How Do You Calculate the Speed of a Marble Rolling Down an Incline?

[lagwagon555]

Homework Statement

A marble of moment of intertia 2.3 x 10^-8 kg.m^2 rolls down an incline of vertical height 10cm. It's speed at the bottom is:

1.2m/s
1.4m/s
1.2cm/s
1.4cm/s

Homework Equations

Well this isn't homework, this is just a worked example question we have. Apparently, the derived formula given is

Sqrt(10.g.h / 7)

The Attempt at a Solution

The problem is, I don't know how to derive that formula. I missed a few lectures back, which I think this covers. I don't even recognise the phrase 'moment of inertia'. Unfortunately, I don't have a textbook to go over. If it's too difficult to explain over the forums, that's fine, I'll go and visit my professor. But if anyone could point me in the right direction, it would be a huge help. Thanks!

 

[tiny-tim]

Hi lagwagon555!

(have a square-root: √ and an omega: ω and try using the X² tag just above the Reply box )

KE = ordinary KE (1/2 mv²) plus rotational energy (1/2 Iω²) …

but you need to understand moment of inertia properly first …

try the PF Library on https://www.physicsforums.com/library.php?do=view_item&itemid=31"

 

[mikelepore]

The problem is, I don't know how to derive that formula.

Unless the syllabus of your course intentionally includes the calculus derivation of the moment of inertia formulas, you probably just go to a reference table to get that formula. You refer to a table of moment of inertia formulas by asking yourself these questions: What is the shape of the object? In your case, sphere. Is the object solid or hollow? In your case, solid. Where is the axis of rotation relative to the object? In your case, through the center. You scan all of the shapes and orientations in the table until you find that one, and you read off the formula that you will need.