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11_02_Rotation_2

# 11_02_Rotation_2 - h R T g S R T g S Must be a 50/50 split...

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11/2 Rotational Energy 2 / Today: ratio of energy for a rolling disk / Presentation “More off to the races” / Upcoming presenters please see me / Bowling Ball Race? / HW “Rotational Energy” Due Wed 11/7 (Will post soon)

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All the mass moving at v R All the mass moving at v R ? No! Slower toward the center. How does the KE R compare for a disk and ring? Same mass and same rolling velocity. More KE R Less KE R
All the mass moving at v R Add up KE R of concentric rings KE R = 1 / 2 m Total v 2 How does the KE R compare for a disk and ring? Same mass and same rolling velocity. 1 / 2 m 1 v 1 2 + 1 / 2 m 2 v 2 2 + 1 / 2 m 3 v 3 2 +... KE R = 1 / 4 m Total v 2 (trust me!) Twice as much KE R in the ring but they have the same KE T . R T g S 0 0 R T g S 0 0 1 / 2 : 1 / 2 1 / 3 : 2 / 3 v T v T v R KE T = 1 / 2 m Total v 2

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More off to the Races. Find the velocity of the ring at the bottom, then find the acceleration.
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Unformatted text preview: h R T g S R T g S Must be a 50/50 split of the PE g KE T = 1 / 2 PE g 1 / 2 mgh = 1 / 2 mv 2 v = gh How do we find the acceleration? ∆ t ∆ x v ave = ∆ x a = ∆ v ∆ t ∆ t = ∆ x v ave v ave = gh 2 ∆ v = gh Because it’s a ring!!!! More off to the Races. Find the velocity of the disk at the bottom, then find the acceleration. h R T g S Pe g split 1 / 3 : 2 / 3 R T g S How do we find the acceleration? ∆ t ∆ x v ave = a = ∆ v ∆ t ∆ t = ∆ x v ave KE T = 2 / 3 PE g 2 / 3 mgh = 1 / 2 mv 2 3 v = 4gh 3 v ave = 4gh 2 3 ∆ v = 4gh ∆ x Because it’s a disk!!!!...
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11_02_Rotation_2 - h R T g S R T g S Must be a 50/50 split...

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