Question

3. Calculate the average values of time, position (height of fall, h), final velocity, and their uncertainties for the falling mass time = .35s, final velocity = 2.3m/s, height = .39m falling mass = .4kg. These are known quantities

4. Using conservation of energy, calculate the rotational kinetic energy, KER, gained by the pulley. PE=KE+KER, I calculated KER to be .4708 J

5. From this, determine the experimental moment of inertia of the pulley.

6. Calculate a theoretical value for the moment of inertia of the pulley from its radii and mass. ​​​​​​​I used I =M/2(R1^2+R2^2) = .00365 kgm

I cannot seem to figure out the experimental moment of inertia in a way that agrees with my theoretical. I'd love some help trying to calculate experimental moment of inertia and confirmation of my other calculations :). Thank you!

3. Calculate a theoretical value for the moment of inertia of the pulley from its radii and mass. For this use the applicable theoretical formula based on the shape of the pulley. Assume the mass of spokes on the pulley are negligible.

Answer 1

I don´t know the actual configuration of the experimental setup. But, I think it looks like the figure below:

You did not supply the radius of the pully (R) and the mass (M) of the pulley.

The disk has a moment of inertia I, and a radius R. The force of tension, T, arising from the disk, opposes the acceleration of the suspended weight. a is the acceleration of the entire system. Assuming the definitions of torque, = TR, angular acceleration, a, the relationship between them, = I, where is the angular acceleration and it is related to a by the relation: a = R,

From Newton´s law of motion, you can write

The experimental acceleration can be calculated from the given quantities by using the kinematic equation: v = u + at.

Therefore, the experimental moment of inertial will be

You have the value of the outer radius R₂ of the pulley and its value is 0.105 m. Therefore, the experimental value of moment of inertia (I) will be I = 0.19726 x 0.105² = 0.00217 Kg.m²

The theoretical value of the I is, I = (M/2) (R₁² + R₂²) = 0.5 x 0.250 x (0.085² + 0.105²) = 0.00228 Kg.m²

You have calculated wrong for the theoretical value as 0.00365.