Applied Physics I: Chapter 4: Oscillations and Waves
Moment, Couple and Torque
Definitionm, Explanation, Formula - Moment, Couple and Torque.
MOMENT,
COUPLE AND TORQUE
(i) Moment of a force:
The moment of a force about a point is defined as the product of the magnitude
of the force and the perpendicular distance from the point to the line of
action of force.
Explanation:
Let 'F' be the force acting on a body, at A as shown into Fig 4.3. Then the
moment of force 'F' about 'O' is M0 = F×d
Where
'd' is the perpendicular distance from the point 'O' to the line of action of
force F.
(ii) Couple:
A couple constitutes a pair of two equal and opposite forces acting on a body,
in such a way that the lines of action of the two forces are not in the same
straight line.
Explanation:
Let 'P' and 'Q' be the two equal and opposite forces acting on the body AB as
shown in Fig.4.4 then these two forces form a couple and the moment of the
couple about A is MA and about B is MB, then we can write
Couple = MA = MB = P×d
(iii) Torque:
Torque is the rotating force and is equal to the moment of the couple. Torque
is the product of one of the forces forming couple and the perpendicular
distance between the two opposite forces.
Explanation: Let us consider two equal and opposite forces F and ‒F acting tangentially on the rim of a circular disc from the extremities of diameter as shown in Fig 4.5.
It
forms a couple. If the couple rotates through a small angle 'θ'. Then,
The
distance moved by the force F in rotating the body through an angle 'θ' = Length
of the arc AB.
Here
the length of the arc AB = гθ
∴ Work done by a single
force = Frθ
Work
done by two forces constituting a couple = 2Frθ.
Here
2Fr is the moment of the couple (or) torque (τ)
Work done by the torque = τθ
Applied Physics I: Chapter 4: Oscillations and Waves : Tag: Applied Physics : - Moment, Couple and Torque
Applied Physics I: Chapter 4: Oscillations and Waves
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