Rotation

1
Chapter 11

• Rotation
• (Rotational Displacement, Rotational Velocity,
  Rotational Acceleration)

2
Section 11.2 The Rotational Variables

• Kinematics Translational Rotational
• Translating Body
• Displacement
• Velocity
• Acceleration
• Rotating Body
• Angular Displacement
• Angular Velocity
• Angular Acceleration

3
Rotational Position

• ? (theta) is the angle subtended w.r.t the x-axis
• 1 rev 360 2? rad

y
v
r
?
x
4
Rotational Position

• How much distance, s , is traversed?
• s is the arc length
• Notice
• ? must be in radians
• Check
• For ??????????C 2?r

y
r
s
?
x
5
Rotational Displacement

• Rotational Displacement, ?? , is the difference
  in the objects final and initial angles
• CCW is , CW is -
• What are the SI units?

y
?2
?1
x
6
Definition of the Radian

• Units?
• The radian is dimensionless!

7
Rotational Velocity

• Rotational angular speed, ?av, is the ratio of
  the rotational displacement to the time interval
  for that rotational displacement
• The instantaneous rotational velocity, ?, is the
  limit of the average rotational velocity as ?t
  approaches zero
• What are the SI units?

8
Rotational Acceleration

• Average rotational acceleration is the ratio of
  the rotational velocity to the time interval for
  that rotational velocity
• The instantaneous angular acceleration is the
  limit of the average angular acceleration as ?t
  approaches zero
• What are the SI units?