Classical Mechanics Quiz

Classical Mechanics

• Definition: The branch of physics dealing with the motion of objects and the forces acting upon them.
• Key Concepts:
  • Newton's Laws of Motion:
    • First Law: An object at rest stays at rest, and an object in motion stays in motion unless acted upon by a net external force.
    • Second Law: Force equals mass times acceleration (F = ma).
    • Third Law: For every action, there is an equal and opposite reaction.
  • Kinematics: Study of motion without considering forces.
    • Key equations (uniform acceleration):
      • ( v = u + at )
      • ( s = ut + \frac{1}{2}at^2 )
      • ( v^2 = u^2 + 2as )
  • Dynamics: Study of the forces causing motion.
  • Work and Energy:
    • Work done (W): ( W = F \cdot d \cdot \cos(\theta) )
    • Kinetic Energy (KE): ( KE = \frac{1}{2}mv^2 )
    • Potential Energy (PE): ( PE = mgh )
    • Conservation of Energy: Total mechanical energy remains constant if only conservative forces act.
  • Momentum:
    • Linear momentum (p): ( p = mv )
    • Conservation of momentum: Total momentum before an event equals total momentum after (isolated system).

Dimensions

• Definition: Physical quantities expressed in terms of basic measurable quantities, providing a qualitative description of their characteristics.
• Fundamental Dimensions:
  • Length (L)
  • Mass (M)
  • Time (T)
  • Electric current (I)
  • Temperature (Θ)
  • Amount of substance (N)
  • Luminous intensity (J)
• Dimensional Analysis:
  • Useful for checking the consistency of equations.
  • Each physical quantity can be expressed in terms of fundamental dimensions (e.g., velocity = L/T).
• Units:
  • SI Units: Standardized system for measurements.
    • Length: meter (m)
    • Mass: kilogram (kg)
    • Time: second (s)
    • Force: Newton (N) = kg·m/s²
  • Conversion between units requires understanding the dimensional formula for each quantity.
• Dimensional Formula: Representation of a physical quantity in terms of its fundamental dimensions (e.g., acceleration: ( [L][T^{-2}] )).

Classical Mechanics

• Classical mechanics is a branch of physics that studies the motion of objects and the forces acting upon them.
• Newton's Laws of Motion:
  • First Law: An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a net external force.
  • Second Law: The force acting on an object is equal to its mass times its acceleration (F = ma).
  • Third Law: For every action, there is an equal and opposite reaction.
• Kinematics is the study of motion without considering the forces that cause the motion.
• Key equations for uniform acceleration:
  • Velocity (v) = initial velocity (u) + acceleration (a) * time (t)
  • Displacement (s) = initial velocity (u) * time (t) + (1/2) *acceleration (a) * time(t)^2
  • Final velocity squared (v^2) = initial velocity squared (u^2) + 2 *acceleration (a) * displacement (s)
• Dynamics is the study of the forces causing motion.
• Work and Energy:
  • Work done (W): Force (F) * distance (d) * cos(angle between F and d)
  • Kinetic Energy (KE): (1/2) * mass (m) * velocity (v)^2
  • Potential Energy (PE): mass (m) * acceleration due to gravity (g) * height (h)
  • Conservation of Energy: Total mechanical energy remains constant in an isolated system, as long as only conservative forces are acting on the system.
• Momentum:
  • Linear Momentum (p): mass (m) * velocity (v).
  • Conservation of Momentum: Total momentum before an event equals total momentum after in an isolated system.

Dimensions

• Definition: Physical quantities are expressed in terms of basic measurable quantities called dimensions. Dimensions provide a qualitative description of the characteristics of a physical quantity.
• Fundamental Dimensions:
  • Length (L)
  • Mass (M)
  • Time (T)
  • Electric Current (I)
  • Temperature (Θ)
  • Amount of Substance (N)
  • Luminous Intensity (J)
• Dimensional Analysis:
  • Dimensional Analysis is used to check the consistency of equations by ensuring that all terms in an equation have the same dimensions.
• Units: Standardized system for measurements.
  • SI Units:
    • Length: meter (m)
    • Mass: kilogram (kg)
    • Time: second (s)
    • Force: Newton (N) = kg * m/s²
• Dimensional Formula: Representation of a physical quantity in terms of its fundamental dimensions (e.g., acceleration: [L][T^-2]).