19.5: Angular Impulse and Change in Angular Momentum
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If there is a total applied torque →τS about a point S over an interval of time Δt=tf−ti, then the torque applies an angular impulse about a point S, given by
→JS=∫tfti→τSdt
Because →τS=d→Ltotal S/dt the angular impulse about S is equal to the change in angular momentum about S,
→JS=∫tfti→τSdt=∫tftid→LSdtdt=Δ→LS=→LS,f−→LS,i
This result is the rotational analog to linear impulse, which is equal to the change in momentum,
→I=∫tfti→Fdt=∫tftid→pdtdt=Δ→p=→pf−→pi