School Science Lessons
Physics - Rotational dynamics
Updated: 2008-02-20 L
Please send comments to: J.Elfick@uq.edu.au
See also: Interesting websites
Table of contents
18.3.0 Rotational dynamics
18.3.1 Moment of inertia, angular momentum, conservation of angular momentum
18.3.2 Rotational energy
18.3.3 Transfer of angular momentum
18.3.4 Conservation of angular momentum
18.3.5 Gyros, gyroscope, precession
18.3.6 Rotational stability, dynamic stability
18.3.1 Moment of inertia, angular momentum, conservation of angular momentum
18.3.1.1 Inertia wands
18.3.1.2 Torsion pendulum inertia, spinning eggs
18.3.1.3 Rolling bodies on incline
18.3.1.4 Rigid and non-rigid rotations, parallel axis wheels
18.3.2 Rotational energy
18.3.2.1 Adjustable angular momentum
18.3.2.2 Angular acceleration machine, angular acceleration wheel
18.3.2.3 Spool on incline, rolling down an incline, rolling spool
18.3.2.4 Faster than gravity, falling chimney, coins on a metre stick
18.3.3 Transfer of angular momentum
18.3.3.1 Passing the wheel, pass bags of rice, catch the ball on the stool
18.3.3.2 Satellite derotator
15.3.0.5 Spinning ice skater, angular momentum
18.3.4 Conservation of angular momentum
18.3.4.1 Spinning funnel, marbles and funnel
18.3.4.2 Hero's engine, lawn sprinkler
18.3.4.3 Pulling on the whirligig
18.3.4.4 Centrifugal governor, rotating stool and weights, "squeezatron", Watt's regulator
18.3.4.5 Skiing
18.3.4.6 Toy train on a circular track
18.3.4.7 Counter spinning
18.3.4.8 Wheel and brake
18.3.4.9 Pocket watch
18.3.4.10 Buzz button
18.3.4.11 Sewer pipe pull
18.3.4.12 Air rotator with deflectors, Feynman inverse sprinkler
18.3.5 Gyros, gyroscope, precession
18.3.5.1 Cardboard boomerang
18.3.5.2 Precession, spinning top, precessing ball, precession of the equinoxes
18.3.5.3 Gyros, gyroscope, bicycle wheel gyro, gyro in gimbals, air bearing gyro
18.3.5.4 Gyrocompass, gimbal mount
18.3.5.5 Gyro pendulum
18.3.6 Rotational stability, dynamic stability
18.3.6.1 Humming top, tipped top, tippy top
18.3.6.2 Yo-yo top, yo-yo, Chinese diabolo
18.3.6.3 Spinning coin
18.3.6.4 Football spin, spinning football, spinning egg, spinning lariat (lasso)
18.3.6.5 Tossing the book, tossing the board, tossing the hammer
18.3.6.6 Static / dynamic balance
18.3.0 Rotational dynamics, rotational motion: angular displacement, velocity and acceleration, torque, moments of inertia, couples, principle of moments
18.3.1.0 Moment of inertia, angular momentum, conservation of angular momentum
18.3.1.1 Inertia wands
Twirl 2 equal mass wands (a) with the mass at the ends (b) with the mass at the middle. Use hollow cylinders containing hidden weights. Use weights taped to metre sticks.
18.3.1.2 Torsion pendulum inertia, spinning eggs
Use the period of a torsion pendulum to find the moment of inertia. Put objects on a trifilar supported torsional pendulum. A raw egg in a torsion pendulum damps more quickly than a boiled egg due to internal friction.
18.3.1.3 Roll down an incline, bearing Inertia, racing discs, weary roller, rolling bodies on incline, rolling cylinder, rolling hoop, rolling ball, restored force in a rolling can
Roll a ring and sphere of the same diameter down an incline. Roll a set of discs and hoops of different diameters down an incline. Roll an empty and full coffee can down an incline. Roll down an incline 2 wooden discs, same mass, diameter, and weight (a) weighted in the centre (b) weighted at the rim. The discs have different moments of inertia but have the same kinetic energy at the bottom. Load a roller with fine dry sand or powdered tungsten or iron then roll down an incline.
18.3.1.4 Rigid and non-rigid rotations, parallel axis wheels
Spin with a falling weight 2 masses on a horizontal bar fixed to a vertical shaft so that you can lock or free the masses to rotate in the same plane as the vertical shaft. Measure with the wheel spinning or locked, the period of a bicycle wheel suspended as a pendulum.
18.3.2.0 Rotational energy
Other experiments: bike wheel angular acceleration, bike wheel on incline, hinged stick and ball, penny drop stick
18.3.2.1 Adjustable angular momentum
Hang various weights from the axle of a large wheel and time the fall. A falling weight on a string wrapped around a spindle spins objects to show Newton's second law for angular motion
18.3.2.2 Angular acceleration wheel
Measure the angular acceleration of a bike wheel due to the applied torque of a mass on a string wrapped around the axle Use a spring scale to apply a constant torque to a bike wheel and measure the angular acceleration.
