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Summary16

# Summary16 - Summary Lecture 16 Rotational and Linear Motion...

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Summary Lecture 16 Rotational and Linear Motion D isplacement Linear: Δ x, measured in [m] Rotational: Δθ difference in angle , difference in angle measured in [rad] 360 degrees = 2 π rad C i θ [ d] θ [d ] *2 /360 Conversion: [rad] = [degrees] *2 π /360 Arc-length l : l = θ r; θ in [rad] V l it Velocity Linear: v = Δ x/ Δ t, measured in [m/s] Rotational: ω = Δθ / Δ t, measured in [rad/s] Period T = time for one revolution Frequency f = # of revs per second f = 1/T ω = 2 π /T = 2 π f Acceleration Linear: a = Δ v/ Δ t, measured in [m/s 2 ] Rotational: α = Δθ / Δ t; measured in [rad/s 2 ]

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Uniformly Accelerated Motion: (constant acceleration) Linear v = v 0 +at Rotational ω = ω 0 + α t 1 2 x = x 0 +v 0 t+ 1 / 2 at 2 v 2 = v 0 2 +2a Δ x θ = θ 0 + ω 0 t+ / 2 α t ω 2 = ω 0 2 + 2 αΔθ v = (v+v 0 )/2 ω = ( ω + ω 0 )/2 + centripetal acceleration