Studying for my exam, please help. 1.) You are on a hike in the woods with your
ID: 1446324 • Letter: S
Question
Studying for my exam, please help.
1.) You are on a hike in the woods with your CD player when a rather large bug of mass 5.0g manages to land on the edge of your favorite CD (mass 9.0kg and radius 6.0cm). How does the affect of that effect the CD’s moment of inertia?
2.)The planar molecule ClF3 is T-shaped with the F atom at the midpoint of the cross-piece of the “T”.
(a) If the F-Cl distance in the stem of the T is 160 pm and the F-Cl distances in the cross-bar of the T are 170 pm, find the position of the centre of mass. (You may assume a bond angle of 90 , which is almost correct.)
(b) Calculate the moment of inertia (in kg m2 ) about an axis normal to the molecular plane which passes through the centre of mass. [Relative isotopic masses: mF =19.00u; mCl= 34.97u]
3.)The CC and CH bond lengths in benzene are 139 pm and 109 pm respectively. Assuming benzene to be perfectly hexagonal calculate the moment of inertia of the benzene molecule about the following three axes, each of which passes through the centre of mass of the molecule:
(a) an axis perpendicular to the plane of the molecule
(b) an axis in the plane of the molecule, passing through opposite C atoms.
(c) an axis in the plane of the molecule, bisecting opposite CC bonds.
Thank you in advance
Explanation / Answer
1)Given;
mass of bug = m = 5 g = 0.005 kg ;
Mass of CD = M = 9 kg ( CD with mass 9 kg, Pls check once again)
Radius = R = 6 cm = 0.06 m
The intial moment of inertia of the system is due to CD only.
The CD acn be modelled as a disk with moment of inertia, I = 1/2 M R2
Ii = 1/2 M R2 = 0.5 x 9 x (0.06)2 = 0.0162 kg-m2
The moment of inertia of the bug sitting at the edge(distant R from the center), considering it as the point mass will be = I' = m R2
After the but sat over the edge of the CD, the moment of inertia of the CD-bug system will become:
If = I + I'
If = 1/2 M R2 + m R2
If = 0.5 x 9 x (0.06)2 + 0.005 x (0.06)2 = 0.016218 kg-m2
Hence, Ii = 0.0162 kg-m2 and If = 0.016 kg-m2 ; So the moment of inertia has increased but the change is very small.