The gyroscope, often simply called a gyro (not to be confused with the Greek food wrap), doesn't get a great deal of press. But without this marvel of engineering, the world – and notably, humankind's exploration of other worlds – would be fundamentally different. Gyroscopes are indispensable in rocketry and aeronautics, and as a bonus, a simple gyroscope makes a great child's toy.
A gyroscope, though a machine with plenty of moving parts, is actually a sensor. Its purpose is to keep the motion of a rotating part in the center of the gyroscope steady in the face of shifts in the forces imposed by the gyroscope's external environment. They are constructed so that these external shifts are counterbalanced by movements of the gyroscope's parts that always oppose the imposed shift. This is not unlike the way a spring-loaded door or mousetrap will oppose your attempts to pull it open, all the more forcefully if your own efforts increase. A gyroscope, however, is much more intricate than a spring.
Why Do You Lean Toward the Left When a Car Turns Right?
What does it mean to experience an "outside force," that is, to be subjected to a new force when nothing new is actually touching you? Consider what happens when you are in the passenger seat of a car that has been traveling in a straight line at a constant speed. Because the car is not speeding up or slowing down, your body experiences no linear acceleration, and because the car is not turning, you experience no angular acceleration. Because force is the product of mass and acceleration, you experience no net force under these conditions, even if you are moving at a speed of 200 miles per hour. This is in accordance with Newton's first law of motion, which states that an object at rest will remain at rest unless acted on by an outside force, and also that an object moving at constant velocity in the same direction will continue along its exact path unless subjected to an external force.
When the car makes a turn to the right, however, unless you make some physical effort to counteract the sudden introduction of angular acceleration into your car ride, you will topple toward the driver to your left. You have gone from experiencing no net force to experiencing a force pointing straight out from the center of the circle the car has just begun to trace out. Because shorter turns result in greater angular acceleration at a given linear velocity, your tendency to lean to the left is more pronounced when your driver makes a sharp turn.
Your own, socially ingrained practice of applying just enough anti-leaning effort to keep yourself in the same position in your seat is analogous to what gyroscopes do, albeit in a far more complex – and effective – way.
The Origin of the Gyroscope
The gyroscope can be formally traced back to the middle of the 19th century and the French physicist Leon Foucault. Foucault is perhaps better known for the pendulum that takes his name and did most of his work in optics, but he came up with a device that he used to demonstrate the rotation of the Earth by figuring out a way to, in effect, cancel out or isolate the effects of gravity on the innermost parts of the device. Thus meant that any change in the axis of rotation of the gyroscope wheel during the time it was spinning had to have been imparted by the rotation of Earth. Thus unfolded the first formal use of a gyroscope.
What Are Gyroscopes?
The basic principle of a gyroscope can be illustrated using a spinning bicycle wheel in isolation. If you were to hold the wheel on each side by a short axle placed through the middle of the wheel (like a pen) and someone rotated the wheel while you held it, you would notice that if you tried to tip the wheel to one side, it would not go in that direction nearly as easily as it would if it were not spinning. This holds for any direction of your choosing and no matter how suddenly the movement is introduced.
It is perhaps easiest to describe the parts of a gyroscope from innermost to outermost. First, in the center is a rotating shaft or disk (and when you think about it, geometrically speaking, a disk is nothing more than a very short, very wide shaft). This is the heaviest component of the arrangement. The axle passing through the center of the disk is attached by near-frictionless ball bearings to a circular hoop, called a gimbal. This is where the story gets strange and highly interesting. This gimbal is itself attached by similar ball bearings to another gimbal that is just a tiny bit wider, so that the inner gimbal can just spin freely within the confines of the outer gimbal. The points of attachment of the gimbals to each other are along a line perpendicular to the axis of rotation of the central disk. Finally, the outer gimbal is attached by yet more smooth-gliding ball bearings to a third hoop, this one serving as the frame of the gyroscope.
(You should consult a diagram of a gyroscope or watch the short videos in the Resources if you haven't already; otherwise, all of this is almost impossible to visualize!)
The key to the function of the gyroscope is that the three interconnected but independently spinning gimbals allow for motion in three planes, or dimensions. If something were to potentially perturb the axis of rotation of the interior shaft, this perturbation can be simultaneously resisted in all three dimensions because the gimbals "absorb" the force in a coordinated way. What essentially happens is that as the two inner rings rotate in response to whatever disturbance the gyroscope has experienced, their respective axes of rotation lie within a plane that stays perpendicular to the axis of rotation of the shaft. If this plane does not change, then neither does the shaft's direction.
