Outline
Rotation about a Fixed Axis - part 2
Department of Applied Mathematics
University of Stellenbosch
Wednesday, February 10, 2012
Applied Math B224
Rotation about a Fixed Axis - part 2
Theory
Examples
Homework
Angular Motion of Rigid Body
Equations
v = rω = rθ̇
at = rα = rθ̈
v2
an =
= rθ̇2
r
Applied Math B224
Rotation about a Fixed Axis - part 2
Theory
Examples
Homework
Vector Notation
Applied Math B224
Rotation about a Fixed Axis - part 2
Theory
Examples
Homework
Vector Notation
Equations
v=ω×r
an = ω × (ω × r)
at = α × r
Applied Math B224
Rotation about a Fixed Axis - part 2
Theory
Examples
Homework
Example 2
Question
The two attached pulleys are
driven by the belt with
increasing speed. When the
belt reaches a speed v = 0.6
m/s, the total acceleration of
point P is 8 m/s2 . For this
instant determine the angular
acceleration α of the pulleys
and the acceleration of point B
on the belt (magnitudes only).
Applied Math B224
Rotation about a Fixed Axis - part 2
Theory
Examples
Homework
Example 3
Question
Gear B is rotating clockwise with a speed of 300 rev/min when
a torque is applied to gear A at time t = 2 s to give gear A a
counterclockwise acceleration α which varies with time for a
duration of 4 seconds as shown (αA (t) = t + 2). Determine the
speed NB of gear B when t = 6 s.
Applied Math B224
Rotation about a Fixed Axis - part 2
Theory
Examples
Homework
Suggested Exercises
Review
Section 16/3, pages 311-319
Homework
Ex 16.1, 16.2, FP 16-1 - 16-6
Applied Math B224
Rotation about a Fixed Axis - part 2