# Torque

When a net force operates on a body, it causes linear motion in the applied force's direction. If the body is fixed to a point or an axis, a force like this spins the body depending on where the force is applied. Torque, or moment of force, is the ability of a force to induce rotational motion in a body. Any influence that, if left unchanged, will modify the motion of an object is referred to as a force.

Twisting force:

Torque denotes to the twisting force that causes a revolution. The center of gravity is the point at which the body rotates.

Turning force:

A pivot is a specific point at which a fixed object can rotate around it, and it is known as a turning force. When a force is applied to the object's surface, it is pushed to rotate around that pivot point, which is known as the turning force.

In everyday life, examples of such motion include the opening and closing of a door on its hinges and the turning of a nut with a wrench.

The extent of the rotation is influenced by the size of the force, its direction, and the distance between the fixed point and the point of application. When a body rotates due to torque, the angular momentum of the body varies with time.

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Definition:

The moment of an externally applied force about a point or axis of rotation is defined as torque. The rotational equivalent of linear force is torque. Depending on the subject of study, it is also known as the moment, moment of force, rotating force, or turning effect.

Direction of the Torque:

The right hand grip rule is used to indicate the position of the torque vector. The torque vector points in the direction of the thumb if a hand is twisted around the axis of rotation with the fingers pointing in the force direction.

## Derivation of torque:

A torque is a twist of an item around a given axis, similar to how a linear force is a push or a pull. The product of the force's magnitude and the perpendicular distance between the force's line of action and the speed of rotation is another definition of torque.

The expression for torque is

Where,

vector r - the position vector of the point

vector F - the force acting on the body

Here, the product of vector r and vector F is called the vector product or cross product.

When two vectors are vectorized, a new vector is created that is perpendicular to both vectors. As a result, torque is a vector quantity.

Torque has a magnitude of rFsinθ and direction perpendicular to r and F. Its unit is Nm.

Here, θ is the angle between r and F and in the direction of n cap is the unit vector. Because it requires the other two vectors r and F for its existence, torque is sometimes referred to as a pseudovector.

The right hand rule is used to determine the direction of torque. This rule states that if the fingers on the right hand are held parallel to the position vector with the palm facing the force direction and the fingers are curled, the thumb points in the torque direction. The torque's direction aids in determining the sort of rotation induced by the torque.

The torque is maximum when r and F are perpendicular to each other, i.e. when θ=90o and sin90o=1. Hence, max=rF

The torque is zero when r and F are parallel or antiparallel. If parallel, then θ=0o and sin0=0. If antiparallel, then θ=180o and sin180o=0. Hence, τ=0

If the force occurs at the reference point, the torque is zero. i.e. as r=0, τ=0

Consider an inflexible body that can rotate around an axis XY. Make the force F act at the point Pof a rigid body. It is possible that the force Fis not on the plane XYP. The origin O can be placed at any position along the axis XY.

The torque of the force F about O is The component of the torque along the axis is the torque of F about the axis. To find it, we should first find the vector and then find the angle of ∅ between and XY. The torque about XY is the parallel component of the torque along XY which is and the torque perpendicular to the axis XY is .

The torque around the axis rotates the objects around it, while the torque perpendicular to the axis turns the rotation axis. When both occur on a rigid body at the same time, the body will rotate counterclockwise. When a spinning top is about to come to a stop, the processional motion could be seen. As a result, it's expected that there are constraints in place to neutralise the effect of the perpendicular components of the torques and keep the axis in its fixed location. As a result, perpendicular torque components do not need to be considered.

• Include those forces that lie on a plane perpendicular to the axis and do not intersect the axis when calculating torques on rigid bodies.
• Think about perpendicular to the axis position vectors.
• Forces parallel to the axis will give torques perpendicular to the axis of rotation and need not be taken into account.
• Forces that intersect the axis cannot produce torque
• Position vectors along the axis will result in torques perpendicular to the axis and need not be taken into account.

Torque about an axis is independent of origin:

A force's torque around an axis is independent of its origin as long as it's chosen on that axis.

Let O be the origin on the axisXY, which is the rigid body's rotational axis. The force F acting at point P is denoted by the letter F. Choose a different pointO'on the axis now.

The torque of F about O' is,

O'PXF=(O'O+OP)F

=O'OXF+OPXF (vectors are bolded here)

As O'OXF is perpendicular to O'O, this term will not have a component along XY. Thus the component of O'PXF is equal to that of OPXF

## Different types of torque:

• Deflecting torque
• Controlling torque
• Damping torque

Deflecting torque:

The electromagnetic action of the current in the coil and the magnetic field generates the deflecting torque. When the torques are balanced, the moving coil will come to a halt, and the angular deflection of the coil will represent the quantity of electrical current to be measured against a fixed reference, referred to as a scale.

Controlling torque:

With the deflection of the moving system, the controlling torque rises, and the final position of the pointer on the scale corresponds to the magnitude of the electrical quantity to be measured (current, voltage, or power). The purpose of Controlling Torque is to limit the motion of the pointer or spindle and to stop the pointer at the appropriate location in order to obtain accurate readings. When the quantity under measurement is eliminated, the pointer is reset to zero.

Damping torque:

Damping torque is a physical mechanism for managing the movement of a system by providing motion that opposes the system's natural oscillation. It acts only while a system is in motion, similar to friction, and is absent when the system is at rest. The damping torque is related to the moving system's rotational speed. Under the influence of the deflecting torque, the instrument's moving system will tend to move.

## Applications of torque:

There is a pivot point in any object that is subjected to torque.

The following are some examples of applications:

• Gyroscopes with Seesaws and Wrenches
• When a pendulum or a parachute swings, it generates torque.

Applied Torque:

Torque is a force applied to a point on an object that rotates around its axis. The magnitude of torque is determined by the magnitude of the applied force and its perpendicular distance from the rotation axis.

Couple:

Definition:

A couple is a concept that includes the forces of equal magnitude but the opposite direction that are distanced by a perpendicular distance such that their lines of action do not meet, resulting in a turning effect.

There are cases in which the two forces may not cancel each other. If the two forces are not equal or the direction of the forces is not exactly opposite, then the body will have both translational as well as rotational motion.

Consider a thin uniform rod PQ. Its centre of mass is at its midpoint R.Allow two equal-magnitude, opposite-direction forces to be applied at the two ends P and Q of the rod perpendicular to it. A distance of 2r separates the two forces.

Because the two equal forces are in different directions, they cancel each other out, resulting in zero net force on the rod. The rod is now in a state of translational equilibrium. The rod, on the other hand, is not in rotational equilibrium. Let's take a look at how it's not in rotational balance. The anticlockwise rotation is caused by the moment of the force exerted at the endP in relation to the centre point R. Similarly, the anticlockwise rotation is caused by the moment of the force exerted at the end Q. The moments of both forces lead the rod to rotate in the same way. Despite the fact that the rod is in translational equilibrium, it rotates or turns.

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