(revised 08-13-05)

Parallel Forces Notes

Torque = Force applied x Distance to pivot point

T = F x D

Torque = The attempt of a force to rotate the body to which it is applied about a pivot point.

The desire to rotate a body is influenced by two variable:

1. Force applied

2. Distance between the force and a given pivot point.

Large Torque:

A large force applied over a given distance:

T = F x D

T = 20 Nt x 1 m = 20 Nt·m

Small Torque:

A small force applied over the same distance:

T = F x D

T = 2 Nt x 1 m = 2 Nt·m

Large Torque:

A given force over a long distance:

T = F x D

T = 5 Nt x 10 = 50 Nt·m

Small Torque:

A given force over a short distance:

T = F x D

T = 5 Nt x 5 m = 25 Nt·m

Rotational Equilibrium requires a balance between all clockwise torques (T_CW) and all counterclockwise torques (T_CCW).

Σ(T_CW) = Σ(T_CCW)

F₁ x D₁ = F₂ x D₂

(2 Nt)(1 m) = (1 Nt)( 2 m)

2 Nt·m = 2 Nt·m

Torque or Moment

(A) Torque = Force x perpendicular Distance to pivot point

The distance from the applied force to the pivot, known as the torque arm (resistance arm, lever arm, or moment arm) must be measured (_┴) to the direction of the force.

F_E

When the line of action of the applied force exerted against the body is not perpendicular to the body, as in the diagram below, and you are asked to solve for the torque produced by the force as stated, you must designate a lever arm (D) that is perpendicular to the applied effort (F_E). In this case, the lever arm is perpendicular to the “line of action” of the applied force.

(B) Torque = perpendicular Force x Distance to pivot point

Couple

A “couple” refers to two parallel forces of equal magnitude acting in opposite directions, attempting to cause rotation of a body in the same direction.

A couple can be balanced, or brought into rotational equilibrium only by employing another couple having a torque equal, but in opposite direction, to the first.