Question

1. In class, we completed three (3) self-experiments concerning angular inertia, radius of gyration, and axis of rotation: 1. We threw the closed Biomechanics book into the air and rotated it about its axis. 2. We opened the book to page 10 and applied a force couple while the book was on the desk and rotated the book through an angular displacement of 180°. 3. We opened the book to the center of the book and applied a force couple again and rotated the book through an angular displacement of 180°. Utilizing these three areas: angular inertia, radius of gyration and axis of rotation, explain in detail these three sefl-experiments.

Answer 1

1.In the experiment the when the closed book is thrown into the air i.e. a torque is applied which sets the book into rotation about an axis.

The torque(T) depends upon angular inertia(I) of the closed book

   T= Ia,

where a is angular acceleration.

2. In the experiment 2, the book is opened to page 10 i.e. the center of mass of book is changed and hence the radius of gyration is also changed. If I₁ is the angular inertia, k₁ is radius of gyration, m is mass of the book, a₁ is angular acceleration, F₁ is the force applied and r₁ is the distance from point of applied of force couple from axis of rotation, then

I₁a₁=r₁F₁

i.e. m₁(k₁)²a_{1 =} r₁F₁

3. In experiment 3, the book is opened to half. This time the center of mass of book, radius of gyration, hence angular inertia changes.