Statistics of Rigid Bodies

PIRA classification 1J

1J10. Finding Center of Gravity

PIRA #

Demonstration Name

Abstract

1J10.09

center of gravity

Many examples of simple center of mass demonstrations.

1J10.10

map of state

Suspend a map of the state from holes drilled at large cities to find the "center of the state".

1J10.10

map of state

Sandwich of a map of the state between two plexiglass sheets and suspend from holes drilled at large cities to find the "center of the state".

1J10.10

map of Minnesota

A plexiglass map of the state is suspended from several points.

1J10.11

find the center of gravity

Use a chalk line on the plumb bob and snap it to make a quick vertical line.

1J10.12

hanging shapes

Use the plumb bob method to find the center of gravity of various geometric shapes.

1J10.12

hanging board

Suspend an irregular board from several points and use a plumb bob to find the center of gravity.

1J10.12

irregular object center of mass

Suspend an irregular object from several points and find the center of mass with a plumb bob.

1J10.15

hanging potato

Hang a potato from several positions and stick a pin in at the bottom in each case. All pins point to the center of gravity.

1J10.20

meter stick on fingers

Slide your fingers together under a meter stick and they meet at the center of gravity. Add a baseball hat to one end and repeat.

1J10.20

friction and pressure

Slide your fingers under the meter stick to find the center of mass.

1J10.20

meter stick on fingers

Slide your fingers under a meter stick to find the center of mass.

1J10.25

center of gravity of a broom

Bring your fingers together under a broom the find the center of gravity.

1J10.25

center of gravity of a broom

Find the center of gravity of a broom, hang a kg mass somewhere on the broom, find the new center of gravity, calculate the weight of the broom by equating torques.

1J10.26

balance beam and bat

1J10.30

meter stick on fingers

1J10.30

loaded beam - moving scales

Slide the scales together under a loaded beam noting the scale readings of the moving and stationary scales.

1J10.30

loaded beam - moving scales

Instead of moving the masses on the beam, move the scales under the beam. Same as bringing your fingers together under the meter stick.

1J10.41

your center of gravity

Two methods for measuring the center of gravity of a person are shown.

1J11. Exceeding Center of Gravity

PIRA #

Demonstration Name

Abstract

1J11.10

leaning tower of Pisa

Add a top to a slanted cylinder and it falls down. Also hang a plumb bob from the center of mass in each case.

1J11.10

leaning tower of Pisa

A model of the tower constructed in sections. Adding the top will cause it to tip over.

1J11.10

leaning tower of Pisa

Add on to the leaning tower and it falls down.

1J11.10

leaning tower of Pisa

The leaning tower of Pisa.

1J11.11

falling cylinders

A tube, weighted at the bottom, falls when a cap is added. An upright cylinder, containing two balls, falls when a weighted cap is removed.

1J11.11

toppling cylinders

The standard leaning tower and an upright cylinder that topples when the cap is removed. It has two balls in the tube.

1J11.12

irregular object center of mass

1J11.15

tipping block on incline

Raise an incline plane until a block tips over.

1J11.15

tipping block on incline

A very clever modification of the leaning tower of Pisa demonstration.

1J11.15

tipping block on incline

A block is placed on an incline and the incline is raised until the block tips.

1J11.20

leaning tower of Lire

Stack blocks stair-step fashion until the top block sticks out beyond any part of the bottom block.

1J11.20

leaning tower of Lire

Use 6"x6"x2' wood blocks and have a student sit under the stack as it is built.

1J11.20

leaning tower of lire

A note discussing the derivation of the harmonic series describing the leaning tower of Lire.

1J11.20

leaning tower of Lire

Use the center of mass of a composite object to support a block beyond the edge of the lecture bench. This article emphasizes a lab approach. Ref. AJP 23,240 (1955).

1J11.20

leaning tower of Lire

Stack blocks until the top block sticks out beyond any part of the bottom block.

1J11.21

cantilevered books

The number of books necessary to overhang 2,3,4, etc lengths.

1J11.30

instability in flotation

A device to raise the center of mass in a boat until the boat flips. Diagram.

1J11.40

people tasks, etc.

