Lecture18 - Moment of Inertia Discrete object Continuous...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
I = x 2 dm 0 M Moment of Inertia I = Σ i m i r i 2 Discrete object I = r 2 dm Continuous object r is the distance from the axis of rotation m 2 r 1 m 1 r 2 I = m 1 r 2 1 + m 2 r 2 2 dm x dm x dm = M/L dx K tot = K CM + K rot = 1/2 m v 2 + 1/2 I ω 2 Kinetic Energy Remember : I and K depend from the axis of rotation!
Background image of page 1

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

View Full DocumentRight Arrow Icon
Example : Which object will arrive first? h θ Sliding (box) : Potential Rolling : Potential I sphere (CM) = 2/5 M R 2 I cylinder (CM) = 1/2 M R 2 BALLS (Rolling) BOX (Sliding) Bodies will slide faster than they roll! Same M Kinetic translation Rotation Kinetic translation Faster?!
Background image of page 2
h θ I sphere (CM) = 2/5 M R 2 I cylinder (CM) = 1/2 M R 2 BALLS (Rolling) Same M V = 2gh / β +1
Background image of page 3

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

View Full DocumentRight Arrow Icon
h θ
Background image of page 4
Example : Which object will make it? Same M m R Y
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

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

View Full DocumentRight Arrow Icon
I sphere (CM) = 2/5 M R 0 2 I hoop (CM) = M R 0 2 I solid cylinder (CM) = 1/2 M R 0 2
Background image of page 8
Background image of page 9

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

View Full DocumentRight Arrow Icon
Example : A uniform thin rod of length L and mass M is pivoted at one end. Held horizontal and released from rest.
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 18

Lecture18 - Moment of Inertia Discrete object Continuous...

This preview shows document pages 1 - 11. Sign up to view the full document.

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