previous lecture | next lecture | 5200 index

Reading

F&C ch 8.3 - 8.6

Recall

Angular velocity vector, v = w×r

Moment of inertia: I_z = S_im_ir_i² 

Correspondance between laws of motion for translation and rotation:

Parallel and Perpendicular Axis Theorem

Perpendicular axis theorem: I_z = I_x + I_y for a planar object, z chosen perpendicular to the plane.

Parallel axis theorem: I = I_cm + ml² for the moment of inertia about an axis displaced a distance l from the center of mass, and parallel to the axis of I_cm.

Radius of Gyration

Notice that moment of inertia is like mass times the average distance from the axis of rotation squared. We define a quantity called the radius of gyration as:

k = (I/m)^1/2 or k² = I/m.

Table 8.3.1 lists values for k² for many common shapes. The term "lamina" is used here for a thin flat object. Synonyms are sheet or plane.

Applications:

Physical Pendulum:

One Dimensional Translation and Rotation:

© 23 March 1999 R. Harr