TBR & TPR ROTATIONAL PROBLEM CONTRADICTION ?

[crazy person]

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Hey guys ! I ran into a problem with a rotational questions that TBR AND TPR given different answers to a one concept. I don't know if its the concept or what that I'm lacking but here are the questions and answers.

TBR PASSAGE II CHAPTER 2: QUESTION 9

It says three identical bugs (A, B, C) are standing on a turntable as it begins to spin. As the spinning increases, which of the bugs is most likely to slip first ( with respect to the turntable surface) ?

OK so the answer is bug C. It says that objects revolving further from a rotational axis move faster ( have a greater tangential speed) and have a larger centripetal acceleration than closer objects and this is why Bug C will fall first. But in TPR passage 4 pg 57 # 4, it says the following:

Suppose the platform rotates freely without friction so that angular momentum is conserved. If the woman moves in toward the center, what happens to the period of rotation of the platform?

The answer is : it decreases.

Now, TPR says if the women walks closer to the center, the platform will start to rotate faster.
So, I don't understand it because I thought if the women is closer to the center than it will rotate slower just like what TBR said in the other example. I'm confused.

So which one is it, does an object rotate faster when its closer to the center or when its further away?

Thank you guys !!!

 

[SOOyC52H1Sof]

I think Wikipedia says it best:

Rotational speed is not to be confused with tangential speed, despite some relation between the two concepts. Imagine a rotating merry-go-round. No matter how close or far you stand from the axis of rotation, your rotational speed will remain constant. However, your tangential speed does not remain constant. If you stand two meters from the axis of rotation, your tangential speed will be double the amount if you were standing only one meter from the axis of rotation.

bugs flying off due to speed on a rotating platform? Think of a washer. The clothes in the rotating drum will be against the edges when its rotating quickly.

The lady on the rotating platform? I thinking it has to do with rotational inertia, so think of an Ice skater holding arms in vs out while rotating.

 

[premed1001]

Hey guys ! I ran into a problem with a rotational questions that TBR AND TPR given different answers to a one concept. I don't know if its the concept or what that I'm lacking but here are the questions and answers.

TBR PASSAGE II CHAPTER 2: QUESTION 9

It says three identical bugs (A, B, C) are standing on a turntable as it begins to spin. As the spinning increases, which of the bugs is most likely to slip first ( with respect to the turntable surface) ?

OK so the answer is bug C. It says that objects revolving further from a rotational axis move faster ( have a greater tangential speed) and have a larger centripetal acceleration than closer objects and this is why Bug C will fall first. But in TPR passage 4 pg 57 # 4, it says the following:

Suppose the platform rotates freely without friction so that angular momentum is conserved. If the woman moves in toward the center, what happens to the period of rotation of the platform?

The answer is : it decreases.

Now, TPR says if the women walks closer to the center, the platform will start to rotate faster.
So, I don't understand it because I thought if the women is closer to the center than it will rotate slower just like what TBR said in the other example. I'm confused.

So which one is it, does an object rotate faster when its closer to the center or when its further away?

Thank you guys !!!

if she walks to the center, she will make more rotations per time so the period will decrease wont it? i think these questions are asking different things

also for the first questions, think about a merry go round. the further to the outskirt you are the faster you move, the more likely you are to fly off

 

[crazy person]

if she walks to the center, she will make more rotations per time so the period will decrease wont it? i think these questions are asking different things

also for the first questions, think about a merry go round. the further to the outskirt you are the faster you move, the more likely you are to fly off

I asked the next step tutor about these questions. Maybe he will enlight us ! 🙂

 

[sps27]

Hey guys ! I ran into a problem with a rotational questions that TBR AND TPR given different answers to a one concept. I don't know if its the concept or what that I'm lacking but here are the questions and answers.

TBR PASSAGE II CHAPTER 2: QUESTION 9

It says three identical bugs (A, B, C) are standing on a turntable as it begins to spin. As the spinning increases, which of the bugs is most likely to slip first ( with respect to the turntable surface) ?

OK so the answer is bug C. It says that objects revolving further from a rotational axis move faster ( have a greater tangential speed) and have a larger centripetal acceleration than closer objects and this is why Bug C will fall first. But in TPR passage 4 pg 57 # 4, it says the following:

Suppose the platform rotates freely without friction so that angular momentum is conserved. If the woman moves in toward the center, what happens to the period of rotation of the platform?

The answer is : it decreases.

Now, TPR says if the women walks closer to the center, the platform will start to rotate faster.
So, I don't understand it because I thought if the women is closer to the center than it will rotate slower just like what TBR said in the other example. I'm confused.

So which one is it, does an object rotate faster when its closer to the center or when its further away?

Thank you guys !!!

Angular momentum (L = I.w (rotational inertia * angular speed)) is the key word here. When mass walks towards the center, the rotational inertia (I=m.r^2) decreases as radius essentially decreases. Since Angular momentum is conserved, angular speed has to increase, which will decrease the time period. This is beyond the scope of MCAT I think because most books have not covered Angular momentum and rotational inertia. Anyways, those are my thoughts.....the TBR questions does not specifically state that Angular momentum is conserved.

 

[crazy person]

Yes, you are right, most books don't cover this but its always good to know a little bit more so you can be prepared.

I get it now. Thanks 🙂

 

[BerkReviewTeach]

i think these questions are asking different things

Great point premed1001. I have a feeling this is the case.

In the TBR question, the woman is moving towards the center on a spinning platform that is rotating at a constant speed. So both r and tangential-v are decreasing. Because force depends on v^2/r, an equal drop in v and r (which is what is observed as she moves closer to the center) will impact the numerator more than the denominator, so the force will diminish until she reaches the center, where it will be zero. You can stand in the very center with no acceleration, because the pivot point never moves.

I'm not familiar with the other question here, but if it's a case where the woman is spinning on her own (like an ice skater), then they are asking about her angular momentum. Without seeing the question I'm assuming they are making angular momentum constant, because that is typical of such questions. As her points of mass move closer to the axis-of-rotation (when she pulls her arms in for instance), she must spin at a faster rate in order to keep momentum constant.

If that is the scenario in the TPR question, then it is in fact a different scenario than the TBR question. As edited as both books are, I assume they are both correct for their scenarios.