Rotational Inertia about Rotation Axis Through COM

[Reefy]

Homework Statement

A constant horizontal force of magnitude 10 N is applied to a
wheel of mass 10 kg and radius 0.30 m as shown in the 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 rotational inertia of the wheel about the rotation
axis through its center of mass?

Homework Equations

angular acceleration α = acceleration (COM) over radius

net torque = Iα

The Attempt at a Solution

I finished part a and found out that I have to use the equations above for part B. What I'm confused about is why I can't use the rotational inertia for a hoop about its central axis I = MR^2

 

[Reefy]

Also, torque = RFsin∅. What is ∅ in this case because R can be measured from any point...

edit: actually i might have figured this angle part out. the frictional force is at the point where the wheel is touching the floor (pointing to the left or negative x-direction) and the distance from the center of the wheel to that point is R (point straight down or negative y-direction), making the angle 90 degrees.

 

[tiny-tim]

Hi Reefy!

(never first-reply top your own question … it takes you off the "Unanswered" list!)

…why I can't use the rotational inertia for a hoop about its central axis I = MR^2

because the picture shows clearly that the wheel has an outer radius and an inner radius, and you're not told what they are (also the spokes are clearly not negligibly thin, as in a bicycle wheel)

the frictional force is at the point where the wheel is touching the floor (pointing to the left or negative x-direction) and the distance from the center of the wheel to that point is R (point straight down or negative y-direction), making the angle 90 degrees.

yes