The Physics of the Gyroscope
Torque is force applied about an axis of rotation rather than straight on. It thus has effects on rotational motion rather than linear motion. In standard units, it is force times the "lever arm" (the distance from the real or hypothetical center of rotation; think "radius"). It therefore has units of N⋅m.
What a gyroscope in action accomplishes is a redistribution of any applied torques so that these do not affect the motion of the central shaft. It is vital to note here that a gyroscope is not intended to keep something moving in a straight line; it is meant to keep something moving with constant rotational velocity. If you think about it, you can probably imagine that spacecraft traveling to the moon or to more distant destinations do not go point-to-point; rather, they make use of the gravity exerted by different bodies and travel in trajectories, or curves. The trick is to ensure that the parameters of this curve remain constant.
It was noted above that the shaft or disk forming the center of the gyroscope tends to be heavy. It also tends to spin at extraordinary speeds – the gyroscopes on the Hubble Telescope, for example, spin at 19,200 rotations per minute, or 320 per second. On the surface, it seems absurd that scientists would equip such a sensitive instrument with suck a recklessly freewheeling (literally) component in the middle of it. Instead, of course, this is strategic. Momentum, in physics, is simply mass times velocity. Correspondingly, angular momentum is inertia (a quantity incorporating mass, as you'll see below) times angular velocity. As a result, the faster the wheel is spinning and the greater its inertia by way of greater mass, the more angular momentum the shaft possesses. As a result, the gimbals and exterior gyroscope components have a high capacity for muting the effects of external torque before that torque reaches levels sufficient to disrupt the shaft's orientation in space.
An Example of Elite Gyroscopes: The Hubble Telescope
The famed Hubble Telescope contains six different gyroscopes for its navigation, and these periodically need to be replaced. The staggering rotational speed of its rotor implies that ball bearings are impractical to impossible for this caliber of gyroscope. Instead, the Hubble makes use of gyroscopes containing gas bearings, which offer as close to a truly frictionless rotational experience as anything built by humans can boast.
Why Newton's First Law Is Sometimes Called the "Law of Inertia"
Inertia is a resistance to change in speed and direction, whatever they are. This is the lay version of the formal declaration set forth by Isaac Newton centuries ago.
In everyday language, "inertia" usually refers to a reluctance to move, such as, "I was going to mow the lawn, but inertia kept me pinned to the couch." It would be odd, however, to see someone who has just reached the end of a 26.2-mile marathon refuse to stop owing to the effects of inertia, even though from a physics standpoint the use of the term here would be equally permissible – if the runner continued to run in the same direction and at the same speed, technically that would be inertia at work. And you can imagine situations in which people do say they failed to stop doing something as a result of inertia, like, "I was going to leave the casino, but inertia kept me going from table to table." (In this case, "momentum" might be better, but only if the player is winning!)
Is Inertia a Force?
The equation for angular momentum is:
L = Iω
Where L has units of kg ⋅ m2/s. Since the units of angular velocity, ω, are reciprocal seconds, or s-1, I, the inertia, has units of kg ⋅ m2. The standard unit of force, the newton, breaks down into kg ⋅ m/s2. Thus inertia is not a force. This has not kept the phrase "force of inertia" from entering the mainstream vernacular, as happens with other things that "feel" like forces (pressure being a good example).
Side note: While mass is not a force, weight is a force despite the two terms being used interchangeably in everyday settings. This is because weight is a function of gravity, and since few people ever leave Earth for long, the weights of objects on Earth are effectively constant just as their masses are literally constant.
What Does an Accelerometer Measure?
An accelerometer, as the name implies, measures acceleration, but only linear acceleration. This means that these devices are not especially useful in many three-dimensional gyroscope applications, although they are handy in situations in which the direction of motion can be taken to occur in one dimension only (e.g., a typical elevator).
An accelerometer is one type of inertial sensor. A gyroscope is another, except that the gyro measures angular acceleration. And, although outside the purview of this topic, a magnetometer is a third kind of inertial sensor, this one used for magnetic fields. Virtual reality (VR) products incorporate these inertial sensors in combination to produce more robust and realistic experiences for users.
About the Author
Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.