lecture35[1] - 1 Physics 1D03 1 The Physical Pendulum SHM...

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Unformatted text preview: 1 Physics 1D03 1- The Physical Pendulum- SHM and Circular Motion- other oscillators Serway 15.4, 15.5 Practice: chapter 15, problems 26, 29, 31, 32, 35, 55, 57 Physics 1D03 2 Simple pendulum: a particle on a massless string. θ θ P CM mg “Physical” pendulum: any rigid body, pivoted at P, and free to swing back and forth. To find the period: 1) Consider the torque due to gravity 2) Write τ ( θ ) = I α = I (d 2 θ / dt 2 ) 3) SHM if τ is proportional to -θ 2 Physics 1D03 3 Calculate torque about the end: α θ α τ ⋅ = ⋅- = 2 3 1 2 sin ML L Mg I Example: a metre stick, pivoted at one end. What is its period of oscillation? “Uniform thin rod, pivot at end”: I = 1 / 3 ML 2 θ θ α sin 2 3 2 2 L g dt d- = = and so Note, this does not describe SHM! θ Mg L Physics 1D03 4 But for small oscillations, sin θ ≅ θ This is like a simple pendulum of length 2 / 3 L . L g 2 3 = ω g L T 3 2 2 2 π ω π = = θ ω θ θ 2 2 2 2 3- =- ≅ L g dt d so The angular frequency is and the period is θ Mg L 3...
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lecture35[1] - 1 Physics 1D03 1 The Physical Pendulum SHM...

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