Torque Physics with definition and Examples

Torque physics & Definition of Torque: Torque is the Moment of Force (Rotational domain equivalent of Force). It is the determining factor of how effectively a force can twist or turn something. It is expressed as the cross product of force and the lever arm length.

In Physics, Torque is also defined as the rate of change of angular momentum. Torque can also be defined as the cross product of Moment of Inertia and Angular Acceleration.
Now if we have to understand the words in the first para above we need some examples from torque physics.

Torque meaning in physics and torque formula

We will discuss this with some practical examples. Let’s first consider the Bank Vault door.

derivation
Max Torque

Now, What determines a torque produced by a particular force?

When we try to push open a massive bank vault door, certainly we would push as hard as we can.
The torque certainly is proportional to the magnitude of the force.

But just by applying a huge force we can’t expect to get a huge torque.

In torque physics, It also matters where and in what direction we are applying the force.

In what direction to apply force to get max torque?

formula of torque

For maximum effectiveness, we have to push perpendicularly to the door ( Fig. a – above).

formula for torque

If we push radially, i.e. straight in toward the axis of rotation that passes through the hinges, the door wouldn’t rotate, no matter how hard we push ( Fig. b ).

derivation

A force acting in any other direction can be decomposed into horizontal and perpendicular components, with the horizontal component contributing nothing to the torque ( Fig. c ). Only the perpendicular component of the force ( F ⊥ ) produces a torque.

Where to apply the force for maximum torque as per Torque physics?

Furthermore, where we apply the force is critical.

Instinctively, we would push at the outer edge, as far from the rotation axis as possible.
If we push close to the axis, it would be difficult to open the door.

Torque is proportional to the distance between the rotation axis and the point of application of the force (the point at which the force is applied).

We define the magnitude of the torque as the product of the distance between the rotation axis and the point of application of the force ( r ) with the perpendicular component of the force ( F ⊥ ):

Torque is the moment of force

So we can write, t = ±rF
where r is the shortest distance between the rotation axis and the point of application of the force and F ⊥ is the perpendicular component of the force.

While opening a door that is free to rotate about its hinges, the greatest torque is produced when the force is applied farthest from the hinges and at an angle perpendicular to the door.

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Torque Physics with definition and Examples

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