Torque Board, 1J40.25a

Topic and Concept:

[:RigidBodies#StaticTorque: 1J40. Statistics of Rigid Bodies, Static Torque]

Location:

Floor Item: ME, East Wall

attachment:TorqueBoard01-400.jpg

Abstract:

A whiteboard tear drop shaped wheel is mounted vertically on its CM horizontal axis so that it can spin freely. Various weights can be hung on it at various points. The wheel will then rotate to its new equilibrium.

Equipment	Location	ID Number

Torque Board	Floor Item: ME, East Wall

Important Setup Notes:

Some preparation may be advisable since there are several variables in this demo that can be adjusted.

Setup and Procedure:

Roll the board to the desired position with the white board side facing the audience.
Select which hole you would like the peg (point of the applied force) to go in. String with a loop at the end should already be hanging from the peg.
The string should run over the pulley. The vertical position of the pulley can be adjusted to attain the desired effect.
Weight hangers should be hung from each of the two dangling strings and weight should be added to the hangars.
The board will rotate until it reaches equilibrium. The dry-erase markers can be used to sketch out the applied forces and the position vectors as shown in the pictures below.

Cautions, Warnings, or Safety Concerns:

Discussion: The board is mounted at its center of mass so we don't need to worry about torque due to gravity. There are two other torques in this demonstration: one on either side of the axis of rotation so that the torques oppose each other. The torques are determined by the net weight of the mass hangars and the distance from the rotational axis at which these forces are applied. Our torque equation is

T_net = 0 = r₁·W₁·sin(θ) - r₂·W₂

where the r's denote the distance of each force from the axis of rotation, W's denote the force do to gravity acting on the masses (giving rise to the tension in the strings), and θ is the angle between the position vector and the applied tension. The angle is omitted on the second torque since the stage left string is always tangent to the board (i.e. θ₂ = 90°). Since the stage left side is circular, r₂ is constant. The peg location determines r₁. Our choice of weights determines the angle of tilt of the board.

sin(θ) = (r₂·W₂) / (r₁·W₁).

attachment:TorqueBoard02-250.jpg	attachment:TorqueBoard04-250.jpg	attachment:TorqueBoard05-250.jpg	attachment:TorqueBoard06-250.jpg
attachment:TorqueBoard08-250.jpg	attachment:TorqueBoard09-250.jpg	attachment:TorqueBoard11-250.jpg	attachment:TorqueBoard14-250.jpg
attachment:TorqueBoard15-250.jpg	attachment:TorqueBoard16-250.jpg

Videos:

[https://www.youtube.com/user/LectureDemostrations/videos?view=1 Lecture Demonstration's Youtube Channel]

References:

[https://en.wikipedia.org/wiki/Torque Torque - Wikipedia]
[https://en.wikipedia.org/wiki/Rigid_body_dynamics Rigid Body Dynamics - Wikipedia]

[:Instructional:Home]

-  ⇤ ← Revision 1 as of 2012-10-17 16:52:00 → 
  Size: 1662
  Editor: srnarf
  Comment:
+   ← Revision 6 as of 2013-06-05 18:19:43 → ⇥
  Size: 3540
  Editor: srnarf
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 7:
-  [:Rigid Bodies#StaticTorque: 1J40. Statistics of Rigid Bodies, Static Torque]
+  [:RigidBodies#StaticTorque: 1J40. Statistics of Rigid Bodies, Static Torque]
 Line 10:
- * '''Cabinet:''' [:MechanicsCabinet:Mechanic (ME)]
 * '''Bay:''' [:MechanicsCabinetBayA1:(A1)]
 * '''Shelf:''' #1,2,3..
+ * '''Floor Item:''' ME, East Wall
-Line 14:
+Line 12:
- attachment: mainPhoto
+attachment:TorqueBoard01-400.jpg
-Line 22:
+Line 20:
-||apparatus||ME, Bay B1, Shelf #2|| ||
||all other parts||ME, Bay B1, Shelf #2|| ||
||...||ME, Bay B1, Shelf #2|| ||
+||Torque Board||Floor Item: ME, East Wall|| ||
-Line 28:
+Line 24:
- *  '''''  '''''
+ *  Some preparation may be advisable since there are several variables in this demo that can be adjusted.
-Line 33:
+Line 29:
-. List steps for setup then procedure.
 1. ...
+. Roll the board to the desired position with the white board side facing the audience. 
 1. Select which hole you would like the peg (point of the applied force) to go in. String with a loop at the end should already be hanging from the peg. 
 1. The string should run over the pulley. The vertical position of the pulley can be adjusted to attain the desired effect.
 1. Weight hangers should be hung from each of the two dangling strings and weight should be added to the hangars.
 1. The board will rotate until it reaches equilibrium. The dry-erase markers can be used to sketch out the applied forces and the position vectors as shown in the pictures below.
-Line 37:
+Line 36:
- *
+ * N/A
-Line 41:
+Line 40:
+The board is mounted at its center of mass so we don't need to worry about torque due to gravity. There are two other torques in this demonstration: one on either side of the axis of rotation so that the torques oppose each other. The torques are determined by the net weight of the mass hangars and the distance from the rotational axis at which these forces are applied. Our torque equation is
 Line 42:
-Discuss the physics behind the demonstration, explaining some of the various steps of the demonstration when appropriate.
+T,,net,, = 0 = r,,1,,·W,,1,,·sin(θ) - r,,2,,·W,,2,,
 Line 44:
-||attachment: photo||attachment: photo||attachment: photo||attachment: photo||
+where the r's denote the distance of each force from the axis of rotation, W's denote the force do to gravity acting on the masses (giving rise to the tension in the strings), and θ is the angle between the position vector and the applied tension. The angle is omitted on the second torque since the stage left string is always tangent to the board (i.e. θ,,2,, = 90°). Since the stage left side is circular, r,,2,, is constant. The peg location determines r,,1,,. Our choice of weights determines the angle of tilt of the board.

sin(θ) = (r,,2,,·W,,2,,) / (r,,1,,·W,,1,,). 
 
||attachment:TorqueBoard02-250.jpg||attachment:TorqueBoard04-250.jpg||attachment:TorqueBoard05-250.jpg||attachment:TorqueBoard06-250.jpg||
||attachment:TorqueBoard08-250.jpg||attachment:TorqueBoard09-250.jpg||attachment:TorqueBoard11-250.jpg||attachment:TorqueBoard14-250.jpg||
||attachment:TorqueBoard15-250.jpg||attachment:TorqueBoard16-250.jpg||
-Line 51:
+Line 57:
- * List any references
+ * [https://en.wikipedia.org/wiki/Torque Torque - Wikipedia]
 * [https://en.wikipedia.org/wiki/Rigid_body_dynamics Rigid Body Dynamics - Wikipedia]

fw: Diff for "Torque_Board"

Torque Board, 1J40.25a