TBR Physics Ch. 4 Passage VII - #45

[gettheleadout]

Passage says:

Experiment 1
A student sits on a stool that rotates freely. He holds a 5-kg mass in each hand. Initially, the student has an angular velocity of 5 rad/s with his arms in his lap.

Question asks:

In Experiment 1, with his arms outstretched, the student drops the weights. How can it be explained that the student's angular velocity does not change?

A. The center of mass does not change for the student, so angular momentum is constant.
B. The position of the weights does not impact angular momentum.
C. The falling weights continue to move in their circular pathway as they fall, so they retain their same angular momentum.
D. The weights are rotating in opposite directions after they are dropped.

My thoughts:

A. Should be true. Weights held are equal and arms are equidistant from the student's body, so reducing mass in each hand to zero doesn't change COM.
B. Wrong, because though this is true (angular moment is conserved no matter where the student holds the weights) this doesn't explain his constant angular velocity upon dropping them.
C. Wrong. This is illogical because "continue to move in their circular pathway" implies that the weights do not follow tangential paths upon release from the student's hands.
D. Wrong. The weights are rotating in opposite tangential direction before they are dropped, but after being dropped they aren't rotating at all.

Key says:

Choice C is the best answer. Just at the instant when the weights are dropped, the skater (sic) is spinning, so the weights are in circular motion about the pivot point until released. They fall once they are dropped, but not straight downward. They fly off from that circle in a tangential fashion, in opposite directions. Together, they exhibit not net momentum, so the skater cannot experience a change in total angular momentum. Dropping the weights does not change the moment of inertia for the system (although its total momentum is split between two systems now). Since they moment of inertia does not change when the student drops the weights, then by conversion of momentum, the angular velocity of the student does not change.

This is BS, right? Their explanation is correct, but doesn't correspond to the right answer choice. The explanation explicitly says moment of inertia (and therefore COM) doesn't change, and also states that the weights fly off along tangential paths instead of following their previous circular path, directly contradicting C.

The presence of reference to a "skater" in the key tells me that TBR screwed up when changing the answer key to match the replacement question for a similar one they got rid of.

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[osprey099]

Passage says:



Question asks:



My thoughts:

A. Should be true. Weights held are equal and arms are equidistant from the student's body, so reducing mass in each hand to zero doesn't change COM.
B. Wrong, because though this is true (angular moment is conserved no matter where the student holds the weights) this doesn't explain his constant angular velocity upon dropping them.
C. Wrong. This is illogical because "continue to move in their circular pathway" implies that the weights do not follow tangential paths upon release from the student's hands.
D. Wrong. The weights are rotating in opposite tangential direction before they are dropped, but after being dropped they aren't rotating at all.

Key says:



This is BS, right? Their explanation is correct, but correspond to the right answer choice. The explanation explicitly says moment of inertia (and therefore COM) doesn't change, and also states that the weights fly off along tangential paths instead of following their previous circular path, direction contradicting C.

The presence of reference to a "skater" in the key tells me that TBR screwed up when changing the answer key to match the replacement question for a similar one they got rid of.

C is the correct answer. The two balls will fall in a tangential manner opposite to each other.

 

[gettheleadout]

C is the correct answer. The two balls will fall in a tangential manner opposite to each other.

How does "continue to move in their circular pathway" say they move in straight tangential pathways to you?

And why is A wrong then?

 

[ur2l8]

Passage says:



Question asks:



My thoughts:

A. Should be true. Weights held are equal and arms are equidistant from the student's body, so reducing mass in each hand to zero doesn't change COM.
B. Wrong, because though this is true (angular moment is conserved no matter where the student holds the weights) this doesn't explain his constant angular velocity upon dropping them.
C. Wrong. This is illogical because "continue to move in their circular pathway" implies that the weights do not follow tangential paths upon release from the student's hands.
D. Wrong. The weights are rotating in opposite tangential direction before they are dropped, but after being dropped they aren't rotating at all.

Key says:



This is BS, right? Their explanation is correct, but doesn't correspond to the right answer choice. The explanation explicitly says moment of inertia (and therefore COM) doesn't change, and also states that the weights fly off along tangential paths instead of following their previous circular path, directly contradicting C.

The presence of reference to a "skater" in the key tells me that TBR screwed up when changing the answer key to match the replacement question for a similar one they got rid of.

Read it and thought C too. Conservation of angular momentum.

 

[gettheleadout]

The weights in fall have no angular momentum. They have linear momentum equal in magnitude to the angular momentum they had in hand. C as written is wrong.

Elsewise, why would A be incorrect?


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[osprey099]

The weights in fall have no angular momentum. They have linear momentum equal in magnitude to the angular momentum they had in hand. C as written is wrong.

Elsewise, why would A be incorrect?


Sent from my iPhone using SDN Mobile

The explanation says: the weights are in circular motion about the pivot point until released. They fall once they are dropped, but not straight downward. They fly off from that circle in a tangential fashion, in opposite directions.

