1. Chapter 9: Rotation Angular Displacement
To measure angular velocity, you need to know about angular displacement, represented by the Greek letter theta.
You should also understand that all objects, in a rigid spinning body move with the same displacement, angular velocity, and angular displacement.

2. Radians
1 rev=2π rad=360o
The SI unit of angular displacement is radians.
S is arc-length and v, below, is tangential velocity, or the velocity of a particle ‘thrown off of the disk’.

3. Chapter 9 Rotation
Much like translational or linear velocity and acceleration, some objects also spin and have angular velocity and acceleration.
We define angular velocity as “change of the angular displacement in a unit of time”. the unit of angular velocity is revolution per unit time or radians per second. We show angular velocity with the Greek letter “ω” omega.
ω=θ/t where ,θ, angular displacement is in radians.

4. Angular Acceleration
Angular acceleration is the rate of change of angular velocity. In SI units, it is measured in radians per second squared (rad/s2), and is usually denoted by the Greek letter alpha (α).

5. Rotational and Linear Analogous Equations
Just as we used linear displacement, velocity, and acceleration, there are equations that are analogous in the ‘rotational’ world:
(Find the analagous linear equations on page 42 and 43 of this text…Chapter 2.)

6. Angular Direction
Angular displacement, velocity, and acceleration are vector quantities.
The positive direction is counterclockwise.

7. 9-2 Torque
Torque can be thought of as a twist, just as force is a push or pull.
Torque= force x lever arm length
Only the force at a right angle counts toward torque.

8. Newton’s Second Law The specific formula for torque is :
If the force is at a right angle to the radius.
F=ma has a rotational analog also:
where I is moment of inertia.
See page 265, Table 9-1 for formulas of I.

9. Moment of Inertia
We use I to represent moment of Inertia.