Chapter 8Rotational Kinematics

Rotation – (rotate)

Revolution – (revolve)

To move around an external axis.

To spin on an internal axis.

The Record Player or Turntable

A penny rotates on the turntable at 45 RPM

How fast is the penny moving?

Angular Velocity Tangential Velocity

(Rotational Speed) (Linear Speed)

45 revolutions/minuteor

45 x (2) = 282.7 rad/min

Depends on the distance (r) away from the center

Angular Velocity = Rotational Velocity = ω

Tangential Velocity = Linear Velocity = v

V depends on distance from axis rotation.

v r

What is pi?

Pi is the ratio of a circle’s circumference to diameter.

Circumference (C)

Diameter (d)

3.14159...

Arc length

r = radius

s = arc length

What is a radian?

A radian is a unit used for measuring angles.

Angles can be measured in degrees or radians

180

r = radius

s = arc length

Angular Displacement (Δθ) -

Can be measured in 1) degrees2) radians3) revolutions (1 rev = 360°)

Angular Velocity (ω) -

t

Measured in rad/sec or rev/min (etc)

Angular Acceleration (α) -

t

Measured in rad/sec2 or rev/min2 (etc)

f ov v at

212ox v t at

x vtf o t

212ot t 2 2 2f o

2 2 2f ov v ax

t

ASSIGN: Ch. 8 #2,12,16,32p. 231

due Friday