18.3.2.3 Rolling down an incline, rolling spool
Roll a large spool down an incline on its axle. When it reaches the bottom it rolls on the diameter of the outer discs showing conservation of linear momentum. Roll a bike wheel rolls down an incline on its axle with the axle pinned to the wheel or free. Time a roller as it rolls up an incline under the constant torque produced by a cord wrapped around over a pulley to a hanging mass.
18.3.2.4 Faster than gravity, falling chimney, coins on a metre stick
A ball at the end of a falling stick jumps into a cup faster then gravity. A hinged inclined board with a ball on the end jumps into a cup a short distance down the board as the incline drops. Line a meter stick with coins and drop one end with the other hinged.
18.3.3.0 Transfer of angular momentum, angular momentum
Corresponding to linear momentum, if an object is in rotational motion, it will have a quantity of motion angular momentum, with symbol L, and with SI unit kg.m2 / s. For rotation about a fixed axis, the angular momentum is the product of the rotational inertia of the object about the axis and its angular velocity: L = I x omega kg.m2 / s. kilogram metre2 / second (kg m2 s-1). Rotational inertia is a quantity describing rotational state, with symbol I or J, and with SI unit kg.m2.
18.3.3.1 Passing the wheel, pass bags of rice, catch the ball on the stool
Pass a spinning bicycle wheel back and forth to a person on a rotating stool or small merry-go-round. Stand on a rotating stool or small merry-go-round and holds out 5 kg bags of rice and drop them. Sit on a rotating stool or merry-go-round and catch a heavy ball at arms length.
18.3.3.2 Satellite derotator
Heavy weights fly off a rotating disc carrying away angular momentum.
18.3.4.0 Conservation of angular momentum
Other experiments: Rotating stool with weights, rotating stool and long bar, centrifugal governor, rotating stool and bicycle wheel, tail wags dog, marbles and funnel
18.3.4.1 Spinning funnel, marbles and funnel
A funnel filled with sand spins faster as the sand runs out to show conservation of angular momentum. The angular speed of marbles increases as they approach the bottom of a large funnel.
18.3.4.2 Hero's engine, Hero's engine lawn sprinkler
Cylindrical boiler pivots on a vertical axis with tangential pressure relief nozzles. Suspend a round bottom flask with two nozzles so that the flask rotates on a horizontal axis. Use a gravity head of water to drive a Hero's engine lawn sprinkler.
18.3.4.3 Pulling on the whirligig
Attach balls to either ends of a string that passes through a hollow tube so you can set one ball twirling and pull on the other ball to change the radius. Shorten the string of a rotating ball on a string.
18.3.4.4 Centrifugal governor, rotating stool and weights, squeezatron, Watt's regulator
Spin a small governor on a hand crank. Spin on a rotating stool or merry-go-round with a dumbbell in each hand so you can extend and retract your arms while rotating on a stool. Expand or contract a fly ball governor by squeezing a handle showing the pirouette effect of ice skaters.
Spin and turn a bike wheel while on a turntable or merry-go-round. Turn yourself around on a turntable by variation of moment of inertia.
18.3.4.5 Skiing
Go skiing while holding a bike wheel gyro so that by conservation of angular momentum you turn yourself with the gyro. Stand on a rotating turntable or merry-go-round with skies on to show the upper part of the body turning opposite the lower part.
18.3.4.6 Train on a circular track
Use a clockwork HO gage train running on a track mounted on a bike wheel rim. The train and track move in opposite directions.
18.3.4.7 Counter spinning
An induction motor is mounted so both the frame and armature can rotate freely. No torque is required to tilt the direction of axis of rotation unless either the frame or armature is constrained.
18.3.4.8 Wheel and brake
Brake a horizontal rotating bicycle wheel attached to a large frame and the combined assembly rotates slower.
18.3.4.9 Pocket watch
Suspend a pocket watch by its ring from a sharp edge.
18.3.4.10 Buzz button
Pull on a twisted loop of string threaded through two holes in a large button to get the button to oscillate.
18.3.4.11 Sewer pipe pull
Put O rings around a section of large PVC pipe to act as tyres Place on a sheet of paper and pull the paper out from under it. When the paper is all the way out the pipe stops. Pull a strip of paper horizontally from under a rubber ball As soon as the ball is off the strip it stops.
18.3.4.12 Air rotator with deflectors, Feynman inverse sprinkler
Run an air sprinkler then mount deflectors to reverse the jet. Place an air jet Hero's engine in a bell jar and pump out some air. The inverse sprinkler moves in a direction opposite to that of a normal sprinkler. An inverse sprinkler made of soda straw in a carboy shows no motion due to conservation of angular momentum.
