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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