7. State the angular analogs of Newton’s laws of motion in words and using equations. Rearrange the 2nd law to reveal angular momentum and the angular impulse-momentum relationship and describe in words each step/rearrangement.
F = m *a
angular analogs
τ=I* α
Force F = torque τ
m ( mass) = I ( moment of inertia )
Linear acceleration (a) = Angular acceleration (α)
if we apply torque on a body, the applied torque is proportional to
the multiplication of moment of inertia and angular
acceleration
τ=I* α = I *dω /dt = d(Iω) /dt = dL/dt
τ = dL/dt
compare it with
F = d( m*v) /dt =dp/dt
so angular momentum = L = Iω
τ = dL/dt
dL = τ dt = angular impulse-momentum = I
I = τ dt = dL
same as we did
F =dp /dt
dp = F.dt
I= F*dt = dp
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