Use conservation of energy to compute the total KE of the can at the bottom, M g *(L sin 22.4) = 3.355 J, where L is the 3.34 m length of the ramp. The translational energy at the bottom will be
(1/2)M V^2, where V = twice the average velocity, 2*3.34/1.89 = 3.534 m/s
TrKE = 1.68 J
It appears that half the KE of the can is translational KE
Set the remaining energy equal to the rotational KE, (1/2) I w^2, and solve for the moment of inertia, I.
Assume w= V/R
A metal can containing condensed mushroom soup has a mass of 269 g, a height of 14.7 cm, and a diameter of 6.79 cm. It is placed at rest on its side at the top of a 3.34 m long incline that is at an angle of 22.4 degrees to the horizontal and is then released to roll straight down. Assuming energy conservation, calculate the moment of inertia of the can if it takes 1.89 s to reach the bottom of the incline.
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