Calculating Inertia and Radius of Gyration for a Rolling Object

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SUMMARY

This discussion focuses on calculating the radius of gyration (K) and inertia (Iz) for a rolling object using specific equations. The user, Shemy, provided values for an object (R = 0.004, g = 9.81, t = 16.45, theta = 5.31, x = 0.66) and derived a radius of gyration of 0.054. Additionally, Shemy calculated the inertia using the formula Iz = MR^2 / 2, resulting in an inertia value of 0.136. The discussion seeks clarification on the correctness of these calculations and their interrelation.

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  • Basic knowledge of rolling motion dynamics
  • Ability to perform calculations involving gravitational acceleration (g = 9.81 m/s²)
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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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