Find moment of Inertia from Force, radius and acceleration

[iva]

Homework Statement

A disc shaped object is made of a non-uniform material. Its radius is r and it is fre to rotate about an axis through its centre. If a force F applied tangentially at the edge of the object produces the angular acceleration a, what is its moment of inertia for rotation about the axis?

Homework Equations

I=mr²
F=ma

The Attempt at a Solution

If F=ma then m=F/a

so that i=mr² becomes I=Fr²/a

The answer in the book is I=Fr/a

Where did i go wrong? is it something to do with the force being tangent to the disc that i didn't do something?

Thanks!

 

[Doc Al]

If F=ma then m=F/a

Careful. "a" is the angular acceleration, not the linear acceleration. (It's better to use alpha for angular acceleration.) What's Newton's law for rotation?

so that i=mr² becomes I=Fr²/a

That formula for moment of inertia does not apply here.

All you need is Newton's 2nd law for rotation.

 

[iva]

Thanks i get it now,

So all i really needed was 1 equation:

rotational force equation: r* F=I * alpha so I=rF/alpha right?

 

[Doc Al]

Right!