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1 Uinitial = Kfinal mgh mv² +-Iw² 2 or – -

1 Uinitial = Kfinal mgh mv² +-Iw² 2 or – -

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1 1 Uinitial = Kfinal mgh =mv² +lw? Еq. 11 or -
Transcribed Image Text:1 1 Uinitial = Kfinal mgh =mv² +lw? Еq. 11 or -
1. Consider a solid sphere and a solid disk with the same radius and the same mass. Explain why the solid disk has a greater moment of inertia than the solid sphere, even though it has the same overall mass and radius. 2. Calculate the moment of inertia for a solid cylinder with a mass of 100 g and a radius of 4.0 cm. 3. In this question you will do some algebra to determine two relations that you will need for Part 2 of this lab. Write down Eq. 11 twice. In the first statement, set the rotational kinetic energy term equal to zero (i.e. -lw? = 0) - call this your "No Krot model". Leave the second as it is written in Eq. 11- call this your "Krot model". For both models, solve for v in terms of g, h, and a. In the Krot model, you will need to use I = kMR? (Eq. 3) and w = V/r. The solution for the Krot model will have a k term as well. Once you have solved for v, use the kinematic relation, v = at, and the trigonometric relationship, h = L sin 0, solve for t for both models separately. NOTE: L is the length of the incline plane. NOTE: a is different for the two models (refer to the "Rotational Mechanics" discussion in the introduction): In the "No Krot model", a = g sin 0 (remember the Newton's 2nd Law lab) In the "Krot model", a is given by equation 8 These two solutions represent the predicted time it will take an object to descend a height, h, down an inclined plane when you assume all kinetic energy in the system is translational (No Krot model) and when you assume the kinetic energy is distributed between translational and rotational motion (Krot model).
Transcribed Image Text:1. Consider a solid sphere and a solid disk with the same radius and the same mass. Explain why the solid disk has a greater moment of inertia than the solid sphere, even though it has the same overall mass and radius. 2. Calculate the moment of inertia for a solid cylinder with a mass of 100 g and a radius of 4.0 cm. 3. In this question you will do some algebra to determine two relations that you will need for Part 2 of this lab. Write down Eq. 11 twice. In the first statement, set the rotational kinetic energy term equal to zero (i.e. -lw? = 0) - call this your "No Krot model". Leave the second as it is written in Eq. 11- call this your "Krot model". For both models, solve for v in terms of g, h, and a. In the Krot model, you will need to use I = kMR? (Eq. 3) and w = V/r. The solution for the Krot model will have a k term as well. Once you have solved for v, use the kinematic relation, v = at, and the trigonometric relationship, h = L sin 0, solve for t for both models separately. NOTE: L is the length of the incline plane. NOTE: a is different for the two models (refer to the "Rotational Mechanics" discussion in the introduction): In the "No Krot model", a = g sin 0 (remember the Newton's 2nd Law lab) In the "Krot model", a is given by equation 8 These two solutions represent the predicted time it will take an object to descend a height, h, down an inclined plane when you assume all kinetic energy in the system is translational (No Krot model) and when you assume the kinetic energy is distributed between translational and rotational motion (Krot model).
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