 2

Answer:

3. Her angular speed increases because her angular momentum is the same but her moment of inertia decreases.

The question is incomplete below is the completed question.

Complete question:

A figure skater on ice spins on one foot. She pulls in her arms and her rotational speed increases. Choose the best statement below:

1. Her angular speed increases because by pulling in her arms she creates a net torque in the direction of rotation. 2. Her angular speed increases because air friction is reduced as her arms come in. 3. Her angular speed increases because her angular momentum is the same but her moment of inertia decreases. 4. Her angular speed increases because her potential energy increases as her arms come in. 5. Her angular speed increases due to a net torque exerted by her surroundings. 6. Her angular speed increases because her angular momentum increases.

Explanation:

Her angular momentum can be defined as;

Angular momentum L = Iω = I₁ω₁ = I₂ω₂

Where I is the moment of inertia and ω is the angular speed. ( I₁ω₁ - is her moment of inertia and angular speed before she pulls in her arm, and I₂ω₂ - after she pulls in her arm)

During the spin on ice, her angular momentum remains constant since there is no external torque acting on her.

After she pulls in her arm, the moment of inertia reduces because her arm now rotates closer to the rotation axis. So I₁ > I₂, and since the angular momentum is constant according to the equation the angular speed would increase, ω₁ < ω₂. Therefore, Her angular speed increases because her angular momentum is the same but her moment of inertia decreases