Lab09_Rotational Motion_Lab Report -...

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PHY 122: Rotational Motion Ryan M. Wood Evan Phillips Group Number: 5 Class Number: 14780 01April2016
Objective: In this lab students will be observing constant angular acceleration for a rigid body rotating about its center mass made by constant torque. Students will observe moment of inertia and how it depends on the axis of rotation. Students will also check to see if the Law of Conservation of Energy applies to this experiment. Experimental Data: Mass (block) Mass (weight) Radius (small pulley) Radius (medium pulley) 0.4327kg 0.0203kg 0.0048m 0.0143m Block Side Lengths a b c 0.04015m (40.15mm) 0.02998m (29.98mm) 0.04903m (49.03mm) Short Axis Long Axis Small Pulley Medium Pulley Small Pulley Medium Pulley Angular Acceleration ( rad s 2 ) 6.21 ± 0.11 17.7 ± 0.67 9.81 ± 0.11 27.6 ± 0.31 Initial Angular Position ( rad ) 40.247 11.711 56.933 10.681 Initial Angular Velocity ( rad s ) 24.43 20.25 36.48 24.26 Final Angular Position ( rad ) 66.27 21.328 96.15 26.389 Final Angular Velocity ( rad s ) 30.37 27.58 45.73 38.4 Data analysis: Static moment of inertia: Short Axis:
I = 1 12 M ( a 2 + c 2 ) = ( 1 12 ) ( 0.4327 kg ) ( 0.04015 m 2 + 0.04903 m 2 ) = 1.45 10 4 kg m 2 dI da = 1 12 M ( 2 a ) ∆a = ( 1 12 ) ( 0.4327 kg ) ( 2 0.04015 m ) ( 0.00001 m ) = 2.90 10 8 kg m 2 dI dc = 1 12 M ( 2 c ) ∆c = ( 1 12 ) ( 0.4327 kg ) ( 2 0.04903 m ) ( 0.00001 m ) = 3.54 10 8 kg m 2 Error Propagation = ( dI da ) 2 + ( dI dc ) 2 ¿ ( 2.90 10 8 kg m 2 ) 2 + ( 3.54 10 8 kg m 2 ) 2 ¿ 4.57 10 8 kg m 2 Long Axis: I = 1 12 M ( a 2 + b 2 ) = ( 1 12 ) ( 0.4327 kg ) ( 0.04015 m 2 + 0.02998 m 2 ) = 9.05 10 5 kg m 2 dI da = 1 12 M ( 2 a )

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