**The Law of Inertia**: A physical object having an inertial state and at the same time being at rest or perhaps in uniform motion continues to be at rest or perhaps in uniform motion till put to work by a force.

1. A force, a form of matter/energy, which is a pull or a push that causes decelerations and accelerations.

2. Just a force may cause a change of the inertial state of the object made up of matter and/or energy.

3. The observation of a change of inertial state implies its cause to be a force of some type.

**The Law of Inertia** and its Corollaries are fundamental to physical phenomena at all physical scalar levels, including the scalar level of quantum mechanics.

Causality, objects and events comprised of energy or matter as causes causing as effects

(A) changes of the inertial states of pre-existing objects and events or

(B) new objects and events, is the basis of determinism.

## What is the Law of Inertia for Rotation

In linear motion, net force and mass determine the acceleration
of an object.

- For rotational motion, torque determines the rotational acceleration.

- The rotational counterpart to mass is rotational inertia
or moment of inertia.

- Just as mass represents the resistance to a change in
linear motion, rotational inertia is the resistance of an object to change in
its rotational motion.

- Rotational inertia is related to the mass of the object.

- It also depends on how the mass is distributed about the
axis of rotation.

**Simplest example: a mass at the end of a light rod**

• To produce the same rotational acceleration, a mass at the end of the rod with larger length must receive a larger linear acceleration than one smaller length

• F = ma

- It is harder to get the system rotating when the mass is at the end of the rod than when it is nearer to the axis.

- I case the distance are equal, it's

harder to move a heavier mass.

## Rotational Inertia and Newton's Second Law

• For an object with its mass concentrated at a point:

- Rotational inertia = mass x square of distance from axis

- I = mr2

• The total rotational inertia of an object like a merry-goround can be found by adding the contributions of all the different parts of the object.

Two 0.2-kg masses are located at either end of a 1- m long, very light and rigid rod as shown. What is the rotational inertia of this system about an axis through the center of the rod?

## Angular Momentum

• *Linear momentum is mass* (inertia) times linear velocity:

**p = mv**

• Angular momentum is *rotational inertia* times **rotational velocity:**

- Angular momentum may also be called rotational momentum.

- A bowling ball spinning slowly might have the same angular

momentum as a baseball spinning much more rapidly, because of

the larger rotational inertia **I** of the bowling ball.

Angular Momentum is a Vector

• The direction of the rotational-velocity vector is given by the right-hand rule.

• The direction of the angular-momentum vector is the same as the rotational velocity.

## Conservation of Angular Momentum

A student sits on a stool holding a bicycle wheel with a rotational velocity of 5 rad./s about a vertical axis. The rotational inertia of the wheel is 2 kg-m2 about its center and the rotational inertia of the student and wheel and platform about the rotational axis of the platform is 6 kg-m2. What is the initial angular momentum of the system?