Ch. 9 Key Equations - University Physics Volume 1 _ OpenStax.pdf

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Unformatted text preview: 2020/12/7 Ch. 9 Key Equations - University Physics Volume 1 | OpenStax Key Equations Definition of momentum p⃗ = mv⃗ Impulse ⃗ J ≡ ∫ tf ⃗ ⃗ ⃗ F (t)dt or J = Fave Δt ti Impulse-momentum theorem ⃗ J = Δp⃗ Average force from momentum ⃗ F = Instantaneous force from momentum (Newton’s second law) Conservation of momentum Δp⃗ Δt ⃗ F(t) = dp⃗ 1 dt dp⃗ dt dp⃗ 2 + = 0 or p⃗ 1 + p⃗ 2 = constant dt N Generalized conservation of momentum ∑ p⃗ j = constant j=1 Conservation of momentum in two dimensions pf,x = p1,i,x + p2,i,x pf,y = p1,i,y + p2,i,y N External forces dp⃗ j ⃗ Fext = ∑ dt j=1 Newton’s second law for an extended object Acceleration of the center of mass ⃗ F = dp⃗ CM dt ⃗ aCM = d N 2 2 dt ( 1 ∑ m j rj⃗ ) = M N 1 M j=1 j=1 N Position of the center of mass for a system of particles ⃗ rCM ≡ Velocity of the center of mass ⃗ vCM = 1 M ∑ m j rj⃗ j=1 N d dt ( 1 M ∑ m j rj⃗ ) = j=1 Position of the center of mass of a continuous object ⃗ rCM ≡ Rocket equation Δv = u ln ( ⃗ ∑ m j aj 1 M ∫ N 1 M ⃗ ∑ m j vj j=1 r ⃗ dm mi m ) 1/1 ...
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