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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