What is it? Gyroscopic motion is what occurs when something is spinning centered on its axis . Give me an example! Have you ever seen how a spinning gyroscope reacts to changes? The gyroscope is always "happiest" when its axis is aligned at a constant angle to the surface of the earth. If something disturbs the precession of the gyroscope, it moves to counteract the disturbance. That's called gyroscopic motion. This "homing" quality of gyroscopic motion is called precession -- and it's why large ships at sea have gyrocompasses. They spin and therefore are not affected by the magnetic forces of the steel hull of the ship like a regular compass would be What is it? The imaginary line down the very center of a spinning object is called its axis. Graph s have both a horizontal and vertical axis. Give me an example! The earth's axis always points in the same direction because the earth has gyroscopic motion and precession . The earth spin s on its axis (with a slight bit of wobble due to outside gravitational forces). If something disturbed the earth's rotation (like a big giant meteor striking it), it would cause a shift in the alignment of the earth's axis. What is it? Precession is the slow rotation of the axis of a spinning object. Give me an example! The slow rotation of the gyroscopes axis is called its precession. Many rotating objects show precession -- including the earth itself! Think of the earth as a gigantic gyroscope! Precession is what makes a spinning object (like a gyroscope) able to stay pointed in the same direction if it is disturbed by an outside force. If you get your gyro spinning and then disturb it, it will try and find a way to right itself with precession. What is it? Spin is when something rotates around a fixed central point or axis .
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What is it?
Gyroscopic motion is what occurs when something is spinning centered on its axis.
Give me an example!
Have you ever seen how a spinning gyroscope reacts to changes? The gyroscope is always "happiest" when its axis is aligned at a constant angle to the surface of the earth. If something disturbs the precession of the gyroscope, it moves to counteract the disturbance. That's called gyroscopic motion.
This "homing" quality of gyroscopic motion is called precession -- and it's why large ships at sea have gyrocompasses. They spin and therefore are not affected by the magnetic forces of the steel hull of the ship like a regular compass would be
What is it?
The imaginary line down the very center of a spinning object is called its axis.
Graphs have both a horizontal and vertical axis.
Give me an example!
The earth's axis always points in the same direction because the earth has gyroscopic motion and precession. The earth spins on its axis (with a slight bit of wobble due to outside gravitational forces). If something disturbed the earth's rotation (like a big giant meteor striking it), it would cause a shift in the alignment of the earth's axis.
What is it?
Precession is the slow rotation of the axis of a spinning object.
Give me an example!
The slow rotation of the gyroscopes axis is called its precession. Many rotating objects show precession -- including the earth itself! Think of the earth as a gigantic gyroscope! Precession is what makes a spinning object (like a gyroscope) able to stay pointed in the same direction if it is disturbed by an outside force. If you get your gyro spinning and then disturb it, it will try and find a way to right itself with precession.
What is it?
Spin is when something rotates around a fixed central point or axis.
Give me an example!
Have you ever looked closely at a bicycle wheel? The wheel and spokes all spin around the center point where the axle holds the wheel to the frame. All wheels work this way -- they spin around a fixed point in their center.
What is it?
The axle is a long skinny rod that attaches to the center of a wheel, gear, or pulley. When the axle turns, whatever is attached to it also turns. This makes it possible to transfer rotary motion from one axle to another with gears or pulleys.
Give me an example!
In the picture above, you'll see a good example of how axles can work together with gears and pulleys to get your project rolling!
What is it?
A bicycle is a two-wheeled vehicle that is moved by using your feet to turn the pedals.
Give me an example!
Bicycles use a lot of mechanical engineering principles in their construction and movement. Bicycles use gears, levers and the brakes are even a non-linear flexible system! Wow!
What is it?
A wheel is a disk shaped object, which transfers linear motion into rotary motion.
The wheel and axle is a simple machine that makes it easier to move heavy loads! Many people consider the wheel and axle as a kind of lever, with the center of the axle serving as a fulcrum. Rollers were the forerunner of the wheel, with several logs placed under some heavy object.
Give me an example!
Have you ever ridden on a bicycle? Bicycles have a wheel in the front that turns for steering and a wheel in the back that you provide torque to by pushing down on the pedals and moving a chain which turns the sprocket in the center of the wheel.
Without wheels, most of the things that move in the world wouldn't be able to go anywhere! Cars, busses, trains even airplanes have wheels (called landing gear) for moving on the ground. How many sets of wheels do you use every day?
What is it?
