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Part of ME-03 — Laws of Motion & Friction

Laws of Motion & Friction — All Formulas with Dimensional Analysis

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Newton's Second Law: F⃗net=ma⃗=dp⃗dt[M1L1T−2](N)\vec{F}_{net} = m\vec{a} = \frac{d\vec{p}}{dt} \quad [M^1L^1T^{-2}] \quad \text{(N)}

Linear Momentum: p⃗=mv⃗[M1L1T−1](kg⋅m/s)\vec{p} = m\vec{v} \quad [M^1L^1T^{-1}] \quad \text{(kg·m/s)}

Impulse: J⃗=F⃗ Δt=Δp⃗[M1L1T−1](N⋅s)\vec{J} = \vec{F}\,\Delta t = \Delta\vec{p} \quad [M^1L^1T^{-1}] \quad \text{(N·s)}

Apparent Weight in Lift: W′=m(g±a)[M1L1T−2](N)W' = m(g \pm a) \quad [M^1L^1T^{-2}] \quad \text{(N)}

Atwood Machine: a=(m1−m2) gm1+m2[M0L1T−2]T=2m1m2 gm1+m2[M1L1T−2]a = \frac{(m_1 - m_2)\,g}{m_1 + m_2} \quad [M^0L^1T^{-2}] \qquad T = \frac{2m_1 m_2\,g}{m_1 + m_2} \quad [M^1L^1T^{-2}]

Friction: 0≤fs≤μsNfk=μkNfr=μrNμ is dimensionless0 \leq f_s \leq \mu_s N \qquad f_k = \mu_k N \qquad f_r = \mu_r N \qquad \mu \text{ is dimensionless}

Angle of Repose: tan⁡θrepose=μs(dimensionless)\tan\theta_{repose} = \mu_s \quad \text{(dimensionless)}

Inclined Plane: N=mgcos⁡θ[M1L1T−2]F∥=mgsin⁡θ[M1L1T−2]N = mg\cos\theta \quad [M^1L^1T^{-2}] \qquad F_{\parallel} = mg\sin\theta \quad [M^1L^1T^{-2}]

Centripetal Force: Fc=mv2r[M1L1T−2](N)F_c = \frac{mv^2}{r} \quad [M^1L^1T^{-2}] \quad \text{(N)}

Maximum Speed on Level Road: vmax=μrg[M0L1T−1](m/s)v_{max} = \sqrt{\mu r g} \quad [M^0L^1T^{-1}] \quad \text{(m/s)}

Banking Angle (no friction): tan⁡θ=v2rg(dimensionless)\tan\theta = \frac{v^2}{rg} \quad \text{(dimensionless)}

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