Tangential Acceleration vs. Tangential component of force

[jumbogala]

Homework Statement

A ball moves counterclockwise in a circle and is speeding up. The radius of the circle is 5 m.

Its angular acceleration is α, (2.09 rad/s²)$$\hat{k}$$

The ball's mass is 0.125 kg.

What is the tangential component of the force on the particle?

Homework Equations

The Attempt at a Solution

So the tangential acceleration is a_t = αr = 10.47 m/s²$$\hat{t}$$

(Define $$\hat{t}$$ to be tangent to the circle. At the top of the circle, it points to the left. At the bottom, it points to the right and so on).

Then the tangential component of the FORCE on this particle should be (10.47 m/s²)$$\hat{t}$$ * 0.125 kg = (1.3 N)$$\hat{t}$$

But I got it wrong, and I have no clue why. Can anyone help me out? I got half the marks so it may just be a small error somewhere =\

 

[kuruman]

The calculation looks OK. Components of vectors do not have unit vectors attached to them. Try without the t-hat.