Chapter11_1-6_FA05

# Chapter11_1-6_FA05 - Rotational Dynamics Chapter 11 Important quantities m R i i 2 i Moment of inertia I Used in =I So I divided by time-squared

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Chapter 11 Rotational Dynamics

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Important quantities i i i R m 2 i i i v m i i i i i m R m Moment of inertia, I. Used in τ =I α . So, I divided by time-squared has units of force times distance (torque). Total linear momentum is the sum of the individual momenta. Center-of-mass is a distance. Has to have units of meters.
Rotational Relationships 2 2 1 ϖ α τ θ I K I I L t t = = = = = Position Velocity Acceleration Momentum Force/Torque Kinetic Energy t t t + = + + = 0 2 0 2 1 Master equations: One-to-one correspondence of rotational equations to linear equations.

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Torque ( 29 ( 29 ( 29 α τ I mr r r m r ma Fr = = = = = 2
Force and Torque Combined: What is the acceleration of a pulley with a non-zero moment of inertia? R a I I TR R a TR I = = = = = α τ Torque relation for pulley: ma T mg = - Force Relation for Mass Put it together: + = = = - 2 2 1 mR I ma mg R a I T ma T mg + = 2 1 1 mR I g a NOTE: Positive down!

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How high does it go? Use energy conservation.
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## This note was uploaded on 08/16/2011 for the course PHY 2053 taught by Professor Vellaris during the Fall '08 term at University of Central Florida.

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Chapter11_1-6_FA05 - Rotational Dynamics Chapter 11 Important quantities m R i i 2 i Moment of inertia I Used in =I So I divided by time-squared

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