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

AI Thread Summary
A constant horizontal force of 17 N is applied to a 6 kg wheel with a radius of 0.70 m, resulting in an acceleration of 1.00 m/s². The discussion revolves around calculating the frictional force acting on the wheel using the equations F=ma and t=I(a/r). There is uncertainty regarding the moment of inertia (I) of the wheel, with considerations of whether it should be treated as a solid disc or a hoop. The initial assumption is that the wheel behaves like a hoop, leading to the use of I=mr² in the torque equation. The participant seeks confirmation on this approach to solve for the frictional force.
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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?
 
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A wheel would be a hoop... hence I = mr^2.
 
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