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ENGR 215 ~ Dynamics Section 17.1. Moment of Inertia. The translational aspects of motion are described by the equation: The rotational aspects of motion are described by the equation:. Golf Ball Drop Demo. Moment of Inertia.
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Moment of Inertia • The translational aspects of motion are described by the equation: • The rotational aspects of motion are described by the equation:
Moment of Inertia • Just as mass is a measure of a body’s resistance to acceleration inertia is a measure of a body’s resistance of a body to angular acceleration.
What is the purpose of the flywheel on this 1942 John Deere Model G tractor?
Definition of Moment of Inertia • We define the moment of inertia as the integral of the “second moment” about an axis of all the elements of mass dm which compose a body? • r = moment arm or perpendicular distance to the axis of rotation
Differential Volume • To obtain the moment of inertia we will only consider symmetrical bodies having surface which can be generated by revolving a curve about an axis.
Shell Elements • If the shell having a height z, radius r, and a thickness dy is chosen then the volume is given by: • We need z as a function of y to integrate.
Disk Elements • If the disk having a radius r and a thickness dz is chosen then the volume is given by: • We need y as a function of z to integrate.
Lecture Example 1: Find the moment of inertia about the z- axis
Lecture Example 2: Find the moment of inertia about the y-axis
Lecture Example 3: Find the Moment of Inertia for a slender rod length, L about its center of mass.
Lecture Example 4: Find the Moment of Inertia for a slender rod length, L about its end.
Radius of Gyration • Occasionally, the moment of inertia of a body about a specified axis is reported as the radius of gyration, k.
Lecture Example 6: The pendulum consists of two slender rods AB and OC which have a mass of 3 kg/m. The thin plate has a mass of 12 kg/m2. Determine the center of mass of the pendulum and the moment of inertia about an axis perpendicular to the page at Point G.