Torque is the ability of a force to produce rotary motion.
Give me an example!
Have you ever climbed a steep hill on a bicycle? Remember how much force you had to use to turn the pedals? That force was torque. It turned the crank that turned the sprockets that turned the wheels of the bicycle to produce rotary motion. It takes more torque to pedal uphill than downhill.
Torque can be measure d by taking the product of the force and the perpendicular distance from the line of action of the force to the axis of rotation.
What is it?
Rotary motion is when an object moves in a circle centered around a specific point called an axis. In other words, when something is turning around and around, it is said to have rotary motion.
Give me an example!
Stand up and turn around. The motion you just completed is called rotary motion because every part of your body turned around an imaginary point in space called an axis. The wheels of a bicycle also turn in rotary motion, and so does the propeller on an airplane and the crankshaft in a car engine.
What is it?
A simple machine is a device that has only one function and a minimum of moving parts.
Give me an example!
Levers, wheels, springs, and the inclined plane are examples of simple machines. They all have simple functions by themselves, such as lifting a load or rolling along. Many simple machines are often grouped together to form a more complex machine, such as an alarm clock.
Gyroscope
One typical type of gyroscope is made by suspending a relatively massive rotor inside three rings called gimbals. Mounting each of these rotors on high quality bearing surfaces insures that very little torque can be exerted on the inside rotor.
Gyroscope DiscussionThe classic image of a gyroscope is a fairly massive rotor suspended in light supporting rings called gimbals which have nearly frictionless bearings and which isolate the central rotor from outside torques. At high speeds, the gyroscope exhibits extraordinary stability of balance and maintains the direction of the high speed rotation axis of its central rotor. The implication of the conservation of angular momentum is that the angular momentum of the rotor maintains not only its magnitude, but also its direction in space in the absence of external torque. The classic type gyroscope finds application in gyro-compasses, but there are many more common examples of gyroscopic motion and stability. Spinning tops, the wheels of bicycles and motorcycles, the spin of the Earth in space, even the behavior of a boomerang are examples of gyroscopic motion.
Gyroscope Precession
If a gyroscope is tipped, the gimbals will try to reorient to keep the spin axis of the rotor in the same direction. If released in this orientation, the gyroscope will precess in the direction shown because of the torque exerted by gravity on the gyroscope.
Conservation of Angular MomentumThe angular momentum of an isolated system remains constant in both magnitude and direction. The angular momentum is defined as the product of the moment of inertia I and the angular velocity. The angular momentum is a vector quantity and the vector sum of the angular momenta of the parts of an isolated system is constant. This puts a strong constraint on the types of rotational motions which can occur in an isolated system. If one part of the system is given an angular momentum in a given direction, then some other part or parts of the system must simultaneously be given exactly the same angular momentum in the opposite direction. As far as we can tell, conservation of angular momentum is an absolute symmetry of nature. That is, we do not know of anything in nature that violates it.
Angular MomentumThe angular momentum of a rigid object is defined as the product of the moment of inertia and the angular velocity. It is analogous to linear momentum and is subject to the fundamental constraints of the conservation of angular momentum principle if there is no external torque on the object. Angular momentum is a vector quantity. It is derivable from the expression for the angular momentum of a particle
Moment of InertiaMoment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion. The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr2. That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.
Mass and WeightThe mass of an object is a fundamental property of the object; a numerical measure of its inertia; a fundamental measure of the amount of matter in the object. Definitions of mass often seem circular because it is such a fundamental quantity that it is hard to define in terms of something else. All mechanical quantities can be defined in terms of mass, length, and time. The usual symbol for mass is m and its SI unit is the kilogram. While the mass is normally considered to be an unchanging property of an object, at speeds approaching the speed of light one must consider the increase in the relativistic mass.
The weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton. Density is mass/volume.
Angular Velocity
Angular velocity can be considered to be a vector quantity, with direction along the axis of rotation in the right-hand rule sense.
Vector angular velocity
For an object rotating about an axis, every point on the object on the object has the same angular velocity. The tangential velocity of any point is proportional to its distance from the axis of rotation. Angular velocity has the units rad/s.
Angular velocity is the rate of change of angular displacement and can be described by the relationship
and if v is constant, the angle can be calculated from
MomentumThe momentum of a particle is defined as the product of its mass times its velocity. It is a vector quantity. The momentum of a system is the vector sum of the momenta of the objects which make up the system. If the system is an isolated system, then the momentum of the system is a constant of the motion and subject to the principle of conservation of momentum.
