Chapter 18, Problem 18.157RP

A homogeneous rectangular plate of mass m and sides c and 2c is held at A and B by a fork-ended shaft of negligible mass, which is supported by a bearing at C. The plate is free to rotate about AB, and the shaft is free to rotate about a horizontal axis through C. Knowing that initially θ₀ = 40°, ${\stackrel{\dot{}}{\theta }}_0=0$, and ${\stackrel{\dot{}}{\varphi }}_0=10\text{ rad/s}$, determine for the ensuing motion (a) the range of values of θ, (b) the minimum value of $\stackrel{\dot{}}{\varphi }$, (c) the maximum value of $\stackrel{\dot{}}{\theta }$.

Fig. P18.157