Calculating Inertia and Radius of Gyration for a Rolling Object

AI Thread Summary
To calculate the radius of gyration for an object rolling down a ramp, the equation K = r √((g.t² sin θ / 2x) - 1) is used, with provided values leading to a result of 0.054. The moment of inertia is calculated using Iz = MR² / 2, yielding an answer of 0.136. There is uncertainty about whether the calculated inertia applies to the radius of gyration. Clarification is sought on the relationship between the two calculations. Understanding both K and Iz is essential for accurate analysis of the rolling object's dynamics.
shemy
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Right,

I need to find out the Radius of gyration of an object as it rolls down a ramp...

So I've got the equation

K=r square root((g.t^2 sin theta/ 2x) -1))

These are the numbers I have...

Object A

R = 0.004
g = 9.81
t = 16.45
theta = 5.31
x = 0.66


I got an answer of 0.054

I think that's right however to work out inertia you use the equation

Iz = MR^2 / 2

Should that give you inertia? I got an answer of 0.136

I don't if that answers still for K and I need to work out inertia still?

Cheers

Shemy
 
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