Angular momentum - can you start spinning while falling?

[hatingphysics]

-- A person is hanging motionless from a vertical rop over a swimming pool. She let's go of the rope and drops straight down. After letting go, is it possible for her to curl into a ball and start spinning? Justify your answer....is there going to be angular velocity? will that allow her to spin?

-- Sit-ups are more difficult to do with your hands placed behind your head instead of on your stomach. Why?...does it have to do with moment of inertia? if not i have no idea where to go from here?!

 

[PhanthomJay]

-- A person is hanging motionless from a vertical rop over a swimming pool. She let's go of the rope and drops straight down. After letting go, is it possible for her to curl into a ball and start spinning? Justify your answer....is there going to be angular velocity? will that allow her to spin?assuming no air, what do you know about the conservation of angular momentum principle? What is her initial angular momentum? Can she apply a torque to start rotating?

-- Sit-ups are more difficult to do with your hands placed behind your head instead of on your stomach. Why?...does it have to do with moment of inertia? if not i have no idea where to go from here?!Is the persons rotational inertia greater with her arms on her head? Why or why not? What does that say about the torque she must apply to start her rotation about the waist?

See comments in red above.

 

[kyle8921]

Angular momentum is a property of a rotating object that is a result of its mass, velocity, and distance from the axis of rotation. In this scenario, the person hanging from the rope has zero angular momentum as they are not moving or rotating. When they let go of the rope and start falling, they will gain angular momentum due to their mass and velocity. However, for them to start spinning, there needs to be a torque acting on their body to change their rotational motion. Without any external torque, they will continue to fall straight down without spinning.

If the person were to curl into a ball while falling, they may create a small amount of angular velocity due to their change in shape and distribution of mass. However, this would not be enough to start spinning as there is still no external torque acting on their body. Therefore, it is not possible for the person to start spinning while falling unless there is an external force or torque acting on them.

As for the question about sit-ups and hand placement, it is indeed related to the moment of inertia. The moment of inertia is a measure of an object's resistance to rotational motion. When your hands are placed behind your head, your body's mass is distributed farther away from the axis of rotation (your hips) compared to when your hands are on your stomach. This increases the moment of inertia, making it more difficult to rotate your body during the sit-up motion. Thus, it requires more effort and strength to perform a sit-up with your hands behind your head.