Force and Newton's laws formula sheet

Here is a formula sheet for Force and Newton's Laws:

Newton's Laws of Motion:

• Newton's First Law (Law of Inertia): 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 an unbalanced force.

  • Mathematically, this is often expressed as: $\sum F = 0 \implies a = 0$

• Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

  • Formula: $\sum F = ma$
    • $\sum F$ is the net force (in Newtons, N)
    • $m$ is the mass (in kilograms, kg)
    • $a$ is the acceleration (in meters per second squared, m/s²)

• Newton's Third Law: For every action, there is an equal and opposite reaction.

  • If object A exerts a force on object B ($F_{AB}$), then object B exerts an equal and opposite force on object A ($F_{BA}$).
  • $F_{AB} = -F_{BA}$

Common Forces:

• Weight (Force due to gravity):

  • Formula: $W = mg$
    • $W$ is weight (in Newtons, N)
    • $m$ is mass (in kilograms, kg)
    • $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$ on Earth)

• Friction Force:

  • Static Friction ($f_s$): The force that opposes the initiation of motion. It can vary up to a maximum value.
    • $f_s \le \mu_s N$
      • $\mu_s$ is the coefficient of static friction
      • $N$ is the normal force
  • Kinetic Friction ($f_k$): The force that opposes motion when an object is sliding.
    • $f_k = \mu_k N$
      • $\mu_k$ is the coefficient of kinetic friction
      • $N$ is the normal force

• Normal Force ($N$): The force exerted by a surface perpendicular to the surface, supporting an object.

• Tension ($T$): The force transmitted through a string, rope, cable, or similar object when it is pulled tight by forces acting from opposite ends.