Finding the moment of inertia and torque for a spinning ball

jumbogala

1. 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.

2. Homework Equations

3. 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.

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rock.freak667

Homework Helper
3. 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

Homework Helper
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!

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