THE MAGIC OF SPINNING OBJECTS: GYROSCOPIC EFFECT

 

If you are an ardent movie watcher, and if you do watch south Indian action or comedy movies, chances are you would have come across a scene where a person is frantically chasing his cycle which rides away on its own. Yes! This could happen. Almost any bicycle can prevent itself from tipping over and losing its balance, even without a rider, as long as its front wheel is rolling fast enough. When the bike leans, the gyroscopic effect tends to steer the handlebars in the direction of the lean bringing the wheels back under the bicycle.

This gyroscopic effect is quite common and is experienced in many places. For instance, think about why a spinning ball is more stable and easy to balance rather than a still one? Professor Eric Laithwaite performs a one of a kind experiment where he lifts a very heavy wheel with just his one hand. He is able to do this only when the wheel spins at a very high velocity! The link to this video is given below.

Fig 1. man chasing bicycle

Why are spinning things so stable?

In physics, there are typically three types of quantities; a scalar (has only magnitude), a vector (has both magnitude and direction) and a tensor (a vector that does not obey the law of vector addition). Imagine an object on a table. If a force is applied to the body, then the body will move in the direction of the applied force with a certain momentum. Momentum is a vector quantity.

A similar observation can be made in rotating bodies. If a torque is applied to a wheel (let us say), the body gains angular momentum. The important point to note here are the directions! The direction of the angular momentum can be obtained by the right hand rule. Curl your fingers in the direction of the force that is applied to spin the wheel. The direction of the thumb gives you the direction of angular momentum.

Fig 2. Right Hand Rule

Just like how an object in linier motion resists change to its momentum, a spinning object resists change to its angular momentum. This gives rise to what is known as reactive gyroscopic couple. It is this reactive gyroscopic couple that actually provides the "stability" to the object.

In the case of balancing a spinning ball, if your finger exerts a torque on the ball (active gyroscopic couple) such as to unbalance it, due to the resistance in change of the angular momentum (which is the reactive couple), you have more time to correct your finger and keep it balanced. 

What is precession?

Imagine that you spin a coin. In a world with no friction, air resistance and gravity, it would keep spinning forever. But that’s not the case in our world. You will notice that the coin, as it loses its energy, it not only rotates slower, but also begins to wobble. This is a classical example of gyroscopic precession. Precession is nothing but the change in the axis of rotation of an object due to an external force. In the case of a coin, the external force would be the Earth’s gravity. 

To understand this better, think about a satellite orbiting around the Earth at a constant velocity.  Now if a vertically downward force is applied, since velocity is a vector quantity, it adds up and the satellite moves in the direction of the resultant velocity. Note here that the new orbit is formed as shown in fig 6  and not as that in fig 5. This means that the effect of the force is seen at phase difference of 90 degrees from the point of application of force. 

Fig 3. Force applied to satellite in orbit around Earth

Fig 4. The direction of the resultant velocity

Fig 5. The direction of motion does not shift like this

Fig 6.  The new correct direction of  motion of  satellite

Getting back to the spinning coin, the phenomenon is the same. The coin reacts to the torque on it due to the Earths gravity 90 degrees ahead. When this happens, the center of mass shifts and so does the direction of this applied torque. The effect of this new torque is once again felt 90 degrees ahead. This goes on and on until the coin loses its energy and does not posses angular momentum, producing the 'wobble'.

Is gyroscopic precession a really important phenomenon?

The importance of gyroscopic precision can be recognised with an example. Helicopters are one of the most important forms of transportation in our world. It has loads of applications including military and rescue operations. The lift and thrust of the helicopter are provided by the fan or blade that spins above it. This fan is a very large mass and it spins at a very high angular velocity.

Imagine a situation where you want the helicopter to move forward. To do this, logically you would want to increase the pitch of the blade at the rear and decrease it at the front to increase the lift of the blades at the rear when compared to the front as shown. Due to gyroscopic precession, the effect of the lift is only seen at 90 degrees ahead, which would make the helicopter tilt sideways! So in reality, to ensure the helicopter tilts forward, you have to control the pitch of the blades in the sides!

Fig 7 Helicopter force and response

A similar effect is present in the propellers of planes and a lot of other applications.

Conclusion

The spin of an object, the gyroscopic couples and gyroscopic precession can be summarised and represented in the following manner.

Fig 8. The Gyroscopic diagram

The gyroscopic effect is one of the most underappreciated physical phenomenon in our daily lives. One with a significant impact though. It finds its application in navigation systems of unmanned vehicles, space shuttles, submarines, guided missiles, supporting structures of rotating bodies among others. It helps in stability assessment of the Hubble Space Telescope. Micro Electro Mechanical Systems (MEMS) gyroscope in our smart phones recognizes the tilt or gesture provided to our phones and gaming systems. It also helps in image stabilization of camera and video systems.

So the next time you are able to balance a football with your little finger, you know why!

References

Prof. Eric Laithwaite: https://www.youtube.com/watch?v=JRPC7a_AcQo

https://medium.com/chip-monks/whats-a-gyroscope-and-accelerometer-doing-in-my-mobile-device-eb7acbdfa4e0#:~:text=A%20gyroscope%20in%20your%20phone,of%20reference%20of%20the%20device.

https://www.slideshare.net/dhopsanda/unit-2-dom