The balance point of an object.

1
Center of Gravity
Section 5

• The balance point of an object.
• For many simple parts, such as a cylinder or
  block, the geometric center is apparent.

2
Complex Parts

• The center of gravity
• of complex parts can be
• determined form a weighted
• average of the coordinates of the individual
  cgs.

3
Problem 5-1

• The plate shown is made from steel
• (0.283 lb/in3). Determine the coordinates of the
  center of gravity.

4
Mass Moment of Inertia, I

• Resistance to rotational acceleration.
• Computed relative to an axis
• Strongly influenced by the amount of mass
  distributed from the axis.

5
Mass Moment of Inertia

• Charts available for common shapes.
• Cylinder

6
Radius of Gyration, k

• Distance from the reference axis, to a point,
  where a concentrated mass would have the same
  moment of inertia.
• Occasionally used in dynamic testing.

7
Problem 5-3

• Calculate the mass moment of inertia and the
  radius of gyration about a centroidal
  longitudinal axis of a shaft that weighs 5 lb and
  has a diameter of 0.625 in.

8
Problem 5-5

• A solid cylinder is 2 ft in diameter, 3 ft long
  and weighs 48 lbs. Determine the mass moment of
  inertia about its centroidal axial axis.

9
Parallel Axis Theorem

• Can transfer the moment of inertia, from one axis
  to another.
• IA IA ? m(d)2
• d is the distance between the two axes
• Add if transfer is away from the centroid.
• Subtract if transfer is towards the centroid.

10
Problem 5-7

• A slender rod, 14 in. long, rotates about an axis
  perpendicular to its length and 3 inches from its
  center of gravity. Knowing that the rod weighs 2
  lb, determine its mass moment of inertia about
  that axis.

11
Composite Body

• The moment of inertia of a body, comprised of
  several simple shapes, can be combined as long as
  there is a single reference axis.
• IA (Total) IA (Body 1) IA (Body 2)

12
Problem 5-14

• Determine the mass moment of inertia of the plate
  about the rotation axis. The plate is made from
  steel, with a density of
• 0.281 lb/in3.