03. Dynamics

03. Dynamics

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[accordion title="1. Newton's Laws of Motion"]

  • Newton's First Law:  a body will remain in its state of rest or uniform motion in a straight line unless acted upon by a resultant force.
  • Newton's Second Law the rate of change of momentum of a body is proportional to the resultant force acting on it and the change takes place in the direction of the resultant force.
    • F =\frac{dp}{dt} in general
    • F =ma when mass is constant.
  • Newton's Third Law:  if body A exerts a force on body B, then body B exerts an equal and opposite force on body A

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[accordion title="2. Linear Momentum"]

  • The linear momentum of a body is defined as the product of its mass and its velocity.
  • Impulse is the product of the force acting on a body and the time interval during which the force is exerted. It is equal to the change in momentum of the body.
    • For constant force, impulse = \Delta p =F \Delta t
    • In general, impulse = \Delta p =\int {F .dt}

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[accordion title="3. Collision Problems"]

  • The principle of conservation of momentum states that the total momentum of a system of colliding objects remains constant provided no resultant external force acts on the system.
  • Conservation of momentum applies to both elastic and inelastic collisions.
    • m_1u_1+m_2u_2=m_1v_1+m_2v_2
  • Conservation of kinetic energy applies only to elastic collisions.
    • \frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2
  • Relative speed of approach = Relative speed of separation
    • u_2-u_1=v_1-v_2

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