Moment of force

When a force is applied on a door handle, it tends to turn (open or close) the door about the hinges.

This rotating or turning effect of a force about a fixed point or fixed axis is called moment of force about that point. This moment of force, i.e., the turning effect is maximum if the applied force is perpendicular to the plane of the door and the point of application is the farthest from the hinges.

Therefore, the moment of force is measured by the product of the magnitude of the force and the perpendicular distance between the fixed point or the fixed axis and the line of action of the force.

The moment of force, also called torque, is a vector quantity and is given as a cross product of the force vector,\(\vec{F}\)and the radius vector, \(\vec{r}\) as,

\(\vec{τ}\) = \(\vec{r}\) ×\(\vec{F}\) and the magnitude of moment of force (torque) is given by

τ = rF sinθ

= F. d

Here, this τ represent moment of force (torque), also called (tau).

Note – if the perpendicular distance between the line of action of the applied force and the fixed point is greater, greater will be the training effect.

Example : Door handles are provided far away from the hinges so that less amount of force is required to obtain greater turning effect.

Question–  find the moment of force if a force 8 N is applied on a door, perpendicular to its plane at distance of 100 cm from its hinge.Solution Given: Force is 8 N Perpendicular distance,  d = 100cm = 1m Moment of force = F×d Thus, moment of force = 2 × 1                                           = 2N

Zero Moment

If the line of action of a force passes through the axis of rotation, its perpendicular distance from the axis is zero. Therefore, its moment about that axis is also zero, In simple way – Turning effect is zero when forces are applied on the fixed point or on the fixed axis.

Unit of Moment of Force

Moment of force = Force × perpendicular distance

Hence, unit of torque = N (unit of force) × m (unit of distance)

Thus, the SI unit of moment of force is N m, CGS unit of moment of force is dyne cm.

Dimension formula of moment of force

Moment of force = Force × perpendicular distance

Thus, [torque] = [Force] [distance]

= [M¹ L¹ T ^-2] × [L]

= [M¹ L² T^-2 ]

Principal of moment

When a number of parallel forces act on a rigid body and the body is in equilibrium, then the algebraic sum of the moments of the individual forces about any point is equal to zero, i.e., sum of anti-clockwise moments is equal to sum of clockwise moments.