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8.5 Rotational Dynamics Σ F = ma τ = mr 2 α Σ τ = I α

8.5 Rotational Dynamics Σ F = ma τ = mr 2 α Σ τ = I α. 8.7 Rotational Kinetic Energy KE tran = ½ mv 2 + v = r ω KE rot = ½ I ω 2 Work done by a torque: W = τΔθ. Δ. 8.8 Angular Momentum. 8.8 Angular Momentum

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8.5 Rotational Dynamics Σ F = ma τ = mr 2 α Σ τ = I α

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  1. 8.5 Rotational Dynamics Σ F = ma τ = mr2α Σ τ = I α APHY201

  2. 8.7 Rotational Kinetic Energy KEtran= ½ mv2 + v = rω KErot = ½ Iω2 • Work done by a torque: W = τΔθ Δ APHY201

  3. 8.8 Angular Momentum APHY201

  4. 8.8 Angular Momentum • Newton’s 2nd Law: Fnet = Δp/Δt → τnet = ΔL/Δt • If τnet = 0 then L = constant → I1ω1 = I2ω2 • Applications: skaters, gymnasts, divers, helicopters • Stability of rotating objects APHY201

  5. 8.8 Angular Momentum APHY201

  6. 8.8 Angular Momentum APHY201

  7. 8.8 Angular Momentum APHY201

  8. In class: Problems 29 and 54 • Other problems ↓ . 28. Since all of the significant mass is located at the same distance from the axis of rotation, the moment of inertia is given by 0.139 kg m2 APHY201

  9. 55. The skater’s angular momentum is constant, since no external torques are applied to her. She accomplishes this by starting with her arms extended (initial angular velocity) and then pulling her arms in towards the center of her body. APHY201

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