Chapter 8
Rotational Kinematics
Rotation – (rotate)
To spin on an internal axis.
Revolution – (revolve)
To move around an external 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/minute
or
45 x (2)
= 282.7 rad/min
Depends on the
distance (r) away
from the center
Tangential Velocity = Linear Velocity = v
Angular Velocity = Rotational Velocity = ω
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
s = arc length
r = radius
What is a radian?
A radian is a unit used for measuring angles.
s = arc length
r = radius
Angles can be measured in degrees or radians
  180
Angular Displacement (Δθ) -
Can be measured in
1) degrees
2) radians
3) 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)
v f  vo  at
 f  o   t
x  vot  at
1
2
x  vt
  t
v  v  2ax
2
2
f
2
o
  o t   t     2
1
2
2
2
f
2
o
ASSIGN: Ch. 8 #2,12,16,32
p. 231
due Friday