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We’re on a roll!
The Physics of Rotation
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Rotational Momentum and Energy
Chapter 12
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Key Concepts …
Rotating masses possess rotational energy and momentum
An object can have both kinetic and rotational energy
Moment of Inertia measures distribution of mass wrt CM
Two identical mass objects can have very different moments of inertia
Simple mathematical relationship links angular velocity to linear velocity as long as no skidding takes place
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Important Analogies…
Mass – Moment of Inertia Force - Torque Momentum – Angular momentum Kinetic Energy – Rotational Energy
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What’s Moment of inertia…
It’s a natural extension of the concept of mass that accounts for how the matter in a body is distributed
2I r dmThe “mass part”The “how it’s distributed” part
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What’s Torque
It’s a natural extension of the concept of force
Fr
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What’s Angular momentum
It’s a natural extension of the concept of linear momentum
L I
Moment of inertia
Angular velocity
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What’s Rotational Energy
It’s a natural extension of the concept of kinetic energy
21
2rotK I
Moment of inertia
Angular velocity
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Going from the translational world to the rotational world…
Radian measure s r
ds d dr r
dt dt dt
v r
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How fast should the billiard ball from last week’s experiment have moved?
Just add a new type of energy term:
0rotV K K