Simple problem about the torque?

[nchin]

A constant horizontal force of magnitude 10 N is applied to wheel of mass 10 kg and radius 0.30 m (Figure). The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.60 m/s2. (a) What are the magnitude and direction of the frictional force on the wheel? (b) What is the rolling inertia of the wheel about the rotation axis through its center of mass?

Solution
http://panda.unm.edu/Courses/Price/Phys160/p25-2.pdf

I understand part a but i have a question on part b.

I know that τ = r x f

so why, in this problem, τ = (.3m)(4N)? why is only friction force calculated and not the force applied to it which was 10N?

 

[grzz]

If the 10N is applied tangentially to the rim of the wheel, then the 10N would result in a torque about the centre of the wheel.

But if the 10N is applied to the centre of the wheel then the 10N would lead to no torque about the centre of the wheel.

 

[nchin]

If the 10N is applied tangentially to the rim of the wheel, then the 10N would result in a torque about the centre of the wheel.

But if the 10N is applied to the centre of the wheel then the 10N would lead to no torque about the centre of the wheel.

so if 10n was applied to the center of the wheel then it wouldn't effect the rotation so the torque would be zero?

 

[grzz]

As you said

τ = r x f.

Hence if force f passes through the centre of the wheel, then the torque τ of f about the centre of the wheel is 0. This follows because in this case the distance r between the line of action of f and the point about which the torque is to be found is 0.

 

[nchin]

As you said

τ = r x f.

Hence if force f passes through the centre of the wheel, then the torque τ of f about the centre of the wheel is 0. This follows because in this case the distance r between the line of action of f and the point about which the torque is to be found is 0.

Thanks !