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. 1/2Iw =
0) – call this your “No K_rot model”. Leave the second as it is written in Eq. 11
– call this your “K_rot model”. For both models, solve for v in terms of g, h,
and a. In the K_rot model, you will need to use I = kmr^2 (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 solve for
t for both models separately. NOTE: a is different for the two models (refer
to the “Rotational Mechanics” discussion in the introduction):
• In the “No K_rot model”, a = g*sin(q) (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 K_rot model) and when you assume
the kinetic energy is distributed between translational and rotational
motion (K_rot model).

Eq. 11: U_initial = K_final OR mgh = 0.5m(v^2)+0.5I(w^2)
Eq. 3: I = kM(R^2)
Eq. 8: a_t = gsinθ/(1 + I/M(R^2)) = gsinθ/(1+k)