Lecture21 - Motion of a gyroscope Spin + precession SP IN...

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Spin + precession Motion of a gyroscope mg N Fall to the ground because of gravity Why? BUT… If spins it won’t fall down ω S P I N Continuous change of the rotation axis It will precess Ω ω PRECESSION
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τ mg = r x F = r x mg = m r x g CM = 0 0 τ mg = 0 mg N r mg N r From the definition τ is in a plane perpendicular to mg and r (xy plane) τ mg L along axis of spinning L τ N = 0 N has zero arm (r N =0 measured from the origin) mg creates a torque mg N r τ L = I ω
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L dL / dt = τ Δ L L L L+ Δ L L+ Δ L Δθ φ PRECESSION dL= τ dt changes same direction of τ τ
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Δ L L Δθ φ Ω precession Show Ω precession = Mgr / L R Note : Ω prec. does NOT depend on φ but only ~ 1/L L = I ω spin Ω prec. = Mgr / I ω The fastest it spins, the slowest it precess! sin φ sin φ
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Static Equilibrium dp dt = 0 dL dt = 0 p = const L = const or = + Condition for equilibrium: 1) F net = 0 2) τ net = 0 Translational equilibrium F F F net = Σ F ext = 0 1 st condition (necessary but not sufficient)
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Lecture21 - Motion of a gyroscope Spin + precession SP IN...

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