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Statement of the problem :
Two ice skaters circle about a point while holding hands. At a certain moment both let go and move along straight lines. Are the two straight lines parallel? Explain.
My attempt : Calling the two ice skaters ##S_1## and ##S_2 ##, they must lie along the same line passing through the centre of the circle at all points. That implies, despite their different masses, they must rotate with the same (linear) velocity ##v##. When they separate, they should move in lines that are tangent to the circle and therefore perpendicular to the diameter to which they were "connected" last. Hence their straight lines must be parallel.
Doubts :
1. The problem is one on angular momentum ##(\mathbf L = \mathbf r \times \mathbf p)## and its conservation. I haven't used any of that in my solution, even if I am correct.
2. If the masses ##(m_1 \neq m_2)## are different, should their linear speeds ##(v_1, v_2)## and radii ##(r_1, r_2)## by the same? Of course, both could be different in a way such that their angular speed ##(\omega = \frac{v}{r})## remains the same.
Two ice skaters circle about a point while holding hands. At a certain moment both let go and move along straight lines. Are the two straight lines parallel? Explain.
My attempt : Calling the two ice skaters ##S_1## and ##S_2 ##, they must lie along the same line passing through the centre of the circle at all points. That implies, despite their different masses, they must rotate with the same (linear) velocity ##v##. When they separate, they should move in lines that are tangent to the circle and therefore perpendicular to the diameter to which they were "connected" last. Hence their straight lines must be parallel.
Doubts :
1. The problem is one on angular momentum ##(\mathbf L = \mathbf r \times \mathbf p)## and its conservation. I haven't used any of that in my solution, even if I am correct.
2. If the masses ##(m_1 \neq m_2)## are different, should their linear speeds ##(v_1, v_2)## and radii ##(r_1, r_2)## by the same? Of course, both could be different in a way such that their angular speed ##(\omega = \frac{v}{r})## remains the same.
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