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ENGR 215 ~ Dynamics Section 17.1

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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ENGR 215 ~ Dynamics Section 17.1

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  1. ENGR 215 ~ Dynamics Section 17.1

  2. Moment of Inertia • The translational aspects of motion are described by the equation: • The rotational aspects of motion are described by the equation:

  3. Golf Ball Drop Demo

  4. 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.

  5. What is the purpose of the flywheel on this 1942 John Deere Model G tractor?

  6. 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

  7. Definition of Moment of Inertia

  8. 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.

  9. 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.

  10. 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.

  11. Lecture Example 1: Find the moment of inertia about the z- axis

  12. Lecture Example 2: Find the moment of inertia about the y-axis

  13. Parallel Axis Theorem

  14. Lecture Example 3: Find the Moment of Inertia for a slender rod length, L about its center of mass.

  15. Lecture Example 4: Find the Moment of Inertia for a slender rod length, L about its end.

  16. Lecture Example 5: Back to the golf ball drop!

  17. Radius of Gyration • Occasionally, the moment of inertia of a body about a specified axis is reported as the radius of gyration, k.

  18. 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.

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