ENGINEERING

Engineering

Engineering

1a)

Static equilibrium occurs when an object is held stationary (static) using multiple forces and torques. There are 2 necessary conditions for static equilibrium these are known as translational equilibrium, and rotational equilibrium. Translational equilibrium is defined in lesson 4 of this unit. Rotational equilibrium occurs when all torques acting on an object are equal in the clockwise and anti-clockwise directions. if the vector sum of the forces acting on a point like object is zero then the object will continues in its state of rest, or of uniform motion in a straight line. If the object is in uniform motion we can always change reference frames so that the object will be at rest.

Conditions for Equilibrium of a Rigid Object

For a rigid object which is not moving at all we have the following conditions:

1.The (vector) sum of the external forces on the rigid object must equal zero. When this condition is satis?ed we say that the object is in translational equilibrium. (It really only tells us that aCM is zero, but of course that includes the case where the object is motionless.)

2.The sum of the external torques on the rigid object must equal zero. When this condition is satis?ed we say that the object is in rotational equilibrium. (It really only tells us that a about the given axis is zero, but —again— that includes the case where the object is motionless.)

b)

The free-body diagram is the most important tool in this book. It is a drawing of a system and the loads acting on it. Creating a free-body diagram involves mentally separating the system (the portion of the world you're interested in) from its surroundings (the rest of the world), and then drawing a simpli?ed representation of the system. Next you identify all the loads (forces and moments) acting on the system and add them to the drawing.

c)

Unit Vectors

The mathematicians have come up with a special kind of vector called a unit vector which comes in very handy in physics. By definition a unit vector has magnitude 1, with no units. By convention, a unit vector is represented by a letter marked with a circumflex. The circumflex is an accent mark that appears above the letter. It looks like an inverted “v” and is typically referred to as a “hat”. So for instance rˆ (read “r-hat”) is a unit vector. There is a special set of three unit vectors that are exceptionally useful for problems involving vectors, namely the Cartesian coordinate axis unit vectors. There is one of them for each positive coordinate axis direction. These unit vectors are so prevalent that we give them special names. For a two-dimensional x-y coordinate system we have the unit vector i pointing in the +x direction, and, the unit vector j pointing in the +y direction. For a three-dimensional x-y-z coordinate system, we have those two, and one more, namely the unit vector k pointing in the +z ...