# lec15 - L ECTURE 15 A PPLICATIONS OF A NGULAR M OTION T...

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L ECTURE 15: A PPLICATIONS OF A NGULAR M OTION T HEORY Rotational impulse (billiards) Transition to rolling Balance Stability

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Translational/Rotational Analogs Translational Rotational Mass m Rotational inertia I Position x , y , ... Angle θ , ... Velocity v Angular velocity ω Acceleration a Angular acceleration α Force F Torque τ Momentum p = mv Angular momentum L = ??? Kinetic energy 1 2 mv 2 Kinetic energy 1 2 ??? Work Fx ?? Newton’s Translational Rotational 1st No F constant mv No τ constant I ω 2nd F = ma τ = I α 3rd Action/reaction force pairs Action/reaction torque pairs
Translational/Rotational Analogs Translational Rotational Mass m Rotational inertia I Position x , y , ... Angle θ , ... Velocity v Angular velocity ω Acceleration a Angular acceleration α Force F Torque τ Momentum p = mv Angular momentum L = I ω Kinetic energy 1 2 mv 2 Kinetic energy 1 2 I ω 2 Work Fx τθ

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1. The formula for the rotational analog of impulse is . ..? (Hint: impulse is F Δ t .) (a) I ω (b) τθ (c) F times (lever arm) (d) I α (e) τ Δ t
Rotational Newton’s laws review Match each of these athletic facts with the most germane of Newton’s laws. 1. A shortstop chokes up on the bat to face a fastball pitcher. (a) Newton’s 1st (b) Newton’s 2nd (c) Newton’s 3rd 2. A bicycle is elevated on a stand for maintenance. After the bearings are cleaned, the wheel spins freely for a very long time. 3. For a triple somersault, a diver leans forward away from the board on takeoff.

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## This note was uploaded on 12/12/2011 for the course PHYS 17 taught by Professor Mcwilliams,r during the Fall '08 term at UC Irvine.

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lec15 - L ECTURE 15 A PPLICATIONS OF A NGULAR M OTION T...

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