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Momentum is a property of an object in motion. An object in translation has linear momentum equal to the product of its mass and velocity. An object in rotation has angular momentum equal to the product of its moment of inertia and angular velocity. p = mv; L = Iω Newton’s second law of motion can be written as an equation using momentum. If a net force is exerted on an object, the force equals the rate of change of the object’s linear momentum. If a net torque is exerted on an object, the torque equals the rate of change of the object’s angular Δp ΔL momentum. F = ;τ= Δt Δt The impulse (or angular impulse) given an object is the average force (or torque) exerted on the object multiplied by the time interval over which the force (or torque) acts. The impulse (or angular impulse) given an object equals the object’s change in linear momentum (or angular momentum). FΔt = Δp; τΔt = ΔL By Newton’s third law of motion, when two objects interact, they exert forces on each other that are equal in magnitude and opposite in direction. Since the forces act over the same time interval, the impulses are equal and opposite. This means the total momentum change of the combined system is zero. This is the law of conservation of momentum. When working momentum problems, first define the system. Then examine the system before and after the event. If the system is closed and isolated, its momentum and angular momentum are conserved. If Fnet = 0, then Δp = 0 or pi = pf. If τnet = 0, then ΔL = 0 or L i = L f . C HAPTER 7 SUMMARY 351