I stared at this problem for 45 minutes trying to figure it out! It seems so easy, what am I missing? A figure skater during her finale can increase her rotation rate from an initial rate of 1.09 revolutions per 2.02 seconds to a final rate of 2.81 revolutions per second. If her initial moment of inertia was 4.77 kg*m^2, what is her final moment of intertia? So, what I have so far is that 1.09 rev/ 2.02 sec is .5396 rev/s and times 2pi that is 3.3904 radians per second. Or is it rad/sec^2? Do I assume from the problem that they mean that she is accelerating by 1.09 rev per every 2.02 seconds? That's what is confusing me. The final velocity is 2.81 rev/s times 2pi to equal 17.6557 rad/s. If that's acceleration, then I can use the equation Torque=Inertia times angular acceleration. But, my problem is, I don't know what to do with the problem, maybe it's because I've been thinking about physics for 6 hours or what, but I know I set two equations equal to each other to solve for final inertia. But what are these equations?? I would really appreciate any help. I'm at a loss for what to do.
That's an odd way to phrase the problem, but my guess is that you're meant to use the conservation of angular momentum. So you know the initial speed and inertia and the final speed. By conservation, the angular momentum remains constant (no torques to worry about; assume she speeds up by, say, bringing her arms in so that her inertia goes down). Angular momentum is given by the product of inertia and angular velocity in this situation.
Can you be my teacher?! Haha. My professor is terrible at explaining things and that just made so much sense. I have just one question. Is the angular momentum always Inertia initial times angular velocity initial = Inertia final * angular velocity final (in the same way as mass initial times velocity initial = mass final times velocity final ??) Thank you so much!
I'm glad that helped. For the types of problems I think you are going to see (at least in that class) the answer to your question is yes. More generally, angular momentum is a vector quantity; when you rotate a rigid body about more than one axis, you have to consider the inertia about each axis (you'll have an inertia tensor) and you multiply that by the angular velocity vector. At the risk of assuming too much, I don't think you have to worry about that at the moment.