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Chapter 9b - Chapter 9 Center of Mass and Linear...

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Unformatted text preview: Chapter 9 Center of Mass and Linear Momentum (part 2) Linear Momentum of a Single Particle • Linear momentum: • It is a measure of the particle’s motion • It is a vector, similar to the velocity • It also depends on the mass of the object, similar to the kinetic energy. r p r p = m r υ p x = m υ x p y = m υ y p z = m υ z Newton’s 2nd Law for a Single Body. • The time rate of the change of the momentum of a particle is equal to the net force acting on the particle. • The momentum formulation of Newton’s law is more inclusive as it is applicable to bodies and systems with variable mass. r F net = m r a = m d r υ dt = d ( m r υ ) dt = d r p dt r F net = d r p dt A few pointers: • The linear momentum of an object changes (and therefore there is a net force acting on it) if • The velocity changes in magnitude • The velocity changes in direction • The mass of the body changes Example- a ball hits a wall ∆ r p = r p f- r p i = - m υ ) i - m υ ) i = - 2 m υ ) i = - 2 r p ∆ r p = r p f- r p i ∆ p x = - m υ sin θ- m υ sin θ = - 2 m υ sin θ ∆ p y = - m υ cos θ + m υ cos θ = ∆ r p = r p f- r p i =- m υ ) i = - m υ ) i = - r p θ x y If the ball sticks to the wall the force is smaller than if it bounces. I II III Linear Momentum of a System of Particles • The vector sum of the linear momentum of all particles in the system! r P = r p 1 + r p 2 + r p 3 + ... + r p n r P = m 1 r υ 1 + m 2 r υ 2 + m 3 r υ 3 + ... + m n r υ n = m i r υ i i = 1 n ∑ r P = m i d r r i dt = i = 1 n ∑ dm i r r i dt = d dt i = 1 n ∑ m i r r i i = 1 n ∑ = M d dt m i r r i M i = 1 n ∑ = M d r r com dt r P = M r υ com r r com Total mass COM velocity Newton’s 2nd Law for a system of particles • The net force (the vector sum of all external forces ) acting on the system of particles is equal to the rate of change of the the total linear momentum of the system....
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Chapter 9b - Chapter 9 Center of Mass and Linear...

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