The center of gravity G of a 1.5-kg unbalanced tracking wheel is located at a distance r = 18 mm from its geometric center B. The radius of the wheel is R = 60 mm and its centroidal radius of gyration is 44 mm. At the instant shown, the center B of the wheel has a velocity of 0.35 m/s and an acceleration of 1.2 m/s2, both directed to the left. Knowing that the wheel rolls without sliding and neglecting the mass of the driving yoke AB, determine the horizontal force P applied to the yoke.
Draw the kinematic diagram as shown:
Here, consider and are positive towards left.
From the kinematic diagram,
Consider the system as follows:
Consider the moments about C.
Here, is the mass of the wheel, is the radius of the wheel, is the distance from B to G, is the centroidal radius of gyration of the wheel, is the acceleration of center B, and is the velocity of center B.
Substitute for , for , for , for , for for , and for in equation (1).
Therefore, the horizontal force P applied to the yoke is.