Newton’s First Law of Motion (text page 388)

1. Newton’s First Law of Motion (text page 388) • Also called “Newton’s Law of Inertia” • “A body will maintain a state of rest or constant velocity unless acted on by an external force that changes that state.”

2. Inertia (text page 62) General definition: A resistance to an action or a change in action. Mechanical definition: A resistance to acceleration. Inertia is the tendency of an object to maintain its current state of motion, whether motionless or moving at a constant velocity. There are no units of measurement for inertia. The greater the mass of an object, the greater the inertia.

3. Moment of Inertia (text page 460) • The resistance of a body to angular acceleration. • The moment of inertia increases as the mass of an object moves away from the axis of rotation.

4. Moment of Inertia • If weight is added to a bat, moving the weight farther from the grip increases to moment of inertia. Bat A has a greater moment of inertia than bat B.

5. Moment of Inertia • Symbol: I • Formula (for a single particle): I = mr2 where m is the mass of a particle and r is the distance from the particle to the axis of rotation. • Formula (for an entire object): I = Smr2 or the sum of the product of the mass times the distance squared for all particles in an object to the axis of rotation.

6. AXIS OF ROTATION r r r r r r See text p. 455 The moment of inertia of each particle is the product of its mass times the distance squared (r2) to the axis of rotation. The sum of all of these moments of inertia is the moment of inertia of an entire object.

7. Moment of Inertia • It’s impractical to calculate the distances from all particles in an object to the center of rotation. (The number of particles would approach infinity as the sizes of the particles get smaller and smaller.) • Mathematical formulas are used to calculate the moment of inertia for objects of regular geometric shapes and known dimension.

8. Moment of Inertia • Various methods have been used to determine the moment of inertia of limb segments in the body • Average measurements from cadaver studies • Measuring the acceleration of swinging limbs • Photogrammetric techniques (calculations based on film and video) • Modeling limb segments as regular geometric figures

9. Radius of Gyration • After determining the moment of inertia, the formula can be changed to the following: I = mk2 where k stands for the radius of gyration. • The radius of gyration represents an object’s mass distribution relative to a specific axis of rotation. (This isn’t exactly the same as the center of mass. See text and figures pp 462 - 463) • EXAMPLE: Choking up on a bat reduces the radius of gyration.

10. Increasing the moment of inertia can increase the transfer of force when striking an object as in increasing the weight of the head of a golf club. Decreasing the moment of inertia can reduce the resistance to rotation when speed is desired. Choking up on a bat reduces the moment of inertia, allowing the athlete to swing the bat at a faster angular velocity. Applications of Moment of Inertia

11. Applications of Moment of Inertia • Changing the moment of inertia during a movement can speed up or slow down rotation. • A skater performing a pirouette will bring the arms closer to the body to speed up the spin. • If a gymnast performing a flip goes from a stretched to a tucked position after starting the skill, the speed of rotation will increase.

12. Applications of Moment of Inertia • As a gymnast goes from a stretched to a tucked position, the moment of inertia decreases and the speed of rotation (angular velocity) increases.