8 - Torque & Equilibrium

An extended object is in static equilibrium if __________.

both the net force acting on the object is zero and the net torque acting on the object is zero

• An extended body is in static equilibrium when the net force and the net torque acting on it are both zero.

Two children want to balance horizontally on a seesaw. The first child is sitting one meter to the left of the pivot point located at the center of mass of the seesaw. The second child has one-half the mass of the first child. Where should the second child sit to balance the seesaw?

2m to the right of the pivot

• Whether the seesaw is balanced or not depends upon whether there is any net torque about its pivot point. This can be determined either by explicitly calculating the torque due to each child about that point, or by finding the location of the center of mass of the two children. If the center of mass is not directly above the pivot point, there will be a net torque about that point.

The center of mass of a thin rectangular shaped metal block of uniform density is located

at the intersection of the 2 diagonals

An object modeled as a rigid body is said to be in static equilibrium if    

the sum of the horizontal components as well as the vertical components of the forces acting on the object is zero, and the sum of the clockwise and counterclockwise torques acting about any axis of rotation is also zero

• The translational and rotational conditions described are those of an object in static equilibrium.

For the net translational force on an object to be zero

the sum of the horizontal components of all the forces acting on the object must be zero and the sum of the vertical components of all the forces acting on the object must be zero.

A person is standing in one end of a paddle board in still water. He then walks forward towards the dock and keeps standing. The paddle board is now

behind its original position and not moving      

• The location of the center of mass of the person-paddleboard system does not change because there is no net external force acting on it, and as the person was moving forward the paddleboard moved backward, leaving the center of mass position with respect to the dock unchanged

What happens to the position of the center of mass of a small boat – boatman system when the boatman moves to the right of the small boat?    

The center of mass of the boat-boatman system moves towards the right.

• The center of mass of the boat-boatman system also moved when the boatman moved.

Extended & Rigid Bodies

an extended object where parts of the object X move relative to e/o

• assume size & shape of object X change

• adds in rotational motion on top of translational motion of before

Center of Mass

point determining where rotation is, rotation at center & balances out

• does all the translation follows the parabolic path

• objects are stable if the center of mass is directly above/below support point

Stability of Equilibrium

A condition where an object returns to its original position after being displaced. It occurs when the center of mass is at its lowest point above the support base.

• stability point is where Fg is acting

Unstable Equilibrium

A condition where an object continues to move away from its original position after being displaced. This occurs when the center of mass is above the support base.

Torque

twist that a F gives an object around an axis of rotation, F causing a rotation motion (Nm)

• when a F acts on an object away from axis = produces T on it

• T causes angular accel

• max when F is farthest possible & perpendicular (90 degree angle) to l

• T = Flsin<

• + = counterclockwise

• - = clockwise

Center of Mass of Combined Objects

average position of all objects in system

• COM = sum of mass*x/sum of mass

2 Conditions of Equilibrium

Fnet = 0, Tnet = 0