Question

A uniform solid disk and a uniform hoop are placed side by side at the top of an incline of height h. If they are released from rest and roll without slipping, which object reaches the bottom first? solid disk uniform hoop it's a tie Verify your answer by calculating their speeds when they reach the bottom in terms of h. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.) v_disk = V_hoop =

Answer 1

(a) the uniform disk has a lower moment of inertia and arrives first.

(b) with no sliping taking place, the two objects will be in rotation and translation.

energy is conserved

$\Delta Ki = -\Delta P$

$1/2M\upsilon ^2 + 1/2I\omega ^2 = Mgh$

$M\upsilon ^2 +I*\upsilon ^2/R^2 = 2Mgh$

For The Disk $I=MR^2/2$ and

for the hoop $I=MR^2$

We finally get $\upsilon = \sqrt{4/3gh}$ for the disk

and $\upsilon = \sqrt{gh}$   for the hoop.