Pictures of three center of mass objects and several person based center of mass tasks e.g., stand on your toes facing the wall, etc.

1J11.40

male & female center of gravity

Stand with right shoulder and foot against the wall and raise your left foot. Stand with your heels against the floor and try to touch your toes.

1J11.50

double cone

As a double cone moves up an set of inclined rails, its center of gravity lowers.

1J11.50

rolling uphill

A simple version of a ball rolling up a "v".

1J11.50

double cone

A double cone rolls up an inclined "v" track.

1J11.50

double cone

Double cone and rails.

1J11.50

double cone

A double cone rolls up an inclined "v" track.

1J11.50

double cone on incline

The double cone appears to roll uphill.

1J20. Stable, Unstable, and Neut. Equilibrium

PIRA #

Demonstration Name

Abstract

1J20.10

bowling ball stability

A bowling ball is placed in, on, and along side a large plexiglass hemisphere.

1J20.11

balance the cone

A cone can show stable, unstable, and neutral equilibrium; a sphere shows only neutral equilibrium.

1J20.11

balance the cone

A large cone shows stable, unstable, and neutral equilibrium.

1J20.11

stability

Balance a cone, show a block is stable and a sphere is neutral.

1J20.12

wood block stability

A block and support have marks that show whether the center of gravity has moved up or down when the block is displaced.

1J20.15

block on the cylinder

A rectangular block of wood is placed on a cylinder first with the width less than the radius (stable) and then with the width greater (unstable).

1J20.15

block on the cylinder

An "elementary" discussion of the oscillatory properties of the block on the cylinder.

1J20.15

block on the cylinder

A thin block on a cylinder is stable, a thick one is not.

1J20.16

catenary surface

A large block is always in stable equilibrium anywhere along this catenary surface.

1J20.17

block on curved surfaces

A block is placed on a catenary surface, a circle, and a parabola.

1J20.20

fork, spoon, and match

Place a spoon and match in the tines of a fork and balance the assembly on the edge of a glass.

1J20.20

fork, spoon, and match

Picture of the fork, spoon, and match balanced on the edge of a glass.

1J20.20

fork, spoon, and match

Stick two forks and a match together and balance on a glass while pouring out the water.

1J20.20

fork, spoon, and match

Two forks and a match can be balanced on the edge of a glass while the water is poured out.

1J20.25

nine nails on one

A technique to balance ten landscape spikes on the head of a single upright spike.

1J20.30

sky hook

A complete solution to the hanging belt problem.

1J20.30

hanging belt

Shows a "belt hook" for the hanging belt.

1J20.32

spoon on nose

Hang a spoon on your nose. Most effective with giant food service spoons.

1J20.35

horse and rider

A horse has an attached weight to lower the center of mass.

1J20.35

horse and rider

Stable equilibrium of a center of gravity object.

1J20.35

horse and rider

A horse has a weight attached to lower the center of mass.

1J20.40

balancing man

Stable equilibrium of a center of gravity object.

1J20.40

balancing man

Stable equilibrium of a center of gravity object.

1J20.45

tightrope walking

Design of a 10' long "low wire" and description of the physical feats possible.

1J20.45

tightrope walking

A toy unicycle rider carrying a balancing pole travels along a string.

1J20.45

clown on rope

A toy clown rides a unicycle on a wire.

1J20.46

tightrope walking model

A model of a tightrope walker shows the center of mass moves up with tipping.

1J20.50

balancing a stool

Wires form a support at the center of gravity of a lab stool.

1J20.50

balancing a stool

Construct a stool so that wires crossed diagonally will intersect at the center of gravity. The stool can be oriented in any direction.

1J20.51

chair on pedestal

Hide heavy weights in the ends of a chair's legs so it will balance on a vertical rod placed under the seat.

1J20.55

broom stand

Spread the bristles and a straw broom will stand upright.

1J20.60

wine bottle

Stick the neck of a wine bottle through a hole in a slanted board and the whole thing stand up.

1J20.65

glass on coin, etc

Pictures show the hanging belt, pin on the point of a needle, and a jar balanced on its edge.

1J30. Resolution of Forces

1J40. Static Torque

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