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MECHANICS UNIT 4
Rotational Dynamics
Author of this note Mr. K. Prasad BSc from University of Calicut, MSc from university of Delhi, and M.B.A from IGNOU Delhi, These notes were prepared during my teaching session for under graduate students (11 Th and 12 Th class) of my school physics department. This note is helpful for under graduate students and junior level graduates. I declare that these notes are my original works based on my knowledge in physics and the books mentioned below are the reference books I used for preparing these notes.
Table of contents (1) Angular momentum of a particle (2) Torque (3) Principle of conservation of angular momentum (4) Principle of conservation of angular momentum example (5) Rotation about a fixed axis (6) Example of rotation about a fixed axis (7) Moment of inertia (8) Moment of inertia equation (9) The theorem of parallel axis of moment of inertia (10)Theorem of parallel axis formula (11)The theorem of perpendicular axes of moment of inertia (12)Rotational Kinetic Energy definition (13) Motion involving both translation and rotation Reference Books: An Introduction to Mechanics, Daniel Kleppner& Robert Kolenkow, 2007, TataMcGrawHill Mechanics, DS Mathur, PS Hemne, 2012, S. Chand University Physics, FW Sears, MW Zemansky& HD Young 13/e, 1986,AddisonWesley MechanicsBerkeley Physics course, v.1: Charles Kittel, et.al. 2007, TataMcGrawHill Physics – Resnick, Halliday & Walker 9/e, 2010, Wiley Engineering Mechanics, Basudeb Bhattacharya, 2nd edn., 2015, Oxford UniversityPress University Physics, Ronald Lane Reese, 2003, Thomson Brooks/Cole
a fixed axis? In this segment, we will find out about the angular momentum of a molecule going through rotational movement about a fixed axis Example of rotation about a fixed axis A simple example of rotation about a fixed axis is the motion of a compact disc in a CD player, which is driven by a motor inside the player. In a simplified model of this motion, the motor produces angular acceleration, causing the disc to spin. Moment of inertia Moment of inertia can be defined as the quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque (turning force). The axis may be internal or external and may or may not be fixed. Moment of inertia equation
I= L/ ɯ
Where I refer to Inertia
L refer to angular momentum ɯ refer to angular velocity The theorem of parallel axis The theorem of parallel axis states that the moment of inertia of a body about an axis parallel to an axis passing through the Centre of mass is equal to the sum of the moment of inertia of body about an axis passing through Centre of mass and product of mass and square of the distance between the two axes. Theorem of parallel axis formula
I = Ic + Mh
Where I refer to moment of inertia of the body
Ic moment of inertia about the center
M is the mass of the body
h
2 is the square of the distance between the two axes The theorem of perpendicular axes of moment of inertia For any plane body, the moment of inertia about any of its axes which are perpendicular to the plane is equal to the sum of the moment of inertia about any two perpendicular axes in the plane of the body which intersect the first axis in the plane
