(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A ring (hollow cylinder) of mass 2.30 kg, inner radius 4.35 cm, and outer radius 5.65 cm rolls (without slipping) up an inclined plane that makes an angle of θ=38.0°, as shown in the figure attached.

At the moment the ring is at position x = 1.95 m up the plane, its speed is 3.00 m/s. The ring continues up the plane for some additional distance and then rolls back down. It does not roll off the top end. How much further up the plane does it go?

2. Relevant equations

Krot=1/2Iw^2 where I is moment of inertia [I=mr^2]

Kcm=1/2mv^2 where v is the speed of the centre of mass

Ug=Mgh

w=rv [using the outer radius?]

I think the moment of inertia should be I=1/2m(Rinner^2 + Router^2) since it is a hollow cylinder.

3. The attempt at a solution

I used the conservation of energy to formulate: Krot + Kcm + Ug = Ug

Where the left side is at position x and the right side is at the new position that we want to find.

so the height on the right side is what is needed to find and from that we get how far it has moved from position x and then subtract it from x to get the difference.

I think I am approaching the question correctly but there may be some where I am going wrong and I have tried this 3 times already only to get 3 different answers that are all wrong. Thank you very much for your help in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Rotational Dynamics of a ring of mass

**Physics Forums | Science Articles, Homework Help, Discussion**