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Post Reopened by gandalf61, Thomas Fritsch, Michael Seifert
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Qmechanic ♦
Qmechanic ♦
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In trying to solve this particular problem:   

enter image description here

I have become confused about the conservation of energy and momentum. Specifically for Case A would angular momentum be conserved because there is net torque of zero? I know that the radius of the string is decreasing and that of course there is a tension force. However, what about the total mechanical energy? If there is not net external net work, then it should be conserved. Would the tension and gravitational forces acting on the mass be considered work then? If it was true that would say that these forces are external and yet they are part of the system. As for translational momentum, my guess is it is not conserved because it is accelerating inwards (using $T = \frac{mv^2}{r}$). Overall from this I am not sure what the speed will be because of this confusion.

Now for case B, my assumption is that angular momentum is not conserved. Evidently the $v_0$ is perpendicular to T, so the direction of displacement is perpendicular to T, and the work is zero (I guess energy is conserved). But how do I know that linear momentum is conserved or not? How do clarify the angular momentum? Also how do I find the speed?

In trying to solve this particular problem:  enter image description here

I have become confused about the conservation of energy and momentum. Specifically for Case A would angular momentum be conserved because there is net torque of zero? I know that the radius of the string is decreasing and that of course there is a tension force. However, what about the total mechanical energy? If there is not net external net work, then it should be conserved. Would the tension and gravitational forces acting on the mass be considered work then? If it was true that would say that these forces are external and yet they are part of the system. As for translational momentum, my guess is it is not conserved because it is accelerating inwards (using $T = \frac{mv^2}{r}$). Overall from this I am not sure what the speed will be because of this confusion.

Now for case B, my assumption is that angular momentum is not conserved. Evidently the $v_0$ is perpendicular to T, so the direction of displacement is perpendicular to T, and the work is zero (I guess energy is conserved). But how do I know that linear momentum is conserved or not? How do clarify the angular momentum? Also how do I find the speed?

In trying to solve this particular problem: 

enter image description here

I have become confused about the conservation of energy and momentum. Specifically for Case A would angular momentum be conserved because there is net torque of zero? I know that the radius of the string is decreasing and that of course there is a tension force. However, what about the total mechanical energy? If there is not net external net work, then it should be conserved. Would the tension and gravitational forces acting on the mass be considered work then? If it was true that would say that these forces are external and yet they are part of the system. As for translational momentum, my guess is it is not conserved because it is accelerating inwards (using $T = \frac{mv^2}{r}$). Overall from this I am not sure what the speed will be because of this confusion.

Now for case B, my assumption is that angular momentum is not conserved. Evidently the $v_0$ is perpendicular to T, so the direction of displacement is perpendicular to T, and the work is zero (I guess energy is conserved). But how do I know that linear momentum is conserved or not? How do clarify the angular momentum? Also how do I find the speed?

Post Closed as "Not suitable for this site" by Farcher, A. P., Hyperon
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John Rennie
John Rennie
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thewhale
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How do I know when in rotational dynamics whether or not mechanical energy, translational momentum, and angular momentum are conserved?

In trying to solve this particular problem: enter image description here

I have become confused about the conservation of energy and momentum. Specifically for Case A would angular momentum be conserved because there is net torque of zero? I know that the radius of the string is decreasing and that of course there is a tension force. However, what about the total mechanical energy? If there is not net external net work, then it should be conserved. Would the tension and gravitational forces acting on the mass be considered work then? If it was true that would say that these forces are external and yet they are part of the system. As for translational momentum, my guess is it is not conserved because it is accelerating inwards (using $T = \frac{mv^2}{r}$). Overall from this I am not sure what the speed will be because of this confusion.

Now for case B, my assumption is that angular momentum is not conserved. Evidently the $v_0$ is perpendicular to T, so the direction of displacement is perpendicular to T, and the work is zero (I guess energy is conserved). But how do I know that linear momentum is conserved or not? How do clarify the angular momentum? Also how do I find the speed?