TBR Physics Psg 8 #53 - angular velocity (spinning student drops weights)

[Gauss44]

Experiment 1
One student sits on a stool that rotates freely. He holds a 5kg mass in each hand. Initially, the student has an angular velocity of 5 radians/sec with his arms in his lap. (no more is written about experiment 1)

# 53
In Experiment 1, with his arms outstretched, the student drops the weights. This will cause the angular velocity of the student to:

A. increase
B. decrease
C. remain the same
D. A change cannot be determined.

Answer Key
C is correct. Dropping the weights does not change the moment of inertia for the system. Since I does not change when the student drops the weights, then by conservation of momentum the angular velocity of the student will not change.

Equations from passage:

torque = rF

L=Iw
I is the moment of inertia
w is the angular velocity
L is angular momentum

I is proportional to mr^2

torque = L/t

L initial = L final

KE=(1/2) Iw^2

Why doesn't dropping the weights change the moment of inertia? I thought it did because I is proportional to mass by the above equation.

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[brood910]

I didnt really understand that question either.

 

[BerkReviewTeach]

Experiment 1
One student sits on a stool that rotates freely. He holds a 5kg mass in each hand. Initially, the student has an angular velocity of 5 radians/sec with his arms in his lap. (no more is written about experiment 1)

# 53
In Experiment 1, with his arms outstretched, the student drops the weights. This will cause the angular velocity of the student to:

A. increase
B. decrease
C. remain the same
D. A change cannot be determined.

What version of the book do you have? This is the third time I've tried to look up a BR question you posted and couldn't find it. And I have the last three editions of physics. Given that it was removed at least four years ago, that question must have been deemed out of circulation for a reason, which I'm guessing is that it's not as applicable to the MCAT today.

I think the best way to think about that question is to visualize what would happen if you dropped the weights without spinning and then what would happen with spinning.

If you are sitting still with weights in your outstretched arms and dropped them, they fall down and your hands recoil up. If you're spinning, then when you drop the weights, they will move in a projectile fashion (falling to the ground in the y-direction and moving in a linear fashion in the x-direction). One will move in the positive x-direction and the other in the negative x-direction, which conserves momentum. The weights take their momentum with them, so the spinning person must retain whatever momentum they had independent of the weights. This means that they will keep spinning exactly the same.

The only way to change the spin rate would be to pull the weigths closer to the axis of spin or move them further from the axis of spin. Dropping them does not make them closer to or further away from the axis, so the moment of inertia did not change.

 

[Meredith92]

I have the most recent version of TBR and I found a similar question

#45 chapter 4 passage 7
"In experiment 1, with his arms outstretched, the student drops the weights. how can it be explained that the student's angular velocity did 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 the angular momentum
C the falling weights continue to move in their circular path as they fall so they retain their same angular momentum
D the weights are rotating in opposite directions after they are dropped

Choice C is the best answer. Just at the instant when the weights are dropped, the skater 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 no net momentum, so the skater cannot experience a change in 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 the moment of inertia does not change when the student drops the weights, then by conservation of momentum, the angular velocity of the student does not change."

 

[Gauss44]

What version of the book do you have?

My Physic I Berkeley Review book, where I got the above question, has a copyright of 2008. My other Berkeley Review books have different copyright dates, most of them fairly recent.

 

[BerkReviewTeach]

I have the most recent version of TBR and I found a similar question #45 chapter 4 passage 7

Thanks. You are right. I'm not sure how I missed it. Must have been lazy and skimmed too fast.

My Physic I Berkeley Review book, where I got the above question, has a copyright of 2008. My other Berkeley Review books have different copyright dates, most of them fairly recent.

That explains it. My oldest one is the paper cover version from 2009. I don't have enough space in my tiny room to keep up with their changes.