1. The Simple Pendulum

2. Energy Considerations
The
“Pendulum Pennant”
h = l - lcosq l
lcosq q

3. A falling pendulum
h = l - lcosq l
lcosq q
Assuming that no external work is done on the pendulum bob …
Max velocity (at bottom)

4. A pendulum being raised up
h = l - lcosq l
lcosq q
External work must be done to raise the bob.

5. q Tension in the String Fcentripetal Fg Ftangential
To analyze the pendulum bob’s motion, break the gravitational force into its centripetal (inward pointing) and tangential (perpendicular to the string) components.

6. The force due to gravity on the pendulum bob is always the same
The force due to gravity on the pendulum bob is always the same. However, as the bob swings downward, the centripetal force (pointing inward) increases while the tangential force (pointing perpendicular to the string) decreases.

7. q Fcentripetal Fg Ftangential
Using a little right triangle trigonometry …

8. q Fg
Ftangential
Fcentripetal
45o o Fg
Ft=Fgsinq
Fc=Fgcosq

9. l T
Fcentripetal q Fg
Ftangential

10. 0o
90o
180o
0o o o

11. Tension
0o o o o o (0o)