homework2

# Hint just think about these three unit vectors can

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This document was uploaded on 03/09/2014 for the course PHYSICS 2210 at Colorado.

Ask a homework question - tutors are online