Question

2) Moment of Inertia for Multiple Objects We have loosely defined the moment of inertia as the difficulty or resistance encountered when trying to change an object's rotational motion. What if we were trying to rotation a combination of objects? a. Suppose you have a very light cloth pouch, and you place an apple of mass M=200 grams in it. You tighten up the satchel and start to swing it around, with the string in the satchel making a length L=0.5 m. What is the moment of inertia of the pouch? b. Now you place another apple in the bag. What is the moment of inertia of the two object (particle) system? c. What if we placed a banana of mass M. = 150 grams in the bag? You have seen that we can determine the moment of inertia of a system by simply adding the moments of inertia of each object. Write the moment of inertia for the following systems (You may look in your book for equation): Uniform disk of mass M of radius R with a small particle of mass m sitting on it a distance R/2 from the axis of rotation A thin rod of length L and mass M with small particles of mass M on each end of the rod. R

Answer 1

- 2 (@ I = mye 0.2X0.5² = 0.24 0.25 = 0.05 kgm² (b) I = 2mol 0.4% 0.25 0-10 kgm². (6 I = (2m+ m₂ 22 =(0.4+ 0.158² = 0.55 x 0.25 = 0·1375 kgm², * Total Moment of disk and mass System MR² + m2 (8 = 8/2) I = MR² + m R² 4 SMR I 4 . 2 * COM Moment of inertia of right mass=o. as its distance roo foom the axis of rotation. . I = moment of inertia of rod about its end + moment of inertia of lett mass + m 1² = 4M22 A. m(z) = m ² Centre of mass of rod, 3 Note: - I= m 1² 3 for rod i rad = Icom + md² = m2² at