Quote:
It gets kind of messy. mu_k is not really constant in real life.
Typically, omega_p would increase as omega_w increases.
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Actually the model contains the answer to this and it is a simple matter of kinematics.
All of the analyses performed are in equilibrium and part of that is the wheel slipping on the floor. In order for the force of friction to be pointed in the radial direction, the velocity of the point on the bottom of the wheel must be in that direction (for this model). Once you accelerate the wheel you will introduce a wheel slip velocity relative to the ground which is not aligned and thus results in an angular acceleration changing omega_p. You will reach a new equilibrium point if you specify a new constant wheel speed.
Quiz 4: Given omega_w determine the steady state omega_p.
Okay... got you between edits
Quiz 5: Qualitatively, what happens to the torque requirements, friction force, and reaction force at the pivot, if the motor and wheel are instead a thin disk of mass m (i.e. with rotational inertia) AND the pivot connection only resists moments about the radial axis (e.g. is a Hooke's joint)? The equations get tough, so we need only discuss the character and origin of the effects.
Answer the following:
Does the answer to quiz 4 still apply? Why or why not?
Is the applied torque requirement constant? Why or why not?
Is the friction force constant magnitude and radially oriented? Why or why not?
Is the reaction force at the pivot different in any meaningful way? How so?