Written by Jerry Ratzlaff on . Posted in Classical Mechanics

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Force is the push or pull of an object resulting in a change from rest or motion.  So when you apply force to an object the velocity changes, the change in velocity is acceleration.  Force is a vector quantity having magnitude and direction, some of these include acceleration, displacement, drag, lift, momentum, thrust, torque, velocity, and weight.

Contact Forces

  • Frictional force
  • Tensional force
  • Normal force
  • Air Resistance force
  • Applied force
  • Spring force

Action at a distance Forces

  • Gravitational force
  • Electrical force
  • Magnetic force                  

Force Formula

\(F = ma\)


\(F\) = force

\(m\) = mass

\(a\) = acceleration

Solve for:

\(m = \frac {F}{a}\)

\(a = \frac {F}{m}\)

Applied Force

Applied force ( \(F_a\) ) can come from different types of forces, one of them could be Newton's Second Law.  There really is no one formula.

Average Force

Average force is used when the velocity was not measured precisely.

Average Force FORMULA

\(\bar F =  m  \frac { \left( v_f \;-\; v_i \right) } {t}  \) 

\(\bar F =  m  \frac { \Delta v } {t}  \)


\(\bar F\) = average force

\(m\) = mass

\(v_f\) = final velocity

\(v_i\) = initial velocity

\(\Delta v\) = velocity differential

\(t\) = time

Centrifugal Force

Centrifugal force is when a force pushes away from the center of a circle, but this does not really exist.  When an object travels in a circle, the object always wants to go straight, but the centripetal force keeps the object traveling along an axis of rotation.

Drag Force

Drag force or drag for any body moving through a fluid (gas or liquid), is the force exerted perpendicular and in opposition to the direction of travel.

Drag Force Formula

\( F_D = \frac {1} {2}  \rho v^2  C_D    A \)


\(F_d\) = drag force

\(\rho\) = density

\(v\) = velocity

\(C_d\) = drag coefficient

\(A\) = area

Lift Force

Lift force for an body moving through a fluid (gas or liquid), is the force exerted perpendicular to the direction of travel.

Lift Force formula

\(L = \frac {1} {2} C_L \rho v^2 A \)


\(L\) = lift force

\(C_L\) = lift coefficient

\(v\) = velocity

\(\rho\) (Greek symbol rho) = density

\(A\) = area

Solve for:

\(C_L = \frac {2 L} {\rho v^2 A} \)

\(\rho = \frac {2 L} { C_L v^2 A} \)

\(v =   \sqrt { \frac {2 L} { C_L \rho A}   } \)

\(A = \frac {2 L} { C_L \rho v^2}   \)

Net Canceling Force

Two forces can cancel each other when the foeces act on are equal.

Net Canceling Force Formula

\(F_n = 0 = F_1 \; - \;  F_2 \)


\(F_n\) = net force

\(F_1\) = force 1

\(F_2\) = force 2

Net Positive or Negative Force

Two forces can add or subtract to the net force when the forces act on each other.  Forces in the same direction working togeather equal a net force.

Net Positive or Negative Force Formula

\(F_n = F_1 \; + \;  F_2 \)

\(F_n = F_1 \; - \;  F_2 \)


\(F_n\) = net force

\(F_1\) = force 1

\(F_2\) = force

Normal Force

Normal force is always perpendicular to the surface it contacts and equal to the weight of the object. Unless there is another external force pushing the object into the contact surface there will be no normal force.

normal force







Normal Force Formula

\(F_n = \frac { f_k }   { \mu_k} \)

\(F_n = \frac { f_s }   { \mu_s} \)


\(F_n\) = normal force

\(f_k \) = kinetic friction

\(\mu_k\) (Greek symbol mu) = kinetic friction coefficient

\(f_s\) = static friction

\(\mu_s\) (Greek symbol mu) = static friction coefficient

Parallel Force

All the forces are parallel (not necessarily in the same direction)

Rotational Force

Rotational Force Formula

\( \tau = I  \alpha  \)


\(\tau\) (Greek symbol tau) = rotational force

\(I  \) = moment of inertia

\(\alpha\) (Greek symbol alpha) = angular acceleration

Weight Force

Weight force is the force of gravity or the weight.  The pull of gravity creates downward acceleration of the object falling and factors such as air resistance can affect the weight force.

Weight Force Formula

\( W = F_g = m g \)


\(W\) = weight

\(F_g\) = weight force

\(m\) = mass

\(g\) = gravitational acceleration


Tags: Equations for Force