#3 : 1 1 Uinitial = Kfinal mgh =mv² +lw? Еq. 11 or – : 1. Consider a solid sphere and a solid disk with

#3 : 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).