The basic definition of momentum applies even at relativistic velocities but then the mass is taken to be the relativistic mass.
The most common symbol for momentum is p. The SI unit for momentum is kg m/s.
You may insert numbers for any of the quantities. Then click on the text or symbol in the
formula above for the quantity you wish to calculate. The numbers will not be forced to be consistent until you click on the desired quantity.
Momentum p = kg m/s = kg * m/s
TorqueA torque is an influence which tends to change the rotational motion of an object. One way to quantify a torque is
Torque = Force applied x lever arm
The lever arm is defined as the perpendicular distance from the axis of rotation to the line of action of the force.
Conditions for EquilibriumAn object at equilibrium has no net influences to cause it to move, either in translation (linear motion) or rotation. The basic conditions for equilibrium are:
Circular Motion
For circular motion at a constant speed v, the centripetal acceleration of the motion can be derived. Since in radian measure,
Centripetal ForceAny motion in a curved path represents accelerated motion, and requires a force directed toward the center of curvature of the path. This force is called the centripetal force which means "center seeking" force. The force has the magnitude
Swinging a mass on a string requires string tension, and the mass will travel off in a tangential straight line if the string breaks.
The centripetal acceleration can be derived for the case of circular motion since the curved path at any point can be extended to a circle.
Note that the centripetal force is proportional to the square of the velocity, implying that a doubling of speed will require four times the centripetal force to keep the motion in a circle. If the centripetal force must be provided by friction alone on a curve, an increase in speed could lead to an unexpected skid if friction is insufficient.
Rotation VectorsAngular motion has direction associated with it and is inherently a vector process. But a point on a rotating wheel is continuously changing direction and it is inconvenient to track that direction. The only fixed, unique direction for a rotating wheel is the axis of rotation, so it is logical to choose this axis direction as the direction of the angular velocity. Left with two choices about direction, it is customary to use the right hand rule to specify the direction of angular quantities.
Direction of other angular quantities
Vector rotation examples
Rotation Vector ExamplesThis is an active graphic. Click on any example.
Rotating Stool
The moment of inertia is large with the masses held out. For a given angular momentum, the angular velocity is relatively low.
If the masses are pulled in, the moment of inertia is considerably decreased. Conservation of angular momentum dictates that the angular velocity must increase.
Right Hand Rule for TorqueTorque is inherently a vector quantity. Part of the torque calculation is the determination of direction. The direction is perpendicular to both the radius from the axis and to the force. It is conventional to choose it in the right hand rule direction along the axis of rotation. The torque is in the direction of the angular velocity which would be produced by it in the absence of other influences. In general, the change in angular velocity is in the direction of the torque.
Precession of Spinning Top
A rapidly spinning top will precess in a direction determined by the torque exerted by its weight. The precession angular velocity is inversely proportional to the spin angular velocity, so that the precession is faster and more pronounced as the top slows down.
The direction of the precession torque can be visualized with the help of the right-hand rule.
Spin a top on a flat surface, and you will see it's top end slowly revolve about the vertical direction, a process called precession. As the spin of the top slows, you will see this precession get faster and faster. It then begins to bob up and down as it precesses, and finally falls over. Showing that the precession speed gets faster as the spin speed gets slower is a classic problem in mechanics. The process is summarized in the illustration below.
This process involves a considerable number of physical and mathematical concepts. The angular momentum of the spinning top is given by its moment of inertia times its spin speed but this exercise requires an understanding of it's vector nature. A torque is exerted about an axis through the top's supporting point by the weight of the top acting on its center of mass with a lever arm with respect to that support point. Since torque is equal to the rate of change of angular momentum, this gives a way to relate the torque to the precession process. From the definition of the angle of precession, the rate of change of the precession angle can be expressed in terms of the rate of change of angular momentum and hence in terms of the torque.
The expression for precession angular velocity is valid only under the conditions where the spin angular velocity is much greater than the precession angular velocity P. When the top slows down, the top begins to wobble, an indication that more complicated types of motion are coming into play.
Precession TorqueThe spin angular momentum is along the rotation axis as shown, but the torque about the support point is in a direction perpendicular to the angular momentum. The torque produces a change in L which is perpendicular to L. Such a change causes a change in direction of L as shown but not a change in its size. This circular motion is called precession.
Index
Go to top view
If the wheel is not spinning, the apparatus just rotates downward toward a vertical orientation. If you curl the fingers of your right hand in the direction of that expected rotation, then your thumb will point perpendicular to the spin axis in the direction of the torque produced by gravity. The tip of the angular momentum vector, and therefore the axle of the wheel, will precess in that direction.
