Please show work and explain :) A rigid object is composed of two thin, uniform
ID: 2057606 • Letter: P
Question
Please show work and explain :)
A rigid object is composed of two thin, uniform discs of mass m and radius R connected at their centers by a massless rod of length L, as shown in the gure below.
(a) What is the moment of inertia I1 of one of the discs about an axis through its center and perpendicular to its plane?
(b) Refer to the Perpendicular-Axis Theorem discussed in Problem 9.95. What is the moment of inertia I2 of one of the discs about an axis through its center and parallel to its plane? Explain how you used the perpendicular-axis theorem.
(c) Refer to the Parallel-Axis Theorem. What is the moment of inertia I3 of one of the discs about axis A? Explain why the parallel-axis theorem applies in this case.
(d) What is the moment of inertia IA of the assembly about axis A shown in the figure above?
Explanation / Answer
a) the moment of inertia I1 = m*R^2/2. b)using perpendicular axes theorem Ix+Iy = Iz here Iz = m*R^2/2 and Ix= I2 => Ix = m*R^2/4 = I2. c) the moment of inertia about axis A is given by I3 = m*R^2/4 + m*L^2/4 = m*(R^2+L^2)/4 d) the net moment of assembly is 2*I3 = m*(R^2+L^2)/2.