Calculating frictional force for a rolling wheel | F=ma and t=I(a/r) equations

[snoggerT]

In the figure below, a constant horizontal force Fapp of magnitude 17 N is applied to a wheel of mass 6 kg and radius 0.70 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 1.00 m/s2.

(a) In unit-vector notation, what is the frictional force on the wheel?



F=ma , t=I(a/r)

The Attempt at a Solution

- I set up both equations with my applied force and frictional force, so I have 2 unknows in my I and frictional force. My problem is coming in not knowing what to sub in for I. I don't know whether a wheel would be considered a solid disc or a hoop. My initial thinking would be I=mr^2, and then I could plug that in into the torque equation and cancel out my r and then solve for frictional force. Would that be correct?

 

[learningphysics]

A wheel would be a hoop... hence I = mr^2.

 

[m2003]

I would approach this problem by first identifying the type of motion that the wheel is experiencing. In this case, it is rolling, which means that both rotational and translational motion are present. This means that both equations, F=ma and t=I(a/r), are applicable.

To determine the frictional force, we need to consider the forces acting on the wheel. The applied force Fapp is causing both translational and rotational motion, while the frictional force is opposing the motion and causing a torque on the wheel.

In order to determine the moment of inertia (I), we need to know the shape and distribution of mass of the wheel. If we assume that the wheel is a solid disk, then the moment of inertia would be I=1/2mr^2. However, if the wheel is a hoop, then the moment of inertia would be I=mr^2.

Once we have determined the moment of inertia, we can use the torque equation t=I(a/r) to solve for the frictional force. We know the acceleration (a) and the radius (r), and we can calculate the moment of inertia based on the assumption of the wheel's shape.

In unit-vector notation, the frictional force on the wheel would be in the opposite direction of the applied force Fapp, and its magnitude would be equal to the torque divided by the radius. So, in this case, the frictional force would be in the negative x-direction and its magnitude would be 6.43 N.

Overall, it is important to consider the type of motion and the forces acting on the object in order to accurately calculate the frictional force. Additionally, it is crucial to make assumptions about the object's shape and distribution of mass in order to determine the moment of inertia.