Why does a disk go farther up an incline than a ring if they start with the same velocity?

[eyehategod]

a disk and ring have the same mass, radii, and velocities.if they both go up an incline, how will the distances that the objects move up before coming to rest compare? which one reaches the top first and why? help me understand.

 

[DyslexicHobo]

You can look at this question as conservation of energy:

$$KE_i (trans) + KE_i (rot) = PE$$

The PE is determined by how high the object has gone up the incline (specifically, $$m*g*h$$). The translational kinetic energy is going to be equal, because they both have the same velocities. The rotational kinetic energy is the only difference. Rotational kinetic energy is equal to $$1/2 I\omega^2$$. This means that whichever one has the higher rotational inertia is going to raise further, because it has more kinetic energy to convert to potential.

Hope this helps! :)

 

[eyehategod]

wow i understand it now. thanks a lot bro.