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Transcript Slide 1

EGR 280
Mechanics
11 – Newton’s Second Law
Newton’s Second Law
Define the linear momentum of a particle as the product of its mass and
velocity:
L = mv
Newton said: The resultant force acting on any particle is equal to the time
rate of change of its linear momentum
R = ∑F = d(mv)/dt = dm/dt v + m dv/dt
If the mass of the particle is constant, then
∑F = m dv/dt = ma
Rectangular coordinates:
∑Fx = max
∑Fy = may
∑Fz = maz
Intrinsic coordinates
∑Ft = mat = m dv/dt
∑Fn = man = m v2/ρ
Define the angular momentum (or the moment of the momentum) of a
particle about a point as
y
H0 = r × mv
H0 = r(mv)sinφ
v
φ
m
r
x
z
The time derivative of the angular momentum is
r mv r mv
H
O
v mv r ma
r ma r F
MO