Hint just think about these three unit vectors can

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Unformatted text preview: dinates is given by: ˙ˆ ˙ˆ ￿ = rr + rθθ + r sin θφφ v ˙ˆ (6) ˆ ￿ (d) Use the previous part to compute the angular momentum L = ￿ × p in terms of r, θ and φ, and then r￿ ˆˆ 2 2˙ show that Lz = mr φ sin θ. Hint! Just think about these three unit vectors - can you very quickly and intuitively argue what the cross product of r is with each of the spherical unit vectors without doing any calculations at all? Just ˆ be careful of signs. Extra credit (up to 4 bonus points, but won’t count off if you don’t do it) If a particle is restricted to move on the surface of a sphere, r(t) = R, and if angular momentum (in particular Lz ) is conserved (meaning, Lz doesn’t change with time) and assuming the particle starts its motion somewhere on the z axis, what can ˙ you say about φ at later times? 5. The pair of coupled ODEs dx(t) = Ax(t) − Bx(t)y (t) dt dy (t) = −Cy (t) + Dx(t)y (t) dt (7) (8) is referred to as the L...
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This document was uploaded on 03/09/2014 for the course PHYSICS 2210 at Colorado.

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