posted by jeff .
a uniform disk and a uniform sphere are rolled down an incline plane from the same point and intially they are at rest. Find the difference in time they arrive at a mark on the plane which is 6 meters from the starting point. The sphere has twice the mass and the same radius as the disk. The disk has a mass of 3kg and a radius of 0.4m. The angle of inclination is 30 degress.
Use conservation of energy, and make sure you include both the translational energy (1/2) M V^2 (due to linear motion of the center of mass), and the rotational kinetic energy (1/2) I w^2 = (1/2)I(V/R)^2. The sphere will go down the ramp faster because less of the energy gets tied up in rotation.
Show your work if you need further assistance. I is the moment of inertia and w is the angular rotation rate, which equals V/R.