lec09-10-203-08rot-dyn-mod

lec09-10-203-08rot-dyn-mod - Dynamics Rotational...

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Δθ ω= Δt θ Δω α= Δt I all 2 i i i = m r r F rF τ = = 1 K = I 2 2 ω x=rθ a=α r v=ωr 2 1 K= mv 2 F m Δv a= Δt x Δx v= Δt Rotational Translation [radians] rad 1 [ = ] sec s 2 rad s rolling without slipping [m/s] [m] [m/s 2 ] [Kg] [N] [Nm] [Kg m 2 ] [J] [J] Dynamics Equilibrium conditions all i i F =0 h all i i =0 h Statics F=ma I α = [Nm] [N] 10-1
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10-2 F ma = ( ) rF r ma = ( ) mr a τ = ( ) m r r α = 2 m r = one object – circular (non-uniform !!) motion + axis m 1 and m 2 rigidly attached (“rigid body rotation”) Now add 2 nd mass + axis 1 r 2 r m 1 m 2 2 2 1 1 2 2 m r m r = + I [ ] = I=moment of inertia many masses I 2 i all i i m r = τ the same 2 2 1 1 2 2 [ ] m r m r = +
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10-3
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+
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lec09-10-203-08rot-dyn-mod - Dynamics Rotational...

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