Question

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.

Answer #1

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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