In this chapter you will:  Learn how to describe and measure rotational motion.  Learn how torque changes rotational velocity.  Explore factors that determine the stability of an object.  Learn the nature of centrifugal and Coriolis “forces.”

Chapter 8 Sections Section 8.1: Describing Rotational Motion Section 8.2: Rotational Dynamics Section 8.3: Equilibrium

Section 8.1 Describing Rotational Motion Objectives Describe angular displacement. Calculate angular velocity. Calculate angular acceleration. Solve problems involving rotational motion.

INTRODUCTION Degree – 1/360 of a revolution. Radian – is ½ Π of a revolution. Abbreviated as rad. One complete revolution is equal to 2Π radians. Note Π is Greek Letter Pi

ANGULAR DISPLACEMENT The Greek letter theta θ is used to represent the angle of revolution. Go over Figure 8.1 with the Angles. Counterclockwise rotation is designated as positive and clockwise is negative. Angular Displacement – the change in the angle as an object rotates. Earth makes one complete revolution or 2Π rad in 24 hours. For rotation through an angle θ a point at a distance “r” from the center moves a distance given by ***** d = rθ. ***** “d” is measured in meters.

ANGULAR VELOCITY Angular Velocity – is equal to the angular displacement divided by the time required to make the rotation. It is denoted by Greek letter omega ω. It is measured in rad/s. **** ω = Δθ / Δt ***** This is average angular velocity. Instantaneous angular velocity is equal to the slope of a graph of angular position versus time. Angular Velocity of earth is ω E = Δθ / Δt ω E = 2Π rad / [(24 h)(3600s/h)] = 7.27 * rad/s

ANGULAR VELOCITY If an object’s angular velocity is ω, then the linear velocity of a point a distance, “r” from the axis of rotation is ***** v = rω. ***** The speed at which an object on Earth’s equator moves as a result of Earth’s rotation is given by v = rω = (6.38 * 10 6 )(7.27 * ) = 464 m/s. All parts of a rigid body (such as Earth) rotate at the same rate.

ANGULAR ACCELERATION Angular Acceleration – is equal to the change in angular velocity divided by the time required to make that change. It is denoted by Greek letter α. It is measured in rad/s 2. ***** α = Δω / Δt ***** The linear acceleration of a point at a distance “r” from the axis of an object with angular acceleration is ***** a = rα. ***** Table 8.1 p. 199 summarizes the equations.

TABLE 8.1

ANGULAR ACCELERATION Do Practice Problems p. 200 # 1-4 Angular Frequency – is the number of revolutions made by an object in 1 second. ***** f = ω / 2Π ***** Do 8.1 Section Review p. 200 # 5-10