Moments of Inertia

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# Moments of Inertia - PowerPoint PPT Presentation

Moments of Inertia. Lesson 7.6. Review. Recall from previous lesson the first moment about y-axis The moment of inertia (or second moment) is the measure of the tendency of an object to resist change in motion. Moment of Inertia. For a system of n masses

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## PowerPoint Slideshow about 'Moments of Inertia' - stuart-smith

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### Moments of Inertia

Lesson 7.6

Review
• Recall from previous lesson the first moment about y-axis
• The moment of inertia (or second moment) is the measure of the tendency of an object to resist change in motion
Moment of Inertia
• For a system of n masses
• If the masses were at the same distance r from the axis of rotation we have
• Radius of gyration about x-axis(where m is total mass of system)
Example
• Suppose we have 3g at (2,3), 4g at (-2,-4), and 3g at (-4,5)
• Find Iy
• Iy = 3*2 2 + 4*(-2)2 + 3*(-4)2 = 76
• Find Ix
• Ix = 3*32 + 4*(-4)2 + 3*52 = 166
• Find r0
• r0- = 4.9193

Density of region

Moment of Inertia for a Region
• Given a region bounded by curves of two functions and lines x = a, x = b
• The moment of inertia about the y-axis

f(x)

g(x)

x = b

x = a

f(x)

• Given the same region
• Radius of gyration, ry with respect to the y-axis is

g(x)

x = b

x = a

Try It Out
• Given the region bounded by y3 = x2 , y = 4 and the y-axis. Density = 4g/cm2
• Moment of Inertia about x-axis
Try It Out
• Given the region bounded by y3 = x2 , y = 4 and the y-axis. Density = 4g/cm2
For a Solid of Revolution
• Moment of inertia of a solid of revolution formed by generating a region around the y-axis
• The radius of gyration is
Example
• Consider region bounded by y = x2 , the y-axis, and y = 2 rotated
• What is the moment ofinertia about the x-axis
Interesting Application
• Sweet spot for a baseball bat
• What happens when you hit the ball …
• At point A?
• At point B or C?

Note the interesting description of this lab assignment from Colorado State

Assignment
• Lesson 7.6
• Page 299
• Exercises 1, 3, 5, 9, 11, 15, 17
• Second day7, 13, 19, 21, 23