Dynamics, Work, and Momentum

• Dynamics is the study of the causes of motion.
• Perfectly Inelastic Collision is an extreme case where all the kinetic energy relative to the center of mass is converted to thermal energy or internal energy of the system, and the two objects stick together.
• The first law of motion, also known as the law of inertia, states that an object will remain at rest or in a constant motion unless acted upon by an external force.
• Inertia is the tendency of things to resist changes in motion.
• The second law of motion, also known as the law of acceleration, states that the acceleration of an object is directly proportional to the net force of an object and inversely proportional to the mass of an object.
• The unit of force is newton (N).
• The third law of motion, also known as the law of action-reaction, states that for every action there is an equal and opposite reaction.
• Normal force (N) is a perpendicular force exerted by a surface to an object placed on it.
• Friction (f) is an opposing force between two surfaces in contact.
• Tension (T) is the force applied on the body whose direction is away from the body and along the cord at the point of attachment.
• Work is the product of the force applied on the body and the displacement it undergoes.
• The unit of work is Joule = 1Nm (J).
• Work is done only if a force moves an object through a certain distance.
• Work is a scalar quantity.
• Work is positive if the force has the same direction as its displacement.
• Work is negative if the force has an opposite direction as the displacement.
• Work is zero if the force is perpendicular to its displacement.
• Power is the amount of work done per time it takes to do it.
• Power (Watt = W) = work (J) / time (sec).
• Completely inelastic collision is when the colliding bodies stick together and move as one body after the collision.
• Mechanical energy is a form of energy due to the relative position of the interacting bodies, which can be potential energy or kinetic energy.
• The law of energy conservation states that energy is never created nor destroyed, but it may be changed from one form to another, and the total energy of a system remains the same.
• Collisions are any strong interaction between bodies that lasts a relative short time, in which the total momentum of the system is always conserved, meaning the total momentum before the collision is equal to the total momentum after the collision.
• Potential energy is energy associated with the position of the body in the stored state and has the potential to do work.
• Impulse is the change in linear momentum, represented by the equation I = F (t f - t i), or I = F Δ t, where I = impulse (Ns), F = force (N), and t = Time (s).
• Gravitational potential energy is the product of the weight of the body and its height from the reference level, represented by the equation PE = mgh (Joules).
• Kinetic energy is the energy of a body in motion, represented by the equation KE = ½ mv2 (Joules).
• Momentum is the inertia in motion and is the moving power of an object, represented by the equation p = mv, where p = momentum (kg m/s), m = mass (kg), and v = velocity (m/s).
• Inelastic collision is when the total kinetic energy after the collision is less than before the collision.
• Conservation of momentum states that if the net force of a system is zero, the total momentum of the system remains the same, represented by the equation P initial = P final.
• Conservation of mechanical energy states that mechanical energy initial = mechanical energy final.
• Energy is the capacity to do work.