Finding the moment of inertia and torque for a spinning ball

[jumbogala]

Homework Statement

A ball is going around in a circle of radius 5 m.
It starts from rest, and goes through an angle change of 26 rad in 5 seconds.

The ball weighs 0.3 kg.

Find its moment of inertia, and find the torque about the origin.

Homework Equations

The Attempt at a Solution

What I'm doing seems too simple, so I bet it's wrong...

I thought moment of inertia was just mass times radius². My textbook doesn't give it for this situation but it gives the moment of inertia for other shapes, all of which are this but multiplied by some factor.

And I think the torque would be zero because the force acting on the ball would be towards the center of the circle, and since torque is r x F, and F is 180 to r, rFsin(180) = 0.

 

[rock.freak667]

The Attempt at a Solution

What I'm doing seems too simple, so I bet it's wrong...

I thought moment of inertia was just mass times radius². My textbook doesn't give it for this situation but it gives the moment of inertia for other shapes, all of which are this but multiplied by some factor.

And I think the torque would be zero because the force acting on the ball would be towards the center of the circle, and since torque is r x F, and F is 180 to r, rFsin(180) = 0.

Well it is just a point mass so the inertia is just mr². The torque would be equal to the moment of inertia*angular acceleration.

 

[jumbogala]

Why is the torque equal to the angular acceleration though?

 

[rock.freak667]

Why is the torque equal to the angular acceleration though?

Torque is the rate of change of angular momentum.

$$\tau = \frac{d}{dt}(I \omega)= I \frac{d\omega}{dt}=I \alpha$$

 

[jumbogala]

Oh okay, thank you.

This made me wonder if you can find the radial component of the force on the ball using torque, since torque is the rotational equivalent of force.

I was going to find the radial acceleration, but I don't know how seeing as the radial acceleration is equal to ω²r, and ω is constantly changing!