Assuming that the wheel of Prob. 18.97 weighs 8 lb, has a radius a = 4 in., and a radius o...

Assuming that the wheel of Prob. 18.97 weighs 8 lb, has a radius a = 4 in., and a radius of gyration of 3 in., and that R = 20 in., determine the force exerted by the plate on the wheel when Ω = 25 rad/s.

Prob. 18.97

A stationary horizontal plate is attached to the ceiling by means of a fixed vertical tube. A wheel of radius a and mass m is mounted on a light axle AC which is attached by means of a clevis at A to a rod AB fitted inside the vertical tube. The rod AB is made to rotate with a constant angular velocity Ω causing the wheel to roll on the lower face of the stationary plate. Determine the minimum angular velocity Ω for which contact is maintained between the wheel and the plate. Consider the particular cases (a) when the mass of the wheel is concentrated in the rim, (b) when the wheel is equivalent to a thin disk of radius a.

Fig. P18.97