Rotational+Inertia+Demonstrator

Experiment 1 __Goal__ Find experimental α __Select an equation__ ∆θ = wot + 1/2αt^2 __Substitute__ 10π = 0 + 1/2α(9.5)^2 __Solve__ α = 0.696 rad/s^2

__Goal__ Find a __Select an equation__ ∆x = vot + 1/2at^2 __Substitute__ 0.92 = 0 + 1/2a(9.5)^2 __Solve__ a = 0.02 rad/s^2

__Goal__ Find actual α __Select an equation__ α = a/r __Substitute__ α = 0.0204/0.3 __Solve__ α = 0.68 rad/s^2

__Goal__ Find percent error for experimental α __Select an equation__ % error = (| experimental - actual | / (experimental + actual)/2) x 100% __Substitute__ % error = (| 0.696 - 0.68 | / (0.696 + 0.68)/2) x 100% __Solve__ % error = 2.325%

The percent error shows that the experimental and actual values agree with each other reasonably.

__Goal__ Find tension __Select an equation__ F = ma **or** T = mg __Substitute__ (0.23)(9.81) = T __Solve__ T = 2.256 N
 * Experiment 2**

__Goal__ Find experimental moment of inertia __Select an equation__ I = T/α __Substitute__ I = 0.06762/0.6962 __Solve__ I = 0.0971 kg*m^2

__Goal__ Find actual moment of inertia __Select an equation__ Need 3: I = 1/3ML^2 (thin rod) I = 1/2MR^2 (disk) ∑I = I1 + I2 + I3 __Substitute__ I =1/3(0.0748)(0.34)^2 (rod) I = 1/2(0.018)(0.02125^2) (disk) I = 5.8 x 10^-4 kg*m^2 (pulley) __Solve__ I = 0.0115 kg*m^2 (rod) I = 1.6 x 10^-5 kg*m (disk) I = 5.8 x 10^-4 kg*m^2 (pulley)

Which when substituted: ∑I = 0.0121 kg*m^2

__Goal__ Find percent error for experimental moment of inertia __Select an equation__ % error = (| experimental - actual | / (experimental + actual)/2) x 100% __Substitute__ % error = (| 0.0971 - 0.0121 | / (0.0971 + 0.0121)/2) x 100% __Solve__ % error = 155.678%

The experimental and the actual do not seem to agree at all, meaning there must have been a large error in the experiment.

__Goal__ Find PE __Select an equation__ PE = mgh __Substitute__ PE = 0.23 x 9.8 x 0.9 __Solve__ PE = 2.0286 j
 * Experiment 3**

__Goal__ Find KE (translational) __Select an equation__ KE = 1/2mv^2 __Substitute__ KE = 1/2(0.23)(0.189) __Solve__ KE = 0.0217 j

__Goal__ Find KE (rotational) __Select an equation__ KE = 1/2Iw^2 __Substitute__ KE = 1/2(0.0971)(6.3)^2 __Solve__ KE = 1.93 j

__Goal__ Find KE (total) __Select an equation__ KE = 1/2mv^2 + 1/2Iw^2 __Substitute__ KE = 0.0217 + 1.93 __Solve__ KE = 1.9517

__Goal__ Find percent error for experimental energy __Select an equation__ % error = (| experimental - actual | / (experimental + actual)/2) x 100% __Substitute__ % error = (| 2.0307 - 1.9517 | / (2.0307 + 1.9517)/2) x 100% __Solve__ % error = 3.97%

According to the data, the energy was reasonably conserved.