Find the experimental value for the Moment of Inertia of the arm plus the two ma

Question

Find the experimental value for the Moment of Inertia of the arm plus the two masses using the information and the graph above.

The theoretical is 0.093843 kg m^2
What is the experimental? I got 0.0003827 (which does not make sense, so please tell me what I am doing wrong here).

Here is the data:

Hanging mass = 0.1118 kg

Radius of pulley = 0.018 m

Mass 1: 0.2792 kg out 18 cm from the center of the arm.

Mass 2: 0.2757 kg out 10 cm from the center of the arm.

And here is my work shown, the experimental and theoretical are nowhere close to each other, and I am pretty sure I am doing the experimental wrong.

Experimental:

y-yo=vyt+ ½ ayt2

At2+Bt+C

A = ½ ay

B = Vy

C = yo

                        ½ ay = 0.424,

therefore ay = 0.848

I=mr^2 (g/ ay) – 1

Ia= (0.1118)(0.018)2 [(9.807/0.848)-1] = 3.827*10-4

Theoretical:

I(arm) = 0.01204 kg×m2 or 12.04*10-3

I(mass 1) = m1r2 = 0.2792(0.18)2 = 9.046*10-3

I(mass 2) = m2r2 = 0.2757(0.10)2 = 2.757*10-3

            I(total)= (12.04(9.046+2.757) *10-3 = 93.843*10-3 or .093843 kg m2

Linear mt + b m = 0.84196 ± 0.0021 b = 0.0796 13 ± 0.0099 r= 0.999 25 Quadratic 20 At2 t Bt + C A=0.424 ±3.3x104 B=0.0749 ±0.0032 c =-0.0322 ± 0.0056 u 15 RMSE = 0.0240 10 0.0 0.5 1.0 1.5 2.0 2.53.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.07.5 Time (s)

Explanation / Answer

Since you have Asked, I am pointing out only the mistakes in this experimentation. It would be obviously not possible to provide for a model solution since you have to make few fundamental changes

1. The biggest mistake is in the second graph. Carefully see your graph axes. This is angle vs time graph wheras to find the moment of inertia you will have to plot position vs time graph and then find the coefficient like you did in this question. It might come in negative and in that scenario you will hve to take the acceleration due to gravity as negative i.e, g=-9.81 m/s^2.

2. In the experimental calculation, the formula is about multiplying the mass with square of radius of pulley and not diameter (you have done the latter)

3. The last calculation: perform it once more by adding the terms.

Hope it helps :)

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