Precession, Top ViewThe spin angular momentum is along the rotation axis as shown, but the torque about the support point is in a direction perpendicular to the angular momentum. The torque produces a change in L which is perpendicular to L. Such a change causes a change in direction of L as shown but not a change in its size. This circular motion is called precession.
Precession of Spinning Wheel
Load video
A spinning wheel which is held up by one end of its axle will precess in the sense shown if it has that direction of spin. If the spin is reversed, it will precess in the opposite direction. The sense of precession is determined by the direction of the torque due to the weight of the spinning wheel. That torque is perpendicular to the angular momentum of the wheel.
Rotating Stool
Begin with the wheel rotating so that its angular momentum is upward. The man and the stool are at rest. The stool is on a bearing mount so that it can freely rotate.
If the wheel is turned over, its angular momentum is now downward. But since there is nothing to exert a significant torque on the system, the angular momentum must have the original value upward. The man and the stool begin to rotate with angular momentum twice that of the wheel.
The Earth's Spin Maintains its Direction in Space
The Earth acts like a gyroscope in its orbit around the sun in that it maintains the direction of its spin axis in space. The implication of the conservation of angular momentum is that the angular momentum of the rotor maintains not only its magnitude, but also its direction in space in the absence of external torque. Thus the axis and the northern hemisphere will be tipped toward the sun for part of the year (summer) and away from it at another time of year (winter). This is the cause of the seasons of the Earth.
Boomerang
A boomerang is an example of gyroscopic precession. The throw of the boomerang gives it an angular velocity perpendicular to its path as shown. The cross-section of the boomerang is an airfoil which gives it more lift on the top, leading edge than on the bottom. This gives it a torque in the sense shown, which always acts to precess the boomerang counterclockwise as seen from above. Since it will tend to "fly" in the direction of the airfoil, the precession causes it to fly in a curved path, circling back toward the thrower
Boomerang as Vector Rotation ExampleThe returning trajectory of a boomerang involves the aerodynamic lift of its airfoil shape plus the gyroscopic precession associated with its rapid spin. The precession
redirects the airfoil so that it "flys" around the returning path.
The three diagrams above address the nature of the boomerang's flight. Click on one of the diagrams for further details about the boomerang.
Boomerang
A boomerang is an example of gyroscopic precession. The popular variety at left is thrown by grasping it at the bottom and throwing it so that it rotates about an axis perpendicular to the plane shown. This plane is tilted enough from the vertical enough to get enough lift to keep the boomerang airborne. The cross-section at each end is shaped as an airfoil with its leading edge pointed so that it is facing forward when that end is at the top. The airfoil causes it to "fly" in the direction thrown, but the higher aerodynamic lift on the top end creates a torque which causes the angular momentum to precess, gradually changing the heading of the airfoil and moving it in the curved path.
Boomerang
A boomerang is an example of gyroscopic precession. The boomerang throw gives it angular momentum. This angular momentum is caused to precess by the fact that the top edge is traveling faster with respect to the air and gets more lift. This produces a torque on the spinning boomerang which continually rotates it's axis of spin, changing the heading of the airfoil so that it follows the curved path.
Boomerang StructureThe structure of a boomerang is such that each end forms an airfoil heading into the wind when it is at the top of its motion. Therefore the sideways "lift" force is always
greater on the top of the spinning structure.
A boomerang is an example of gyroscopic precession. The throw of the boomerang gives it an angular velocity perpendicular to its path. The cross-section of the
boomerang is an airfoil which gives it more lift on the top, leading edge than on the bottom. This gives it a torque , which always acts to precess the boomerang
counterclockwise as seen from above. Since it will tend to "fly" in the direction of the airfoil, the precession causes it to fly in a curved path, circling back toward the
thrower.
Bicycle WheelThe angulur momentum of the turning bicycle wheels makes them act like gyroscopes to help stabilize the bicycle. This gyroscopic action also helps to turn the bicycle.
Having pointed to the gyroscopic nature of the bicycle wheel, it should be pointed out that experiments indicate that the gyroscopic stability arising from the wheels is not a significant part of the stability of a bicycle. The moments of inertia and the speeds are not large enough. The experiments and review of Lowell and McKell indicate that the stability of the bicycle can be described in terms of centrifugal force. A rider who feels an unbalance to the left will turn the handlebars left, producing a segment of a circular path with resulting centrifugal force which pushes the top of the bicycle back toward vertical and a balanced condition.
