How Does Friction Affect Wheel Motion on a Horizontal Surface?

[kara]

The question is:

A wheel is rolling smoothly on horizontal surface. There is a constant horizontal force of magnitude 10 N. Wheel has mass of 10 kg, and radius of 0.3 m. The accel. of its centre of mass has mag. of 0.6 m/s^2.

I am asked to find frictional force in unit-vector notation. This is what i did:
(10N) = f - (10kg)(9.8m/s^2)sin0* = (10kg)(0.6 m/s^2)
(10N)-f = 6.0
-f = -4.0

Since there is clockwise angluar acccel the friction is a negative value. So my answer is f = (-4.00 N)i

For part b it asks for the rotational inertia of the wheel about its centre of mass. This is what I've done so far:

(-4 N)(0.3m) = I (-0.6m/s^2/0.3m)
-1.20 = I(-2)
I = 0.600 rad/s

Am i on the right track?? Please help!

 

[OlderDan]

Friction tends to retard the motion, and I assume the applied force and the acceleration are in one direction, with friction in the opposite direction. Your positive answer for f is because you have it in the wrong place in your equation for it to be negative. If you wrote F + f = ma, then f would be found to be negative. Your result for I has the wrong dimensions.