lec09-10-203-12rot-dyn-mod3-20-12

lec09-10-203-12rot-dyn-mod3-20-12 - Dynamics Rotational...

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Δθ ω= Δt θ Δω α= Δt I all 2 i i i = m r r F rF   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 all i i =0 Statics F=ma I  [Nm] [N] 10-0
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10-1 F ma  () rF r ma mr a m r r  2 mr a = r a one object – circular (non-uniform !!) motion F m r + 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 22 1 1 2 2 m r m r  I [] I=moment of inertia many masses I 2 i all i i the same 1 1 2 2 m r m r
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Objects tendency to resist changes in rotational velocity (like mass does for translation). Two hoops with same mass R R/2 I = m R 2 I = m ( ) 2 = mR 2 R 2 1 4 Harder to change its rotation speed! Moment of Inertia I    2 1 (MR )   1 2 (MR )  2 2 1 4 (MR )   2 2 4 (MR ) Exert same torque, on both. 4 times the angular acceleration 10-2
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I = MR 2 I = MR 2 I = MR 2 1 2 I = MR 2 2 5 For Rolling, Moment of Inertia independent of length of cylinder. Shape is important. A sphere will roll faster than a solid cylinder and a solid cylinder faster than a hoop cylinder .
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This note was uploaded on 04/03/2012 for the course PHY 1020 taught by Professor Kodera during the Spring '11 term at University of Florida.

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lec09-10-203-12rot-dyn-mod3-20-12 - Dynamics Rotational...

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