Physics Chapter 8 – Rotational Motion
Chapter Objectives
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”.
Section 8.1: Describing Rotational Motion
Objectives
Describe angular displacement.
Calculate angular velocity.
Calculate angular acceleration.
Solve problems involving rotational motion.
A. Introduction
1. a fraction of one revolution can be measured in grads, degrees, or radians
a. grad – a grad is 1/400 of a revolution
b. degree – a degree is 1/360 of a revolution
c. radian – a radian is defined as 1/ 2π of a revolution
2. One complete revolution is equal to 2π radians. The abbreviation of radian is ‘rad’.
B. Angular Displacement
1. Greek letter theta, θ, is used to represent the angle of revolution; Fig. 8-1, p. 198, top
2. angular displacement – the change in the angle of rotation; Fig. 8-2, p. 198, bottom
a. for rotation through an angle, θ, a point at a distance, r, from the center moves
a distance given by d = rθ
b. if r is measured in meters; radians indicate the ratio between d and r; and thus
d is measured in meters
C. Angular Velocity
1. angular velocity – angular displacement divided by the time required to make the
displacement; represented by the Greek letter omega, ω
ω = Δθ/ Δt
2. if the velocity changes over a time interval, the average velocity is not equal
to the instantaneous velocity at any given instant
PHYS 8.1b
3. angular velocity is measured in rad/s; for Earth,
ωE = (2π rad)/[(24.0 h)(3600 s/h)] = 7.27 • 10─5 rad/s
4. in the same way that counterclockwise rotation produces positive angular
displacement, it also results in positive angular velocity
a. if an object’s angular velocity is ω, then the linear velocity of a point at
distance, r, from the axis of rotation is given by v = rω
b. the speed at which an object on Earth’s equator moves as a result of Earth’s
rotation is given by:
v = r ω = (6.38×106 m) (7.27×10─5 rad/s) = 464 m/s
5. Earth is an example of a rotating, rigid object; different points on Earth rotate
different distances in each revolution, all points rotate through the same angle
6. The Sun, on the other hand, is not a rigid body. Different parts of the Sun rotate at
different rates.
D. Angular Acceleration
1. angular acceleration – the change in angular velocity divided by the time required
to make that change:  = Δω / Δt
a. angular acceleration, α, is represented by the Greek letter alpha
b. angular acceleration is measured in rad/s2
2. If the change in angular velocity is positive, then the angular acceleration is also
positive.
3. angular acceleration defined in this way is also the average angular acceleration over
the time interval Δt.
4. to find the instantaneous angular acceleration; find the slope of a graph of angular
velocity as a function of time.
5. the linear acceleration, a, of a point at a distance, r, from the axis of an object with
angular acceleration, α, is given by a = r α.
6. summary of linear and angular relationships; Table 8-1, p. 199, bottom
E. Angular Frequency
1. angular frequency – number of complete revolutions made by an object in 1 s is
called angular frequency
2. angular frequency, f, is given by the equation:
f = ω / 2π