Presumably the larger masses and speeds of motorcycle wheels do make the gyroscopic torques a much larger factor with motorcycles.
Turning a Bicycle
A bicycle held straight up will tend to go straight. It is tempting to say that it stabilized by the gyroscopic action of the bicycle wheels, but the gyroscopic action is quite small.
If the rider leans left, a torque will be produced which causes a counterclockwise precession of the bicycle wheel, tending to turn the bicycle to the left.
This is a good visual example of the directions of the angular momenta and torques, but the gyroscopic torques of bicycle wheels are apparently quite small (see Lowell and McKell). The gyroscopically motivated descriptions like "leaning left turns it left" are more appropriate to motorcycles.
If you lean left, you turn left
A rider leaning left will produce a torque which will cause the bicycle wheel to precess counterclockwise as seen from above, turning the bicycle left. The angulur momentum of the bicycle wheels is to the left. The torque produced by leaning is to the rear of the bicycle, as may be seen from the right-hand rule. This gives a rearward change in the angular momentum vector, turning the bicycle left.
This is a good visual example of the directions of the angular momenta and torques, but the gyroscopic torques of bicycle wheels are apparently quite small (see Lowell and McKell). The gyroscopically motivated descriptions like "leaning left turns it left" are more appropriate to motorcycles. With a bicycle at low speeds, the main turning influence comes from the turning of the handlebars.
In terms of the stability of the bicycle when riding, the association with leaning and turning does hold true. The construction of a bicycle is such that a left lean does cause
the front wheel to turn left, contributing a kind of self-stability to the bicycle. If you feel youself unbalanced and leaning left, then turning left does help you correct the imbalance because the centrifugal force associated with the turn does tend to push the top of the bicycle back toward the vertical. Part of the process of learning to ride a bicyle would then seem to be the learning of how to turn the front wheel to produce the needed centrifugal balancing force to bring you back to an upright and balanced orientation. More drastic turns are needed at low speeds to get the necessary centrifugal force which depends upon the inverse of the radius of curvature. Much more gentle turns are sufficient at higher speeds since the centrifugal force depends upon the square of the velocity.
Directions of Angular QuantitiesAs an example of the directions of angular quantities, consider a vector angular velocity as shown. If a force acts tangential to the wheel to speed it up, it follows that the change in angular velocity and therefore the angular acceleration are in the direction of the axis. Newton's 2nd law for rotation implies that the torque is also in the axis direction. The angular momentum will also be in this direction, so in this example, all of these angular quantities act along the axis of rotation as shown.
What if the torque is perpendicular to the angular
momentum?
Angular Momentum ChangeA force tangential to the wheel produces a torque along the axis as shown (right hand rule). The change in angular momentum is therefore along the axis and the wheel increases in angular velocity. However, if the torque direction is perpendicular to the axis of the wheel the effect is very different. The change in angular velocity is perpendicular to the angular velocity vector, changing its direction but not its magnitude. The resultant motion of the wheel around a vertical axis is called precession.
Gyroscopic Motion
The second major advantage cats have when falling is their unique ability to right themselves midair, while people tend to tumble uncontrollably (and quite uncivilized like, a cat might comment) as they fall. This requires a use of, if perhaps not an understanding of, the concept of angular momentum. Cats have a superb internal gyroscope located in their inner ear which very quickly detects their orientation as hey falls. As can be seen below, a cat rotates its body in one direction and tail in the opposite direction as it falls (conserving angular momentum in the process), and then stretches its legs out and reverses the process. The outstretched legs keep the cat from twisting all the way back to its original orientation. The cat then reverts back to the first motion and continues the process until rotation is complete. Tail-less cats use one of their hind legs extended in place of a tail. The rotation takes a mere two to three feet of descent.
A bicycle wheel is fitted with a long axle, one end of which has a ball. The ball can be seated on a socket which is free to rotate, placed on a heavy vertical stand. Keeping the bicycle wheel axle vertical and the ball seated in the socket, spin the wheel fast while holding the end H of the axle by hand. (The wheel can be rotated by hitting the spokes synchronously). Now let go of the axle. The wheel will start to precess soon (gyroscopic precession) and will stay on its support even in the horizontal (axle) position.
Note: There is a lot of energy stored in the rotating wheel. Take care if you have to brake the wheel. The bicycle wheel could be spun rapidly with a hand-held friction drive.
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