Lesson 19 Torques and Gyroscopes

When a torque acts on a spinning object the angular momentum changes. The rate of change of angular momentum is equal to the applied torque. Under the influence of a torque, a spinning object precesses.

All conservation laws come from F = m a

Newton's Mechanics based on three laws, however everything we do is based off of F = m a

Newton's third law implies conservation, thus a torque on one body implies a reverse torque on another. Angular momentum flows from one body to another and angular momentum is conserved.

The advancement of cultures over the course of history can be traced by advancements in transportation. Transportation dramatically changed with the creation of the wheel.

The force of gravity naturally tips the wheel down. However,  this is different with a spinning wheel.

When there is angular momentum there is a twisting force that changes the angular momentum. When angular momentum is conserved r x F (the radius vector and the force vector) is conserved.

A spinning wheel already has angular momentum, and torque can change that.

T = dl/dt

Below is a video that explains the concept of torque:


Gravity plays a strange trick on a spinning wheel. The force of gravity is downward, however the force of torque is sideways. This is why a spinning wheel will precess when stationed on an axis. When gravity tries to make a non-spinning wheel fall, the spokes push the top of the wheel outward rather than downward, which causes the weel to fall. This creates a component of velocity in the outward direction. This same thing happens at the bottom of the wheel but the force of gravity pulls the wheel inward.

This same idea also occurs when the wheel spins, however, when the outward velocity builds up it is at the side of the wheel. The force is outward on one side and inward on the other -- each spoke exerts its own push at the top -- causing a jog at the side. The net result is a downward but sideways motion when the wheel spins (precessing).


A top and bicycle wheel are a lot alike. A top acts as if all its mass is concentrated at one point, known as the center of mass. When the top is tilted there is a torque created. When this happens to a spinning top the torque nudges the anguar momentumof the top around in a little circle. Heat is produced at the tip of the top where energy is transfered into a random motion of molecules.

If a gyroscope is balanced at its own center of mass, the force of gravity will not make it precess. Even if it supports swivel in all directions the axis will remain stable and keep the gyroscope pointed in the same fixed direction.


Gyroscopes are used in planes in order to fly over magnetic poles using computer aide. Gyroscopes are improved by removing torque.

:C or capital omega is the rate of precession

U = wr

T = :C L

:C = Rg/wr^2

:C is just torque divided by angular momentum.

An object will precess least if wheel is large, spinning fast, and carefully balanced.

The best gyroscope on earth is the earth itself. The plane of the equator where day and night are equal length intersects the earth's orbit at the equinoxes. These points are used to denote seasonal changes and slowly dift to the west each year in the ever expanding universe.