PH2014_Ch13_Rotation part B

# PH2014_Ch13_Rotation part B - 1 Chapter 13 Rotational...

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Unformatted text preview: 1 Chapter 13: Rotational Motion B T h e g r e a t d o w n h i l l r a c e W h o i s t h e w i n n e r ? What is the rotational analog of Newton’s Law? 2 Review of Rotational Motion Translational Motion Rotational Motion Position Angular position Velocity Angular velocity Acceleration Angular acceleration x dt dx v = 2 2 dt x d dt dv a = = 2 2 dt d dt d θ ω α = = dt d θ ω = at v v + = 2 2 1 at t v x x + + = ) ( 2 2 2 x x a v v − + = t α ω ω + = 2 2 1 t t α ω θ θ + + = ) ( 2 2 2 θ θ α ω ω − + = For constant a: For constant : α 3 Torque and Balance Perfect balance Unbalanced seesaw m Torque: F r r r r × = Unbalanced seesaw 2m New balance m m 2 τ τ = 4 Rotational Analog of Newton’s Law A force is applied to a ball of mass M mounted to a massless rod with a fixed end, causing rotational motion. F r F r r r r × = Torque: rF = Acceleration: α r a = α τ ) ( 2 m R ma R F R = ⋅ = ⋅ = Equation for rotational motion: α ⋅ = I Rotational Inertia: 2 mR I = Newton’s Law: ma F = F r R F r R F r R m 5...
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PH2014_Ch13_Rotation part B - 1 Chapter 13 Rotational...

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