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f11smid2 - mR 2 ˙ φ sin 2 θ = M z angular momentum...

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SOLUTIONS MIDTERM PHY 4936 (Fall 2011) PROBLEM 2 2.1 In sperical coordinates with r = R = const L = m 2 R 2 ˙ φ 2 sin 2 θ + ˙ θ 2 - m g R cos θ . 2.2 The conservations laws are E = m 2 R 2 ˙ φ 2 sin 2 θ + ˙ θ 2 + m g R cos θ energy conservation and p φ = ∂L ˙ φ = m R
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Unformatted text preview: mR 2 ˙ φ sin 2 θ = M z . angular momentum conservation. 3.3 Special solution θ ( t ) = θ = const : ˙ φ = M z mR 2 sin 2 θ = ω ⇒ φ ( t ) = ω t + φ ....
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