# 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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