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

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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 particles 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 p x = m x p y = m y p z = m z Newtons 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 Newtons law is more inclusive as it is applicable to bodies and systems with variable mass. r F net = m r a = m d r dt = d ( m r ) 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 ) i - m ) i = - 2 m ) i = - 2 r p r p = r p f- r p i p x = - m sin - m sin = - 2 m sin p y = - m cos + m cos = r p = r p f- r p i =- m ) i = - m ) i = - r p 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 1 + m 2 r 2 + m 3 r 3 + ... + m n r n = m i r 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 com r r com Total mass COM velocity Newtons 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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This note was uploaded on 03/12/2010 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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

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