EWeaver+Lab+20

=Rotational Inertia=

Experiment 1
In method 1 we found that the mass reached the ground in 4 rotations or 8 pi radians. The average time it took for the mass to fall to the ground which was .71 meters from the starting position was 18.03 seconds. θ = θ0 + ω0t + .5αt2 can be used to find the angular acceleration. 8 pi = .5α(18.03^2) α= .155 rad/s^2

The second method used the equation: vertical displacement = initial velocity + (1/2)a (t^2), after plugging in the number you get, .71=0(18.03) + (1/2)a (18.03^2). The linear acceleration, a, comes out to be .0044m/s^2. After measuring the pulleys radius we can find the angular acceleration. a = αr, so after plugging in the values find we get α = .157 rad/s^2.

Finding the percent error between theses two values we get (.157-.155)/(.157)x100 = 1.27% this is within the uncertainty of measurement.

Experiment 2
The first method to find moment of inertia involved calculating tension and using the equation Tension= Moment of Inertia (angular acceleration), which produced a moment of inertia of .0884 kg(m^2).

Next we calculated the moments of inertia of the individual parts by adding them together, this method produced a moment of inertia of .08366 kgm^2.

We then found the percent error to check if it is within uncertainty of measurement. Percent Error = l (.08366-.0884) / .08366 l x 100 = 5.7% error. Therefore, it is within uncertainty of measure.

**Experiment 3**
Initially, the mechanical energy of the system is equal to the gravitational potential energy because the system begins with zero velocity. The gravitational potential energy was .3479J. When the mass falls, the energy is then converted into kinetic energy. The mass has both translational kinetic energy and rotational kinetic energy. The sum of these two is the total KE. The translational KE was 1.45 x 10^-4 and the rotational KE was .327J. Added together we got .3721J Percent Error = (.3479-.3271)/(.3479) x100 = 5.98% error, this is within uncertainty of measurement.