Equilibrium problems - Equilibrium

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Equilibrium problems

Lessons

Notes:

In this lesson, we will learn:

  • Solving statics problems using both translational and rotational equilibrium

Notes:

  • An object or group of objects that are not moving are in static equilibrium.
  • In static equilibrium, the conditions for both translational and rotational equilibrium must be met.
Conditions for Translational Equilibrium

ΣF=0N\Sigma F = 0 N

or equivalently:

ΣFx=0N\Sigma F_{x} = 0 N and ΣFy=0N\Sigma F_{y} = 0 N

ΣF:\Sigma F: sum of all forces, in newtons (N)

ΣFx:\Sigma F_{x}: sum of all force components in x direction, in newtons (N)

ΣFy:\Sigma F_{y}: sum of all force components in y direction, in newtons (N)


Torque

τ=Fd\tau = F_{\perp}d

τ\tau: torque, in newton meters (N·m)

F:F_{\perp}: component of force perpendicular to dd, in newtons (N)

d:d: distance from point of rotation, in meters (m)


Conditions for Rotational Equilibrium

Στ=0\Sigma \tau = 0 N·m

or simpler equation:

total CWCW τ\tau = total CCWCCW τ\tau

Στ:\Sigma \tau : sum of all torques, in newton meters (N·m)

total CWCW τ\tau: magnitude of all torques in the clockwise direction, in newton meters (N·m)

total CCWCCW τ\tau: magnitude of all torques in the counterclockwise direction, in newton meters (N·m)

  • 1.
    Cable and beam in static equilibrium
Teacher pug

Equilibrium problems

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