Differences between revisions 1 and 3 (spanning 2 versions)

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

1J30. Resolution of Forces

1J40. Static Torque

[:Demonstrations:Demonstrations]

[:Instructional:Home]

-  ⇤ ← Revision 1 as of 2009-03-19 14:38:32 → 
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-'''1J10. Finding Center of Gravity '''
+= 1J10. Finding Center of Gravity =
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-'''1J11. Exceeding Center of Gravity '''
+||<:10%>'''PIRA #'''||<:>'''Demonstration Name'''||<:60%>'''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.||
-Line 11:
+Line 30:
-'''1J20. Stable, Unstable, and Neut. Equilibrium '''
+= 1J11. Exceeding Center of Gravity =


||<:10%>'''PIRA #'''||<:>'''Demonstration Name'''||<:60%>'''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 =

fw: Diff for "RigidBodies"

Statistics of Rigid Bodies

1J10. Finding Center of Gravity

1J11. Exceeding Center of Gravity

1J20. Stable, Unstable, and Neut. Equilibrium