Solving for inertia and angular speed

[physicsballer2]

A 60kg skater begins a spin with an angular speed of 6.0 rad/s. By changing the position of her arms, the skater decreases her moment of inertia by 50%. What is the skater's final angular speed?

I(initial)ω(initial) = I(final)ω(final)

I used 60 kg as my inertia, is inertia and mass interchangeable in this example? Then I used 30kg because her inertia is 1/2 in the final inertia

60 (6.0) = 30ω

360 = 30ω

ω = 12 rad/sec

I said above but my biggest problem with this equation is it seems to simple, I did not think mass and inertia were able to be interchangeable, but there is no radius or time given so I am not sure what else I could solve for. If my answer is correct, why is inertia and mass equal in this example?

 

[Doc Al]

If my answer is correct, why is inertia and mass equal in this example?

Mass and moment of inertia are not equal. You won't need any values for the moment of inertia; All that matters in the ratio of before and after she moves her arms.

Just call the initial moment of inertia I. What does that make the final moment of inertia?

 

[physicsballer2]

The final moment of inertia is 1/2 the initial, so .5I

 

[Doc Al]

The final moment of inertia is 1/2 the initial, so .5I

Exactly. So just plug those values into the formula and solve for ω_final. (The "I" will cancel.)

 

[Nickie]

I understand your confusion about the interchangeability of mass and inertia in this example. Inertia is a property of matter that describes its resistance to change in motion, while mass is a measure of the amount of matter in an object. In most cases, mass and inertia are not interchangeable, but in this specific scenario, we are dealing with a rotational motion and the moment of inertia is directly proportional to the mass and the square of the distance from the axis of rotation. This means that by decreasing the moment of inertia by 50%, the mass must also decrease by 50%. Therefore, in this equation, the mass and inertia can be used interchangeably. However, it is important to note that this is not always the case and should not be assumed in other situations.