Torque and Angular Momentum

We all have seen a door rotating about its hinges, the helicopter’s blade circling the nut, the wheels of a racing car spinning at immense speeds, etc. All these phenomena have one thing in common, Rotational motion. 

But what causes rotational motion?

Any change in the state of a body, either putting it into motion after rest or putting it to rest when it is in motion, is due to the application of force. Without force, there would be no perceivable change in the physical world. But different types of forces have different kinds of effects.

What is Torque?

We talked about some daily life examples of rotational motion, and the force responsible for this is called torque. We can describe torque as the measure of any force that causes an object to rotate about a given axis.

Force is the cause of acceleration in linear kinetics, and similarly, torque is the cause of angular acceleration. Like force, torque is also a vector quantity dependent on the direction we apply the force on the rotational axis.

A person can experience an intuitive feeling of torque when they open the door to a room. When force is applied, the door rotates. One can control the speed at which the door opens by the amount of force applied. In other words, the torque applied to the door. 

Torque can be either static or dynamic.

Static Torque

When torque is applied such that it generates no angular acceleration, it is called static torque. 

For example, if a cyclist is riding a bicycle at 10 kmph. The cyclist has to apply torque to turn the pedals. 

But suppose the cyclist is applying only enough torque to ensure that the cycle stays at a constant speed. In that case, no angular acceleration is generated, so the torque is called static torque.

Dynamic Torque

When torque is applied to generate angular acceleration, it is called dynamic torque. 

The drivetrain of a racing car applies torque on the wheels to increase the race car’s speed. Therefore, the angular acceleration of the wheels increases and such torque is called dynamic torque.

What is Angular Momentum?

Newton’s second law says that the application of force brings about a change in the state of a body, either to take it from rest to motion or from motion to rest. But what opposes force when it tries to change the state of a body? 

The answer is momentum.

Momentum is the quantity equal to the force required to bring a body in motion to rest in unit length or put a body in motion from rest to move a unit length. Similarly, the analogue to linear momentum in rotational kinematics is angular momentum. 

What are angular momentum and linear momentum?

We can describe linear momentum as the product of mass and velocity. In contrast, angular momentum is the product of the moment of inertia and the body’s angular velocity. A moment of inertia is the resistance offered by a body to angular acceleration.  

So what is angular momentum? 

Angular momentum is also a vector quantity and depends on both magnitude and direction. Similar to linear momentum, angular momentum also follows the law of conservation. Therefore, the angular momentum of any rotating body is always conserved, provided that there is no external torque acting on the body.

Examples of Angular Momentum

Angular momentum is a vector quantity and depends on both magnitude and direction. But how exactly is the concept of angular momentum used in both cases? Let us have a look.

1.Skaters use angular momentum to change their speed of rotation.

In skating, a popular move is to rotate on the spot at varying speeds to give an awe-inspiring performance. But how exactly does a skater pull off the movement?  

Initially, the skater brings in linear momentum and then uses torque to put their body into rotational motion.

Once their body is in rotational motion, the skater uses their arm to manipulate the moment of inertia of their body. By extending their arms, the moment of inertia of the body increases. 

Since the angular momentum of the skater’s body has to be conserved, increasing the moment of inertia will decrease the body’s angular velocity. This strategy will cause the skater to spin slowly.

Then when the skater has to increase their rotation speed, they bring their arms close to their body. This approach decreases the moment of inertia of the skater’s body. Again since they have to conserve the angular momentum of their body, the angular velocity of the body increases. It causes the skater to spin faster.

2.Holding a spinning bicycle wheel while sitting on a rotating chair is another example of angular momentum.

When a person holds a spinning bicycle wheel, the wheel is rotating perpendicular to the direction in which the person is sitting on the rotating chair. 

If the wheel is spinning in the clockwise direction, due to angular momentum, the person sitting on the chair will start spinning too. The direction of the spin will be along the direction in which the bicycle wheel is spinning.

But suppose the person were to turn the spinning bicycle wheel such that the wheel is now spinning in the counterclockwise direction. Then the rotating chair of the person would also start spinning in the counterclockwise direction. 

It happens because angular momentum is a vector quantity. By turning the direction of the spinning wheel, the direction in which the chair rotates also changes.

Conclusion

Torque is a measure of the force that causes a body to be in rotational motion. It can be of two types: static and dynamic. When the torque on a body does not produce an angular acceleration, it is static torque. In contrast, when the torque on a body has angular acceleration, it is called dynamic torque.

The angular momentum of a rotating body is the product of its moment of inertia and the body’s angular velocity. The angular momentum of a rotating body is conserved provided that no external torque is acting on the body.