18 lines
730 B
Plaintext
18 lines
730 B
Plaintext
== UNIT 5: TORQUE AND ROTATIONAL DYNAMICS ==
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Torque: τ = r*F*sin(θ) = F_perp*r
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r is distance from pivot to force application point
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Lever arm: perpendicular distance from pivot to force line
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τ = I*α (rotational analog of F = ma)
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Moment of inertia: I = Σ(m_i*r_i^2)
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Parallel axis theorem: I = I_cm + M*d^2
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Rotational KE: KE_rot = 0.5*I*ω^2
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Angular momentum: L = I*ω
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Angular momentum conserved if no external torque
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Rotational work: W = τ*Δθ
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Rotational power: P = τ*ω
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Rolling without slipping: v = r*ω, a = r*α
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Static friction enables rolling
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Angular acceleration same for all points
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Angular velocity same for all points
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Angular momentum: L = m*v*r*sin(θ) for point mass
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Rotational inertia depends on mass distribution |