Is My Calculation of a Rolling Steel Hoop's Acceleration Correct?

[dyn]

Homework Statement

Hi.
Question concerns a steel hoop of mass 5kg rolling without slipping down a ramp inclined at 30 degrees to the horizontal. What is it's acceleration ?

Relevant Equations

F=ma and resolving component of weight parallel to ramp

I already have the answer but it doesn't make sense. For starters I think the question is worded badly. I think there are 2 different accelerations here ? The acceleration of the centre of mass and the acceleration due to rotation. I think the acceleration due to rotation doesn't affect the acceleration of the centre of mass so I resolved the component of the weight down the ramp which is mgsinθ ; taking g as 10 gives this as 25 and using F=ma gives the acceleration of the COM as 5 m/s^2
Is my reasoning incorrect ?
Thanks

 

[Antarres]

In case of rolling without slipping, there is a relation between the acceleration of the centre of mass, and angular acceleration which reads $a = R\alpha$. Where $R$ is radius of the hoop. This relation is derived from looking at the point where hoop is touching the ground while rolling. If there is no slipping, that point should be at rest relative to the surface on which the hoop is moving, hence the acceleration that is coming from rotation and translation should cancel at that point.

As for your reasoning, the reason why the hoop is not slipping is because you have friction with the surface it is rolling on, so therefore, you need to add friction into the Newton law for translation, as well as rotation, in order to get the correct answer.