lec11 (2) - Finding Moments of Inertia 1 2.003J/1.053J...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 Finding Moments of Inertia 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Thomas Peacock 3/14/2007 Lecture 11 2D Motion of Rigid Bodies: Finding Moments of Inertia, Rolling Cylinder with Hole Example Finding Moments of Inertia Figure 1: Rigid Body. Figure by MIT OCW. I C = m i | ρ i | 2 i = m i ( x 2 i + y i 2 ) i I C is the Moment of Inertia about C.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. ± 2 Finding Moments of Inertia Example: Uniform Thin Rod of Length L and Mass M Figure 2: Uniform thin rod of length L and mass M . Figure by MIT OCW. I C = m i ( x i 2 + y i 2 )For very thin rod, y i is small enough to neglect. i m i x i 2 i Rod has mass/length = ρ . Convert to integral. I C = x 2 dm rod dm = ρdx ± L/ 2 I C = x 2 ρdx L/ 2 ² 3 ³ L/ 2 L 3 x = ρ = ρ 3 12 L/ 2 We know that mass M = ρL . Therefore: ML 2 I C = 12
Background image of page 2
Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 7

lec11 (2) - Finding Moments of Inertia 1 2.003J/1.053J...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online