Rail 0 Dimension of roller= 180 mm Mass-1.75 kg R=90 mm r= 4 mm W1=5 mm W2=35 mm sin 0 S R Roller Wi W3 W3-5 mm < S=120 mm Trial Height, he Angle of 1st run (s) 2nd run 3rd run (s) Average number (m) < elevation, (s) time (s) < e (0) 1 0.285 13.739 6.77 6.84 6.81 t1=6.806 2 0.78 8.627 8.68 8.53 8.86 t2=8.69 3 0.062 2.962 15.56 17.41 14.57 t3=15.85 1. Calculate the mass and mass moment of inertia of the roller using basic principles (theoretically). 2. Calculate the linear and angular velocities and accelerations of the roller using the results from the first experiment. Assume that no slip occurs. < 3. By applying the conservation of energy to the results from the first experiment and the velocities calculated in Step 2, calculate the mass moment of inertia of the roller 4. Derive the linear and angular equations of motion from the free body diagram, as shown in Figure 2.4 mgsine mgcos Figure 2: Free body diagram. k e 5. By applying the equations of motion that you have derived in Step 4 to the results from the first experiment and the accelerations calculated in Step 2, calculate the mass moment of inertia of the roller. < 6. Compare the theoretical value obtained from Step 1 and the two experimental values obtained from Steps 3 and 5 < 7. Compare the theoretical value obtained from Step 1 and the two experimental values obtained from Steps 3 and 5. < 8. Using the results from the second rail height, calculate the linear acceleration of the roller. < 9. Using the results from the second rail height, calculate the linear acceleration of the roller.