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Force, Work, Power and Energy

Second Law of motion

When a force acts on a rigid body, two kinds of motion are exhibited.

• Linear or Translational Motion: When a rigid body, which is free to move, starts moving in a straight path along the direction of applied force, then such motion is called linear or translation motion.
• Rotational Motion: When a rigid body, pivoted at a point, starts rotating about the axis passing through the pivoted point when a force acts on it, then such motion is called rotational motion.

Torque (Moment of Force)

The given figure shows a wrench and a nut. When a force, F, is applied to the handle of the wrench, the nut turns in a direction as shown in the given diagram.

It is interesting to note that the greater the distance between the nut and the point of application of force (denoted by D in the figures), the easier it will be to turn the nut.

Therefore, the turning of the nut depends on two factors:

i. The greater the applied force F, the more easily the nut can be turned.

ii. The greater the distance d, the more easily the nut can be turned.

It is clear from these points that the turning effect can be increased either by increasing F or by increasing d (distance between the nut and the point of application of force F)

On account of these points, we define a quantity called torque.

Torque (τ) = Force (F) × Perpendicular distance (d)

Torque represents the turning force acting on an object. It can either be clockwise or anticlockwise, depending upon how the force is applied. The given figures show clockwise as well as anticlockwise torque.

A clockwise torque tends to turn an object in the clockwise direction. Similarly, an anticlockwise torque tends to turn an object in the anticlockwise direction.

Torque is also known as moment of force.

Unit of Torque

Torque (τ) = Force (F) × Perpendicular distance (d)

Since the unit of force is N and the unit of distance is m, the unit of torque is Nm (Newton-metre).

Translational Equilibrium

An object is said to be in translational equilibrium if the net force acting on the object is zero. A translational equilibrium corresponds to the state of rest or to a straight-line motion at a constant speed. It means that if an object is in translational equilibrium, the object remains at rest or continues its motion in a straight line at constant speed. The essential condition for translational equilibrium can be given in the form of an equation as:

Σ F = 0

The given figure shows a block on which two forces are acting.

The net force on this block is 120 N − 120 N = 0 N.

Therefore, the given block is said to be in translational equilibrium.

It means that if the block is already at rest, then it will continue to be at rest after the two forces start acting simultaneously.

Also, it means that if the block was already in motion, it will continue the same type of motion after the two forces start acting simultaneously.

Rotational Equilibrium

An object is said to be in rotational equilibrium if the net torque acting on the object is zero.

Consider a drum fitted such that it can rotate around its axis. The given figures show two such drums. Arun and Pankaj tie up ropes, as shown in the given figures and pull the ropes with equal forces.

In which of the given situations will the drum not rotate?

Yes, that is right! The drum will not rotate in situation II. Therefore, in situation II, the drum is in rotational equilibrium. The torque exerted by Arun is equal but opposite to the torque exerted by Pankaj.

Clockwise and Anticlockwise Moment

Torque is also known as moment of force.

The given figure shows a metre scale that can rotate about the fixed point O.

The moment of force F1 is given by:

τ1 = F1 × d1

This tends to turn the metre scale in the clockwise direction.

Hence, it is a clockwise moment.

Similarly, the moment of force F2 is given by:

τ2 = F2 × d2

It is an anti-clockwise moment. It tends to turn the metre scale in the anticlockwise direction.

For an object to remain in remain in rotational equilibrium:

Clockwise moment = Anticlockwise moment

 Example Let us consider a light rod AB of negligible mass with centre at C. Two parallel forces, each of magnitude F, are applied at the ends such that the forces are perpendicular to the rod, as shown in the figure below. Here, total force on the rod = F − F = 0. This is because the forces act in opposite directions. The net force on the rod is zero. Therefore, the rod is in translational equilibrium. The moments of both forces about C are equal (= aF) but they are not opposite. They act in the same direction and cause the anticlockwise rotation of the rod. Thus, the rod is not in rotational equilibrium.

Couple

A pair of parallel forces, which are equal and opposite and are not acting along the same line, form a couple. These two equal and opposite forces always act at two different points. Such couple is always needed to produced a rotation.

Examples: Turning of a tap water, tightening the cap of a bottle, turning a steering wheel are some examples where couple is used.

Moment of Couple

It is the product of either force and perpendicular distance betwee…

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