The fact that they are in circular motion until released is the reason why they fly off in opposite tangential directions instead of just dropping straight to the ground.

A is wrong because angular velocity is not affected by center of mass so the fact that it stays the same is not proof of anything related to angular velocity. (I may be wrong here)

 

[gettheleadout]

The explanation says: the weights are in circular motion about the pivot point until released. They fall once they are dropped, but not straight downward. They fly off from that circle in a tangential fashion, in opposite directions.

The fact that they are in circular motion until released is the reason why they fly off in opposite tangential directions instead of just dropping straight to the ground.

A is wrong because angular velocity is not affected by center of mass so the fact that it stays the same is not proof of anything related to angular velocity. (I may be wrong here)

Answer C says "...continue to move in their circular pathway as they fall..."

That is explicitly inconsistent with the answer explanation. I don't know how I can make it more clear that there is no way C can be correct as written.

With regard to A I'll have think about that more.

Edit: Okay, here's my shot at justifying A:

The explanation admits that the moment of inertia is not changed as a result of dropping the weights. This is Premise 1.

Premise 1: Moment of inertia (I) is constant.

Moment of inertia, defined as equal to kMR^2, related to both system mass and distribution of this mass from the radius. For a radially symmetrical system, the moment of inertia is some fraction of that if all the mass were contained at a point with radius of zero. Based on this relationship for distribution of mass, if moment of inertia is constant, center of mass (COM) must be constant.

Dropping the weights does not result in any sort of external torque on the student-weights system, so by the definition of the law of conservation of angular momentum, the angular moment of the student-weights system will remain constant. Approached from a different perspective, if mass were removed from the system (as with dropping the weights) and the removed mass retained angular momentum, this would necessarily result in an end value for angular momentum of the remainder of the system (the student) less than the initial total value for the system, as angular value would be split between two new systems. However, because the dropped weights lack angular momentum during their fall along tangential paths, the angular momentum of the remainder of the system (the student) is constant. This is Premise 2.

Premise 2: Angular momentum (L) of the system (student + both weights) remains constant.

Given these premises, and given that angular momentum L is defined as Iw, where I is the moment of inertia and w is the angular velocity:

With constant L and constant I, w must be constant.

 

[osprey099]

Answer C says "...continue to move in their circular pathway as they fall..."

That is explicitly inconsistent with the answer explanation. I don't know how I can make it more clear that there is no way C can be correct as written.

With regard to A I'll have think about that more.

Oh ok i see what you were saying now.. yea I agree with you. TBR probably made a mistake here.

 

[gettheleadout]

Oh ok i see what you were saying now.. yea I agree with you. TBR probably made a mistake here.

Just FYI your answer about A really made me think haha, so I've updated by above post with what I think to be a correct explanation. What do you think?

 

[osprey099]

Answer C says "...continue to move in their circular pathway as they fall..."

That is explicitly inconsistent with the answer explanation. I don't know how I can make it more clear that there is no way C can be correct as written.

With regard to A I'll have think about that more.

Edit: Okay, here's my shot at justifying A:

The explanation admits that the moment of inertia is not changed as a result of dropping the weights. This is Premise 1.

Premise 1: Moment of inertia (I) is constant.

Moment of inertia, defined as equal to kMR^2, related to both system mass and distribution of this mass from the radius. For a radially symmetrical system, the moment of inertia is some fraction of that if all the mass were contained at a point with radius of zero. Based on this relationship for distribution of mass, if moment of inertia is constant, center of mass (COM) must be constant.

Dropping the weights does not result in any sort of external torque on the student-weights system, so by the definition of the law of conservation of angular momentum, the angular moment of the student-weights system will remain constant. Approached from a different perspective, if mass were removed from the system (as with dropping the weights) and the removed mass retained angular momentum, this would necessarily result in an end value for angular momentum of the remainder of the system (the student) less than the initial total value for the system, as angular value would be split between two new systems. However, because the dropped weights lack angular momentum during their fall along tangential paths, the angular momentum of the remainder of the system (the student) is constant. This is Premise 2.

Premise 2: Angular momentum (L) of the system (student + both weights) remains constant.

Given these premises, and given that angular momentum L is defined as Iw, where I is the moment of inertia and w is the angular velocity:

With constant L and constant I, w must be constant.

Hmm I think Premise 2 is right: angular momentum of system is constant but I dont see how this relates to "changing the center of mass."

 

[gettheleadout]

Hmm I think Premise 2 is right: angular momentum of system is constant but I dont see how this relates to "changing the center of mass."

Law of Conservation of Angular Momentum gives us that his angular momentum is constant, the question stem gives us that his angular velocity is constant, meaning that his moment of inertia had to have been constant. If his center of mass had changed, his moment of inertia would too. Therefore knowing that his his center of mass was constant confirms that his moment of inertia was constant as well, and thus the reason his angular velocity remained the same.