Is that right? Doesn't that assume the tension in the rope is equal to the weight of the block? I know the tension is less then mg, because the forces on the block must be unbalanced. What am I missing?
I love this question, and I love this question about the question! The change in angular momentum is equal to the unbalanced external torque on the system multiplied by time interval - that's the impulse-momentum theorem applied to angular rather than linear momentum.
So, what external forces act on the pulley-block system? The pulley itself experiences a contact force from its support, and the force of the earth. (These are balanced.) The block experiences the force of the earth. Since nothing balances the gravitational force of the earth on the block, the gravitational force is the net unbalanced force.
What about the tension, then?!? The tension is INTERNAL to the block-pulley system. Yes, sure, I didn't mention that the rope pulls down on the pulley and up on the block, because that doesn't matter. I'm looking for EXTERNAL forces only.
So the unbalanced external force on the system is just mg. This force provides a torque of mgR. And multiply by time interval t to satisfy the impulse momentum theorem, and Bob's your uncle!
Hope this helps... we're never assuming anything at all about the tension, equal to or not equal to mg.
Your answer's right, but there are two things to point out: 1. It's heavily implied, but the axis we're picking is in the center of the pulley. 2. 99% of the time, when asked about angular torque or impulse or momentum, the main object of concern is the pulley itself. True, the hanging mass goes past an angle relative to the axis as it descends, but one has to be dealing with a really specific problem for that to matter--such as an observer (an ant?) sitting on the pulley axis, watching the mass fly away as if watching a shooting star.
ReplyDeleteAnd besides, a lot of the time this question shows up on a conceptual physics test, it's specifically to tempt out the common misconception that mgR equals the torque acting on the pulley. So, my first reaction was, "Are we sure someone didn't misread the question, here?" If it's not a misreading, then it's fine. Just... Odd.
Will, agreed with point 1 - I am paraphrasing the original problem, and the axis of rotation was explicitly stated in the original.
ReplyDeleteAs for point 2... the AP physics 1 exam does regularly ask about angular momentum including both point objects and extended objects. See 2017 problem 3, for example, and one of the multiple choice in the official practice exam, and many others. This problem is based loosely on what my correspondent found on AP Classroom. I agree with you that in my personal history of physics classes I took (in 1990-1996), your "99% ask about the pulley itself" statement holds! Just not in AP Physics 1. :-)
Thanks for the comment!
Interesting problem. I'll make sure to keep it in my pocket when studying rotational dynamics.
ReplyDeleteI noticed a theme in some of the FRQ's for APPHYS1. Some of them involve two "students" making incorrect predictions, and then me having to dissect them and explain which parts are correct and which are not (see "Day 104" in the elite section in your physics 1 book). Do you have a strategy for problems like that? Thanks in advance.
~Rohan
Hi, Rohan! I guess the approach in the moment is for the student to solve the problem themselves, then to carefully parse what the students say. For longer-term preparation, I'd suggest doing an enormous amount of collaborative work, discussion, grading of other students' work, etc. The more students are confronted with misconceptions - their own and others' - the more likely they will be to recognize the misconceptions on the exam.
ReplyDeleteAh, I wish I could take part in that collaborative work. Sadly, that is not realistically possible. I am self-studying for the AP physics exam (not actually taking the class in-school), which makes student-to-student work challenging, especially during a pandemic. I still plan on trying my best with what I find online. Thanks for the advice!
Delete