Wheel Rotation: Force, Mass, Radius, Acceleration

[Cherrybawls]

Homework Statement

A constant horizontal force F_app of magnitude 10N is applied to a wheel of mass 10kg and radius .3m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude .6 m/s² (a) In unit-vector notation, what is the frictional force on the wheel? (b) what is the rotational inertia of the wheel about the rotation axis through its center of mass?

Homework Equations

I don't even know

The Attempt at a Solution

I spent more than an hour on this and I could not figure it out. Needless to say I am extremely frustrated because it seems as though my teacher has not taught us anything we need to know to solve this, so I don't think any of my work is worth typing in this space.

 

[vela]

Start with a free-body diagram. Identify all the forces on the wheel and where they act.

 

[Cherrybawls]

The applied force is horizontal on the center of mass and then there is a tangential frictional force going in the opposite direction on the bottom of the wheel where it is in contact with the ground. And of course there is the normal force. Does the frictional force create torque or does the applied force, it seems to me that it would be the frictional force. And is this problem solved using torque? I am really at a loss for where to even begin

 

[vela]

You forgot to mention the wheel's weight. That's the only other force.

In problems that combine rotational and translational motion, you need to consider both torques and forces. In other words, you want to apply both F=ma and τ=Iα.

As to the question of which forces exert a torque, that depends on where you choose to set your axis. A natural choice would be the center of mass of the wheel, in which case, you'd be right that only the frictional force results in a non-zero torque.