Question

two uniform cylinders have different masses and different rotational inertias.they simultaneously start from rest at top of an inclined plane and rool without sliding down the plane.the cylinder that gets to the bottom first is?

Answer 1

none, because the cylinders not depend of your mass then both arrived in the same time: (only if the cylinders were uniforms, with the same radius and high)

we used theorem of conservation of energy:

Energy initial = energy final

mgh = (1/2)mV² + (1/2)Iw² ---- v is equal a the velocity of center of mass of particle and the cylinder has energy rotational, the rotational inertia for a cylinders or disc is (1/2)mr²


mgh = (1/2)mV² + (1/2)(1/2)mr²w²

and the mass are canceled, next you solve for the velocity (v) or angular velocity (w)

Enjoy and good luck