18.3.5.0 Gyros, gyroscope, precession
Other experiments: Gyroscope with adjustable weights, bike wheel on gimbals, bike wheel precession, double bike wheel, motorized gyroscope, gyroscopic stability. Ship stabilizer
18.3.5.1 Cardboard boomerang
See diagram 15.3.1
See "Boomerang": in Interesting websites
As the boomerang flies in the air, it does two movements, a spinning motion and a general forward motion. The spinning produces two effects, on one hand the angular momentum of spinning should be maintained unchanging, so the speed and plane of spinning are all unchanging; on the other hand spinning changes the direction of the flying boomerang, i.e. the boomerang does not fly in a straight line but a curved line. When the boomerang moves to the farthest point, its momentum has used up and it will drop acted by the gravity. However, as the spinning of the boomerang, the line that the boomerang goes will also a curved line, return to the man who threw it at first. Draw a boomerang on the cardboard in the shape. Cut it off. Hold the centre of the boomerang. Bend two wings gently to make wings slightly turn upward. Hold the edge in centre of the boomerang between index finger and thumb of your left hand, flick it away with the middle finger of your right hand to make it fly inclined upward. The boomerang will fly along a arc line and return by itself.
18.3.5.2 Precession, spinning top, precessing ball, precession of the equinoxes
Behaviour of a real top with a round end spinning on a surface with friction. The regular motion of the inclined axis of the spinning top around the vertical is an example of precession. The stability of torque free rotations and top nutation. Spin a cardboard on a pencil inserted in a hole at the centre and touch a finger to the rim to cause it to precess. Spin a phonograph record or aluminium disc on a nail at the end of a wood dowel and predict which way the record will turn when touched with a finger. Put a ball on a rotating table to precess about the vertical axis with a period 7 / 2 of the table. A rubber band provides a torque to a gyro framework hanging from a string causing precession of the equinoxes
18.3.5.3 Gyros, gyroscope, bicycle wheel gyro, gyro in gimbals, air bearing gyro
Mount a bicycle wheel on a long axle with adjustable counterbalance. Support a spinning bike wheel with two handles by a loop of string around one of the handles and push the ends of the handles horizontally in opposite directions. Make a gyro out of an auto wheel and tyre big enough to sit on. Push a cart with a gyro around the room. Spin a flywheel hidden in a suitcase and turn around with it.
Hold a heavy gyro outfitted with handles. Use a motorcycle as a gyro - the handlebars are twisted but not moved in the direction opposite to the turn to lay the machine over. Tip to one side a hand spun bike wheel on a front fork. Make an air bearing for a bowling ball.
18.3.5.4 Gyrocompass, gimbal, gimbal mount
A gimbal mount is a bearing for supporting an object to keep a horizontal position allowing for rotation about 2 perpendicular axes, e.g. nautical compass, gyroscope, chronometer used on a ship A gyroscope in gimbals is deprived of one degree of freedom A slight change of direction will cause a spin flip. In an aircraft turn indicator the gyro precesses about the axis of the fuselage. A ship stabilizer is like a gyro on a trapeze
18.3.5.5 Gyro pendulum
Swing as a pendulum a gyroscope hung from one end of its spin axles by a string.
18.3.6.0 Rotational stability, dynamic stability
Other experiments: spinning rings, spinning stone bounce on water, spinning Earth, spinning top, bullet, satellite, sports ball, Magnus effect, stable and unstable axes of rotation, spinning rod and hoop on wire, static / dynamic balance
18.3.6.1 Humming top, tipped top, tippy top
Pump up a toy humming top. Spin a tipped top on smoked glass to show the path of the stem. The tipped top spins in the opposite of the expected direction when inverted.
18.3.6.2 Yo-yo top, yo-yo
See diagram: 15.0.4.0 Rigid body motion
Throw with a string to show rigid body rotational motion.
18.3.6.3 Spinning Coin
Wobbling by coins, bottles, and plates when they are spun on horizontal flat surfaces
18.3.6.4 Spinning football, spinning egg, spinning lariat, lasso
Spin a rugby or gridiron football on its side and it rises onto its pointed end. Put an iron slug in the shape of a football on a magnetic stirrer. Spin a fresh egg and eggs boiled for different lengths of time. Use a hand drill held vertically to rotate loops of rope or flexible chain.
18.3.6.5 Tossing the book, tossing the board, tossing the hammer
Throw a book or bread board with 3 different dimensions up in the air and spin it about its three principle axes. Measure the moments of inertia about the three axes before tossing the book. The hammer flip as an example of a centrifugal force in a rotating reference frame.
18.3.6.6 Static / dynamic Balance
Dynamic tyre balancing for motor cars.