Question

A pendulum made of a uniform rod with a length of 70 cm is set into harmonic motion about one end.

1) Calculate the period of its motion.

Answer 1

The period of such physical pendulums are given by
T = 2$\pi$ sqrt (I / m g a)
Where I is the moment of inertia about the axis of rotation and a is distance between the center of mass and the axis of rotation
The rod is uniform , so the center of mass will be the middle point
a = 35 cm
The moment of inertia of a rod about one end is
I = m l² / 3
The time period
T = 2 $\pi$ sqrt (m l² / 3 m g a)
T = 2 $\pi$ sqrt (l² / 3 g a)
T = 2 x 3.14 x sqrt (0.70² / 3 x 9.81 x 0.35)
T = 1.37 s