TORQUE- CENTRE OF GRAVITY | ||||||||||||||||||||||||||||

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DEFINITION | ||||||||||||||||||||||||||||

“ The tendency of a force to produce rotation in a body “about an axis is called torque or momentum of force. | ||||||||||||||||||||||||||||

MATHEMATICAL DEFINITION | ||||||||||||||||||||||||||||

Torque produced in a body is numerically equal to the product of force and moment arm. | ||||||||||||||||||||||||||||

Torque = (force ) ( moment arm) | ||||||||||||||||||||||||||||

VECTORIAL DEFINITION | ||||||||||||||||||||||||||||

Torque produced in a body is equal to the cross product offorce arm ( ) and the force ( ). | ||||||||||||||||||||||||||||

The turning effect of a force depends upon two factors: Magnitude of force (F)Magnitude of moment arm (r)The torque about any axis is given by the product of force and moment arm. | ||||||||||||||||||||||||||||

EXPLANATION | ||||||||||||||||||||||||||||

Consider a particle of mass ‘m’ which is acted upon a force . Let be the position vector of the particle which is also the position vector of the point of application of force. We can resolve this force into two rectangular components: 1. Parallel to the position vector i.e. Or Fcosq 2. Perpendicular to the position vector i.e. Or Fsinq | ||||||||||||||||||||||||||||

From figure it is clear that can pull the particle but it cannot rotate it or it is unable to produce torque in the mass. It is the component which produces rotation in the mass. Let r andbe the magnitude of and respectively.The magnitude of of the torque produced about the centre ‘ O‘ is defined as: | ||||||||||||||||||||||||||||

Where q is the smaller angle between the positive direction of and . | ||||||||||||||||||||||||||||

Using vector notation, above expression can also be written as : | ||||||||||||||||||||||||||||

DIRECTION OF TORQUE | ||||||||||||||||||||||||||||

The direction of torque is directed along the normal to the plane formed by and as given by right hand rule. | ||||||||||||||||||||||||||||

SIGN CONVENTION | ||||||||||||||||||||||||||||

Positive torque:If a body rotates about its axis in anti clockwise direction, then the torque is taken positive . | ||||||||||||||||||||||||||||

Negative torque:If the body rotates in the clockwise direction, then the torque is taken as negative . | ||||||||||||||||||||||||||||

DETERMINANT FORM OF TORQUE | ||||||||||||||||||||||||||||

Let the position vector is = x i+ y j+ z k and the force= F_{x} i+ F_{y} j+ F_{z }k | ||||||||||||||||||||||||||||

The torque is given by: | ||||||||||||||||||||||||||||

UNIT OF TORQUE | ||||||||||||||||||||||||||||

In SI system unit of torque is N-m ( Newton . Metre) | ||||||||||||||||||||||||||||

DIMENSION OF TORQUE | ||||||||||||||||||||||||||||

[L^{2}MT^{-2}]
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