Dynamics

• Newton's First Law of Motion states that an object at rest will remain at rest and an object in motion will remain in motion at constant velocity in the absence of an external resultant force.
• Newton's First Law of Motion is also known as the Law of Inertia.
• Inertia is a measure of the reluctance of an object to change its state of rest or uniform motion in a straight line.
• Mass is a measure of body's inertia to changes in velocity.
• The weight of a body is force acting on the mass in a gravitational field. Its SI unit is Newton ( N ).
• Weight = Mass * Acceleration of Free Fall
• W = m * g
• Mass is a scalar quantity while weight is a vector quantity.
• The linear momentum of a body is the product of the mass and its velocity. Its SI unit is kg m s^-1.
• Momentum = Mass * Velocity
• p = m * v
• Momentum is a vector quantity, and has the same direction as the direction of velocity.
• Newton's 2nd Law of Motion states that the rate of change of momentum of a body is directly proportional to the resultant force acting on the body and occurs in the direction of the resultant force.
• F = dp / dt (general form)
• F = m * a (when mass is constant)
• Newton's 3rd Law of Motion states that if body A exerts a force on body B, body B exerts a force of the same type that is equal in magnitude and opposite in direction on body A.
• Action-reaction pairs fulfils the following conditions:

  • The two forces act on two different bodies
  • The forces are equal in magnitude
  • The forces are opposite in direction
  • The forces must be of the same type
• Impulse is defined as the product of an average force and the time of impact for which the average force acts. Its SI unit is N s or kg m s^-1.
• Impulse = Change in Momentum
• The Principle of Conservation of Momentum state that the total momentum of a system of bodies is constant provided no resultant external force acts on the system.
• $m_1u_1$$+$$m_2u_2$$=$$m_1v_1$$+$$m_2v_2$

  
  

  ,ergo,

  
  

  Total momentum of system before collision = Total momentum of system after collision
• In Elastic Collisions:

  • Total momentum is conserved
  • Total kinetic energy is conserved
  • Relative speed of approach = Relative speed of separation
• In Inelastic Collisions:

  • Total momentum is conserved
  • Total kinetic energy is not conserved
  • Both bodies coalesce after collision
• A completely inelastic collision occurs when colliding bodies stick together and move off as one body after the collision.